From d9b0089d5e0a75147ad09c2ba8ed272d1ac88dc9 Mon Sep 17 00:00:00 2001 From: Zhenzhen Bao Date: Sat, 21 Mar 2020 12:32:35 +0800 Subject: [PATCH] A bug in computing the ANF for 3-bit and 4-bit S-boxes In the function `get_coordinates_ANF()`, for 3-bit and 4-bit S-boxes, at the beginning, to obtain the truth table, the mask should be AND to the value, not XOR. The influence of this bug: For 3-bit and 4-bit S-boxes, the computed ANF of coordinates are all XORed with '1', which should not! There is no influence on other results and on 5/6/7/8-bit S-boxes. --- .../Sboxes3/properties_3-way.txt | 28 +- .../Sboxes3/properties_PRINTcipher.txt | 28 +- .../Sboxes3/properties_SEA.txt | 28 +- .../Sboxes3/properties_ctc2.txt | 28 +- .../Sboxes3/properties_sboxes3_Part0.csv | 5 + .../302classes4bits/properties_001.txt | 406 ++++++++ .../302classes4bits/properties_002.txt | 406 ++++++++ .../302classes4bits/properties_003.txt | 406 ++++++++ .../302classes4bits/properties_004.txt | 406 ++++++++ .../302classes4bits/properties_005.txt | 406 ++++++++ .../302classes4bits/properties_006.txt | 406 ++++++++ .../302classes4bits/properties_007.txt | 406 ++++++++ .../302classes4bits/properties_008.txt | 406 ++++++++ .../302classes4bits/properties_009.txt | 418 +++++++++ .../302classes4bits/properties_010.txt | 418 +++++++++ .../302classes4bits/properties_011.txt | 418 +++++++++ .../302classes4bits/properties_012.txt | 418 +++++++++ .../302classes4bits/properties_013.txt | 438 +++++++++ .../302classes4bits/properties_014.txt | 438 +++++++++ .../302classes4bits/properties_015.txt | 438 +++++++++ .../302classes4bits/properties_016.txt | 438 +++++++++ .../302classes4bits/properties_017.txt | 406 ++++++++ .../302classes4bits/properties_018.txt | 418 +++++++++ .../302classes4bits/properties_019.txt | 418 +++++++++ .../302classes4bits/properties_020.txt | 418 +++++++++ .../302classes4bits/properties_021.txt | 418 +++++++++ .../302classes4bits/properties_022.txt | 418 +++++++++ .../302classes4bits/properties_023.txt | 406 ++++++++ .../302classes4bits/properties_024.txt | 406 ++++++++ .../302classes4bits/properties_025.txt | 438 +++++++++ .../302classes4bits/properties_026.txt | 438 +++++++++ .../302classes4bits/properties_027.txt | 438 +++++++++ .../302classes4bits/properties_028.txt | 438 +++++++++ .../302classes4bits/properties_029.txt | 438 +++++++++ .../302classes4bits/properties_030.txt | 438 +++++++++ .../302classes4bits/properties_031.txt | 438 +++++++++ .../302classes4bits/properties_032.txt | 470 ++++++++++ .../302classes4bits/properties_033.txt | 470 ++++++++++ .../302classes4bits/properties_034.txt | 408 ++++++++ .../302classes4bits/properties_035.txt | 408 ++++++++ .../302classes4bits/properties_036.txt | 408 ++++++++ .../302classes4bits/properties_037.txt | 420 +++++++++ .../302classes4bits/properties_038.txt | 420 +++++++++ .../302classes4bits/properties_039.txt | 408 ++++++++ .../302classes4bits/properties_040.txt | 408 ++++++++ .../302classes4bits/properties_041.txt | 408 ++++++++ .../302classes4bits/properties_042.txt | 408 ++++++++ .../302classes4bits/properties_043.txt | 420 +++++++++ .../302classes4bits/properties_044.txt | 420 +++++++++ .../302classes4bits/properties_045.txt | 420 +++++++++ .../302classes4bits/properties_046.txt | 408 ++++++++ .../302classes4bits/properties_047.txt | 408 ++++++++ .../302classes4bits/properties_048.txt | 408 ++++++++ .../302classes4bits/properties_049.txt | 408 ++++++++ .../302classes4bits/properties_050.txt | 408 ++++++++ .../302classes4bits/properties_051.txt | 420 +++++++++ .../302classes4bits/properties_052.txt | 420 +++++++++ .../302classes4bits/properties_053.txt | 420 +++++++++ .../302classes4bits/properties_054.txt | 420 +++++++++ .../302classes4bits/properties_055.txt | 420 +++++++++ .../302classes4bits/properties_056.txt | 420 +++++++++ .../302classes4bits/properties_057.txt | 420 +++++++++ .../302classes4bits/properties_058.txt | 420 +++++++++ .../302classes4bits/properties_059.txt | 420 +++++++++ .../302classes4bits/properties_060.txt | 420 +++++++++ .../302classes4bits/properties_061.txt | 420 +++++++++ .../302classes4bits/properties_062.txt | 420 +++++++++ .../302classes4bits/properties_063.txt | 420 +++++++++ .../302classes4bits/properties_064.txt | 420 +++++++++ .../302classes4bits/properties_065.txt | 420 +++++++++ .../302classes4bits/properties_066.txt | 420 +++++++++ .../302classes4bits/properties_067.txt | 420 +++++++++ .../302classes4bits/properties_068.txt | 420 +++++++++ .../302classes4bits/properties_069.txt | 420 +++++++++ .../302classes4bits/properties_070.txt | 420 +++++++++ .../302classes4bits/properties_071.txt | 420 +++++++++ .../302classes4bits/properties_072.txt | 420 +++++++++ .../302classes4bits/properties_073.txt | 420 +++++++++ .../302classes4bits/properties_074.txt | 420 +++++++++ .../302classes4bits/properties_075.txt | 420 +++++++++ .../302classes4bits/properties_076.txt | 420 +++++++++ .../302classes4bits/properties_077.txt | 420 +++++++++ .../302classes4bits/properties_078.txt | 420 +++++++++ .../302classes4bits/properties_079.txt | 440 +++++++++ .../302classes4bits/properties_080.txt | 440 +++++++++ .../302classes4bits/properties_081.txt | 440 +++++++++ .../302classes4bits/properties_082.txt | 440 +++++++++ .../302classes4bits/properties_083.txt | 440 +++++++++ .../302classes4bits/properties_084.txt | 480 ++++++++++ .../302classes4bits/properties_085.txt | 420 +++++++++ .../302classes4bits/properties_086.txt | 420 +++++++++ .../302classes4bits/properties_087.txt | 410 ++++++++ .../302classes4bits/properties_088.txt | 410 ++++++++ .../302classes4bits/properties_089.txt | 410 ++++++++ .../302classes4bits/properties_090.txt | 410 ++++++++ .../302classes4bits/properties_091.txt | 410 ++++++++ .../302classes4bits/properties_092.txt | 410 ++++++++ .../302classes4bits/properties_093.txt | 422 +++++++++ .../302classes4bits/properties_094.txt | 422 +++++++++ .../302classes4bits/properties_095.txt | 422 +++++++++ .../302classes4bits/properties_096.txt | 410 ++++++++ .../302classes4bits/properties_097.txt | 410 ++++++++ .../302classes4bits/properties_098.txt | 410 ++++++++ .../302classes4bits/properties_099.txt | 410 ++++++++ .../302classes4bits/properties_100.txt | 410 ++++++++ .../302classes4bits/properties_101.txt | 410 ++++++++ .../302classes4bits/properties_102.txt | 410 ++++++++ .../302classes4bits/properties_103.txt | 410 ++++++++ .../302classes4bits/properties_104.txt | 410 ++++++++ .../302classes4bits/properties_105.txt | 410 ++++++++ .../302classes4bits/properties_106.txt | 422 +++++++++ .../302classes4bits/properties_107.txt | 422 +++++++++ .../302classes4bits/properties_108.txt | 422 +++++++++ .../302classes4bits/properties_109.txt | 422 +++++++++ .../302classes4bits/properties_110.txt | 422 +++++++++ .../302classes4bits/properties_111.txt | 422 +++++++++ .../302classes4bits/properties_112.txt | 422 +++++++++ .../302classes4bits/properties_113.txt | 422 +++++++++ .../302classes4bits/properties_114.txt | 422 +++++++++ .../302classes4bits/properties_115.txt | 422 +++++++++ .../302classes4bits/properties_116.txt | 410 ++++++++ .../302classes4bits/properties_117.txt | 410 ++++++++ .../302classes4bits/properties_118.txt | 410 ++++++++ .../302classes4bits/properties_119.txt | 422 +++++++++ .../302classes4bits/properties_120.txt | 422 +++++++++ .../302classes4bits/properties_121.txt | 422 +++++++++ .../302classes4bits/properties_122.txt | 422 +++++++++ .../302classes4bits/properties_123.txt | 422 +++++++++ .../302classes4bits/properties_124.txt | 422 +++++++++ .../302classes4bits/properties_125.txt | 422 +++++++++ .../302classes4bits/properties_126.txt | 422 +++++++++ .../302classes4bits/properties_127.txt | 422 +++++++++ .../302classes4bits/properties_128.txt | 422 +++++++++ .../302classes4bits/properties_129.txt | 422 +++++++++ .../302classes4bits/properties_130.txt | 410 ++++++++ .../302classes4bits/properties_131.txt | 410 ++++++++ .../302classes4bits/properties_132.txt | 422 +++++++++ .../302classes4bits/properties_133.txt | 422 +++++++++ .../302classes4bits/properties_134.txt | 422 +++++++++ .../302classes4bits/properties_135.txt | 422 +++++++++ .../302classes4bits/properties_136.txt | 422 +++++++++ .../302classes4bits/properties_137.txt | 422 +++++++++ .../302classes4bits/properties_138.txt | 422 +++++++++ .../302classes4bits/properties_139.txt | 422 +++++++++ .../302classes4bits/properties_140.txt | 422 +++++++++ .../302classes4bits/properties_141.txt | 422 +++++++++ .../302classes4bits/properties_142.txt | 442 +++++++++ .../302classes4bits/properties_143.txt | 442 +++++++++ .../302classes4bits/properties_144.txt | 442 +++++++++ .../302classes4bits/properties_145.txt | 442 +++++++++ .../302classes4bits/properties_146.txt | 442 +++++++++ .../302classes4bits/properties_147.txt | 442 +++++++++ .../302classes4bits/properties_148.txt | 442 +++++++++ .../302classes4bits/properties_149.txt | 442 +++++++++ .../302classes4bits/properties_150.txt | 442 +++++++++ .../302classes4bits/properties_151.txt | 442 +++++++++ .../302classes4bits/properties_152.txt | 442 +++++++++ .../302classes4bits/properties_153.txt | 442 +++++++++ .../302classes4bits/properties_154.txt | 442 +++++++++ .../302classes4bits/properties_155.txt | 442 +++++++++ .../302classes4bits/properties_156.txt | 412 ++++++++ .../302classes4bits/properties_157.txt | 412 ++++++++ .../302classes4bits/properties_158.txt | 412 ++++++++ .../302classes4bits/properties_159.txt | 412 ++++++++ .../302classes4bits/properties_160.txt | 412 ++++++++ .../302classes4bits/properties_161.txt | 412 ++++++++ .../302classes4bits/properties_162.txt | 412 ++++++++ .../302classes4bits/properties_163.txt | 424 +++++++++ .../302classes4bits/properties_164.txt | 424 +++++++++ .../302classes4bits/properties_165.txt | 424 +++++++++ .../302classes4bits/properties_166.txt | 424 +++++++++ .../302classes4bits/properties_167.txt | 424 +++++++++ .../302classes4bits/properties_168.txt | 424 +++++++++ .../302classes4bits/properties_169.txt | 424 +++++++++ .../302classes4bits/properties_170.txt | 424 +++++++++ .../302classes4bits/properties_171.txt | 412 ++++++++ .../302classes4bits/properties_172.txt | 424 +++++++++ .../302classes4bits/properties_173.txt | 424 +++++++++ .../302classes4bits/properties_174.txt | 424 +++++++++ .../302classes4bits/properties_175.txt | 424 +++++++++ .../302classes4bits/properties_176.txt | 424 +++++++++ .../302classes4bits/properties_177.txt | 424 +++++++++ .../302classes4bits/properties_178.txt | 424 +++++++++ .../302classes4bits/properties_179.txt | 412 ++++++++ .../302classes4bits/properties_180.txt | 412 ++++++++ .../302classes4bits/properties_181.txt | 412 ++++++++ .../302classes4bits/properties_182.txt | 412 ++++++++ .../302classes4bits/properties_183.txt | 424 +++++++++ .../302classes4bits/properties_184.txt | 424 +++++++++ .../302classes4bits/properties_185.txt | 424 +++++++++ .../302classes4bits/properties_186.txt | 424 +++++++++ .../302classes4bits/properties_187.txt | 424 +++++++++ .../302classes4bits/properties_188.txt | 424 +++++++++ .../302classes4bits/properties_189.txt | 412 ++++++++ .../302classes4bits/properties_190.txt | 424 +++++++++ .../302classes4bits/properties_191.txt | 424 +++++++++ .../302classes4bits/properties_192.txt | 444 +++++++++ .../302classes4bits/properties_193.txt | 444 +++++++++ .../302classes4bits/properties_194.txt | 414 ++++++++ .../302classes4bits/properties_195.txt | 414 ++++++++ .../302classes4bits/properties_196.txt | 414 ++++++++ .../302classes4bits/properties_197.txt | 414 ++++++++ .../302classes4bits/properties_198.txt | 414 ++++++++ .../302classes4bits/properties_199.txt | 414 ++++++++ .../302classes4bits/properties_200.txt | 414 ++++++++ .../302classes4bits/properties_201.txt | 426 +++++++++ .../302classes4bits/properties_202.txt | 426 +++++++++ .../302classes4bits/properties_203.txt | 426 +++++++++ .../302classes4bits/properties_204.txt | 426 +++++++++ .../302classes4bits/properties_205.txt | 426 +++++++++ .../302classes4bits/properties_206.txt | 426 +++++++++ .../302classes4bits/properties_207.txt | 426 +++++++++ .../302classes4bits/properties_208.txt | 426 +++++++++ .../302classes4bits/properties_209.txt | 426 +++++++++ .../302classes4bits/properties_210.txt | 426 +++++++++ .../302classes4bits/properties_211.txt | 426 +++++++++ .../302classes4bits/properties_212.txt | 414 ++++++++ .../302classes4bits/properties_213.txt | 426 +++++++++ .../302classes4bits/properties_214.txt | 426 +++++++++ .../302classes4bits/properties_215.txt | 446 +++++++++ .../302classes4bits/properties_216.txt | 446 +++++++++ .../302classes4bits/properties_217.txt | 416 ++++++++ .../302classes4bits/properties_218.txt | 428 +++++++++ .../302classes4bits/properties_219.txt | 428 +++++++++ .../302classes4bits/properties_220.txt | 416 ++++++++ .../302classes4bits/properties_221.txt | 428 +++++++++ .../302classes4bits/properties_222.txt | 428 +++++++++ .../302classes4bits/properties_223.txt | 418 +++++++++ .../302classes4bits/properties_224.txt | 418 +++++++++ .../302classes4bits/properties_225.txt | 418 +++++++++ .../302classes4bits/properties_226.txt | 418 +++++++++ .../302classes4bits/properties_227.txt | 430 +++++++++ .../302classes4bits/properties_228.txt | 418 +++++++++ .../302classes4bits/properties_229.txt | 430 +++++++++ .../302classes4bits/properties_230.txt | 420 +++++++++ .../302classes4bits/properties_231.txt | 426 +++++++++ .../302classes4bits/properties_232.txt | 442 +++++++++ .../302classes4bits/properties_233.txt | 442 +++++++++ .../302classes4bits/properties_234.txt | 424 +++++++++ .../302classes4bits/properties_235.txt | 446 +++++++++ .../302classes4bits/properties_236.txt | 446 +++++++++ .../302classes4bits/properties_237.txt | 428 +++++++++ .../302classes4bits/properties_238.txt | 428 +++++++++ .../302classes4bits/properties_239.txt | 428 +++++++++ .../302classes4bits/properties_240.txt | 428 +++++++++ .../302classes4bits/properties_241.txt | 432 +++++++++ .../302classes4bits/properties_242.txt | 432 +++++++++ .../302classes4bits/properties_243.txt | 466 +++++++++ .../302classes4bits/properties_244.txt | 450 +++++++++ .../302classes4bits/properties_245.txt | 466 +++++++++ .../302classes4bits/properties_246.txt | 478 ++++++++++ .../302classes4bits/properties_247.txt | 466 +++++++++ .../302classes4bits/properties_248.txt | 478 ++++++++++ .../302classes4bits/properties_249.txt | 478 ++++++++++ .../302classes4bits/properties_250.txt | 478 ++++++++++ .../302classes4bits/properties_251.txt | 478 ++++++++++ .../302classes4bits/properties_252.txt | 478 ++++++++++ .../302classes4bits/properties_253.txt | 502 ++++++++++ .../302classes4bits/properties_254.txt | 502 ++++++++++ .../302classes4bits/properties_255.txt | 502 ++++++++++ .../302classes4bits/properties_256.txt | 502 ++++++++++ .../302classes4bits/properties_257.txt | 502 ++++++++++ .../302classes4bits/properties_258.txt | 550 +++++++++++ .../302classes4bits/properties_259.txt | 470 ++++++++++ .../302classes4bits/properties_260.txt | 470 ++++++++++ .../302classes4bits/properties_261.txt | 482 ++++++++++ .../302classes4bits/properties_262.txt | 482 ++++++++++ .../302classes4bits/properties_263.txt | 482 ++++++++++ .../302classes4bits/properties_264.txt | 470 ++++++++++ .../302classes4bits/properties_265.txt | 474 ++++++++++ .../302classes4bits/properties_266.txt | 486 ++++++++++ .../302classes4bits/properties_267.txt | 486 ++++++++++ .../302classes4bits/properties_268.txt | 486 ++++++++++ .../302classes4bits/properties_269.txt | 478 ++++++++++ .../302classes4bits/properties_270.txt | 478 ++++++++++ .../302classes4bits/properties_271.txt | 470 ++++++++++ .../302classes4bits/properties_272.txt | 486 ++++++++++ .../302classes4bits/properties_273.txt | 486 ++++++++++ .../302classes4bits/properties_274.txt | 478 ++++++++++ .../302classes4bits/properties_275.txt | 482 ++++++++++ .../302classes4bits/properties_276.txt | 474 ++++++++++ .../302classes4bits/properties_277.txt | 486 ++++++++++ .../302classes4bits/properties_278.txt | 490 ++++++++++ .../302classes4bits/properties_279.txt | 482 ++++++++++ .../302classes4bits/properties_280.txt | 482 ++++++++++ .../302classes4bits/properties_281.txt | 490 ++++++++++ .../302classes4bits/properties_282.txt | 506 ++++++++++ .../302classes4bits/properties_283.txt | 506 ++++++++++ .../302classes4bits/properties_284.txt | 510 ++++++++++ .../302classes4bits/properties_285.txt | 490 ++++++++++ .../302classes4bits/properties_286.txt | 494 ++++++++++ .../302classes4bits/properties_287.txt | 526 +++++++++++ .../302classes4bits/properties_288.txt | 550 +++++++++++ .../302classes4bits/properties_289.txt | 526 +++++++++++ .../302classes4bits/properties_290.txt | 542 +++++++++++ .../302classes4bits/properties_291.txt | 558 +++++++++++ .../302classes4bits/properties_292.txt | 550 +++++++++++ .../302classes4bits/properties_293.txt | 478 ++++++++++ .../302classes4bits/properties_294.txt | 550 +++++++++++ .../302classes4bits/properties_295.txt | 550 +++++++++++ .../302classes4bits/properties_296.txt | 518 ++++++++++ .../302classes4bits/properties_297.txt | 598 ++++++++++++ .../302classes4bits/properties_298.txt | 598 ++++++++++++ .../302classes4bits/properties_299.txt | 566 +++++++++++ .../302classes4bits/properties_300.txt | 662 +++++++++++++ .../302classes4bits/properties_301.txt | 694 ++++++++++++++ .../302classes4bits/properties_302.txt | 886 ++++++++++++++++++ .../properties_302classes4bits_Part0.csv | 303 ++++++ .../Sboxes4/properties_Anubis_S0.txt | 48 +- .../Sboxes4/properties_Anubis_S1.txt | 48 +- .../Sboxes4/properties_BLAKE_1.txt | 48 +- .../Sboxes4/properties_BLAKE_2.txt | 48 +- .../Sboxes4/properties_BLAKE_3.txt | 48 +- .../Sboxes4/properties_BLAKE_4.txt | 48 +- .../Sboxes4/properties_BLAKE_5.txt | 48 +- .../Sboxes4/properties_BLAKE_6.txt | 48 +- .../Sboxes4/properties_BLAKE_7.txt | 48 +- .../Sboxes4/properties_BLAKE_8.txt | 48 +- .../Sboxes4/properties_BLAKE_9.txt | 48 +- .../Sboxes4/properties_CLEFIA_SS0.txt | 48 +- .../Sboxes4/properties_CLEFIA_SS1.txt | 48 +- .../Sboxes4/properties_CLEFIA_SS2.txt | 48 +- .../Sboxes4/properties_CLEFIA_SS3.txt | 48 +- .../Sboxes4/properties_CS_cipher_F.txt | 24 +- .../Sboxes4/properties_CS_cipher_G.txt | 48 +- .../Sboxes4/properties_DES_S1_1.txt | 48 +- .../Sboxes4/properties_DES_S1_2.txt | 48 +- .../Sboxes4/properties_DES_S1_3.txt | 48 +- .../Sboxes4/properties_DES_S1_4.txt | 48 +- .../Sboxes4/properties_DES_S2_1.txt | 48 +- .../Sboxes4/properties_DES_S2_2.txt | 48 +- .../Sboxes4/properties_DES_S2_3.txt | 48 +- .../Sboxes4/properties_DES_S2_4.txt | 48 +- .../Sboxes4/properties_DES_S3_1.txt | 48 +- .../Sboxes4/properties_DES_S3_2.txt | 48 +- .../Sboxes4/properties_DES_S3_3.txt | 48 +- .../Sboxes4/properties_DES_S3_4.txt | 48 +- .../Sboxes4/properties_DES_S4_1.txt | 48 +- .../Sboxes4/properties_DES_S4_2.txt | 48 +- .../Sboxes4/properties_DES_S4_3.txt | 48 +- .../Sboxes4/properties_DES_S4_4.txt | 48 +- .../Sboxes4/properties_DES_S5_1.txt | 48 +- .../Sboxes4/properties_DES_S5_2.txt | 48 +- .../Sboxes4/properties_DES_S5_3.txt | 48 +- .../Sboxes4/properties_DES_S5_4.txt | 48 +- .../Sboxes4/properties_DES_S6_1.txt | 48 +- .../Sboxes4/properties_DES_S6_2.txt | 48 +- .../Sboxes4/properties_DES_S6_3.txt | 48 +- .../Sboxes4/properties_DES_S6_4.txt | 48 +- .../Sboxes4/properties_DES_S7_1.txt | 48 +- .../Sboxes4/properties_DES_S7_2.txt | 48 +- .../Sboxes4/properties_DES_S7_3.txt | 48 +- .../Sboxes4/properties_DES_S7_4.txt | 48 +- .../Sboxes4/properties_DES_S8_1.txt | 48 +- .../Sboxes4/properties_DES_S8_2.txt | 48 +- .../Sboxes4/properties_DES_S8_3.txt | 48 +- .../Sboxes4/properties_DES_S8_4.txt | 48 +- .../Sboxes4/properties_Enocoro_S4.txt | 48 +- .../Sboxes4/properties_Fox_S1.txt | 48 +- .../Sboxes4/properties_Fox_S2.txt | 48 +- .../Sboxes4/properties_Fox_S3.txt | 48 +- .../Sboxes4/properties_GIFT.txt | 48 +- .../Sboxes4/properties_GOST2_1.txt | 48 +- .../Sboxes4/properties_GOST2_2.txt | 48 +- .../Sboxes4/properties_GOST_1.txt | 48 +- .../Sboxes4/properties_GOST_2.txt | 48 +- .../Sboxes4/properties_GOST_3.txt | 48 +- .../Sboxes4/properties_GOST_4.txt | 48 +- .../Sboxes4/properties_GOST_5.txt | 48 +- .../Sboxes4/properties_GOST_6.txt | 48 +- .../Sboxes4/properties_GOST_7.txt | 48 +- .../Sboxes4/properties_GOST_8.txt | 48 +- .../Sboxes4/properties_GOST_IETF_1.txt | 48 +- .../Sboxes4/properties_GOST_IETF_2.txt | 48 +- .../Sboxes4/properties_GOST_IETF_3.txt | 48 +- .../Sboxes4/properties_GOST_IETF_4.txt | 48 +- .../Sboxes4/properties_GOST_IETF_5.txt | 48 +- .../Sboxes4/properties_GOST_IETF_6.txt | 48 +- .../Sboxes4/properties_GOST_IETF_7.txt | 48 +- .../Sboxes4/properties_GOST_IETF_8.txt | 48 +- .../Sboxes4/properties_Golden_S0.txt | 48 +- .../Sboxes4/properties_Golden_S1.txt | 48 +- .../Sboxes4/properties_Golden_S2.txt | 48 +- .../Sboxes4/properties_Golden_S3.txt | 48 +- .../Sboxes4/properties_Hummingbird_2_S1.txt | 48 +- .../Sboxes4/properties_Hummingbird_2_S2.txt | 48 +- .../Sboxes4/properties_Hummingbird_2_S3.txt | 48 +- .../Sboxes4/properties_Hummingbird_2_S4.txt | 48 +- .../Sboxes4/properties_Iceberg_S0.txt | 48 +- .../Sboxes4/properties_Iceberg_S1.txt | 48 +- .../Sboxes4/properties_JH_S0.txt | 48 +- .../Sboxes4/properties_JH_S1.txt | 48 +- .../Sboxes4/properties_KLEIN.txt | 48 +- .../Sboxes4/properties_KNOT.txt | 438 +++++++++ .../Sboxes4/properties_Khazad_P.txt | 48 +- .../Sboxes4/properties_Khazad_Q.txt | 48 +- .../Sboxes4/properties_Kuznyechik_nu0.txt | 48 +- .../Sboxes4/properties_Kuznyechik_nu1.txt | 48 +- .../Sboxes4/properties_Kuznyechik_phi.txt | 24 +- .../Sboxes4/properties_Kuznyechik_sigma.txt | 48 +- .../Sboxes4/properties_LAC.txt | 48 +- .../Sboxes4/properties_LBlock_0.txt | 48 +- .../Sboxes4/properties_LBlock_1.txt | 48 +- .../Sboxes4/properties_LBlock_2.txt | 48 +- .../Sboxes4/properties_LBlock_3.txt | 48 +- .../Sboxes4/properties_LBlock_4.txt | 48 +- .../Sboxes4/properties_LBlock_5.txt | 48 +- .../Sboxes4/properties_LBlock_6.txt | 48 +- .../Sboxes4/properties_LBlock_7.txt | 48 +- .../Sboxes4/properties_LBlock_8.txt | 48 +- .../Sboxes4/properties_LBlock_9.txt | 48 +- .../Sboxes4/properties_Lucifer_S0.txt | 48 +- .../Sboxes4/properties_Lucifer_S1.txt | 48 +- .../Sboxes4/properties_Luffa.txt | 48 +- .../Sboxes4/properties_Luffa_v1.txt | 48 +- .../Sboxes4/properties_MANTIS.txt | 48 +- .../Sboxes4/properties_MIBS.txt | 48 +- .../Sboxes4/properties_Magma_1.txt | 48 +- .../Sboxes4/properties_Magma_2.txt | 48 +- .../Sboxes4/properties_Magma_3.txt | 48 +- .../Sboxes4/properties_Magma_4.txt | 48 +- .../Sboxes4/properties_Magma_5.txt | 48 +- .../Sboxes4/properties_Magma_6.txt | 48 +- .../Sboxes4/properties_Magma_7.txt | 48 +- .../Sboxes4/properties_Magma_8.txt | 48 +- .../Sboxes4/properties_Midori_Sb0.txt | 48 +- .../Sboxes4/properties_Midori_Sb1.txt | 48 +- .../Sboxes4/properties_Minalpher.txt | 48 +- .../Sboxes4/properties_Noekeon.txt | 48 +- .../Sboxes4/properties_Num1_DL_04_0.txt | 48 +- .../Sboxes4/properties_Num1_DL_04_1.txt | 48 +- .../Sboxes4/properties_Num1_DL_13_0.txt | 48 +- .../Sboxes4/properties_Num1_DL_13_1.txt | 48 +- .../Sboxes4/properties_Num1_DL_13_2.txt | 48 +- .../Sboxes4/properties_Num1_DL_13_3.txt | 48 +- 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EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_302classes4bits_Part0.csv create mode 100644 EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KNOT.txt create mode 100644 EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_sboxes4_Part0.csv diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_3-way.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_3-way.txt index 64d1f5f..d25a946 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_3-way.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_3-way.txt @@ -4,18 +4,18 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + x1x2; deg = 2, term_n = 3, related_n = 3 -y1 = + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 -y2 = + x0 + + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 +y0 = 1 + x0 + x1 + + + + x1x2; deg = 2, term_n = 4, related_n = 3 +y1 = 1 + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 +y2 = 1 + x0 + + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + = + x0 + x1 + + + + x1x2; deg = 2, term_n = 3, related_n = 3 - + y1 + = + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 +y0 + + = 1 + x0 + x1 + + + + x1x2; deg = 2, term_n = 4, related_n = 3 + + y1 + = 1 + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + = + x0 + + x2 + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 - + + y2 = + x0 + + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 = 1 + x0 + + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 y0 + + y2 = + + x1 + x2 + x0x1 + + x1x2; deg = 2, term_n = 4, related_n = 3 + y1 + y2 = + x0 + x1 + + x0x1 + x0x2 + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + y2 = + + + + x0x1 + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 = 1 + + + + x0x1 + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = @@ -128,18 +128,18 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + x1x2; deg = 2, term_n = 3, related_n = 3 -y1 = + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 -y2 = + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 +y0 = 1 + x0 + + x2 + + + x1x2; deg = 2, term_n = 4, related_n = 3 +y1 = 1 + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 +y2 = 1 + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + = + x0 + + x2 + + + x1x2; deg = 2, term_n = 3, related_n = 3 - + y1 + = + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 +y0 + + = 1 + x0 + + x2 + + + x1x2; deg = 2, term_n = 4, related_n = 3 + + y1 + = 1 + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + = + + x1 + x2 + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 - + + y2 = + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 = 1 + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 y0 + + y2 = + x0 + x1 + + x0x1 + + x1x2; deg = 2, term_n = 4, related_n = 3 + y1 + y2 = + x0 + + x2 + x0x1 + x0x2 + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + y2 = + + + + x0x1 + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 = 1 + + + + x0x1 + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_PRINTcipher.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_PRINTcipher.txt index c16ed76..a5550cd 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_PRINTcipher.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_PRINTcipher.txt @@ -4,18 +4,18 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 5, related_n = 3 -y1 = 1 + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 -y2 = 1 + + + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 +y0 = + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 4, related_n = 3 +y1 = + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 +y2 = + + + x2 + x0x1 + + ; deg = 2, term_n = 2, related_n = 3 ANF of components: -y0 + + = 1 + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 5, related_n = 3 - + y1 + = 1 + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 +y0 + + = + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 4, related_n = 3 + + y1 + = + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 y0 + y1 + = + x0 + + + + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 - + + y2 = 1 + + + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 = + + + x2 + x0x1 + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 = + x0 + x1 + + x0x1 + + x1x2; deg = 2, term_n = 4, related_n = 3 + y1 + y2 = + + x1 + + x0x1 + x0x2 + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 = 1 + x0 + + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 6, related_n = 3 +y0 + y1 + y2 = + x0 + + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 5, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = @@ -128,18 +128,18 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 5, related_n = 3 -y1 = 1 + + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 -y2 = 1 + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 +y0 = + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 4, related_n = 3 +y1 = + + x1 + + + x0x2 + ; deg = 2, term_n = 2, related_n = 3 +y2 = + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 ANF of components: -y0 + + = 1 + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 5, related_n = 3 - + y1 + = 1 + + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 +y0 + + = + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 4, related_n = 3 + + y1 + = + + x1 + + + x0x2 + ; deg = 2, term_n = 2, related_n = 3 y0 + y1 + = + x0 + + x2 + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 - + + y2 = 1 + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 = + + x1 + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 = + x0 + + + x0x1 + + x1x2; deg = 2, term_n = 3, related_n = 3 + y1 + y2 = + + + x2 + x0x1 + x0x2 + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 = 1 + x0 + x1 + + x0x1 + x0x2 + x1x2; deg = 2, term_n = 6, related_n = 3 +y0 + y1 + y2 = + x0 + x1 + + x0x1 + x0x2 + x1x2; deg = 2, term_n = 5, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_SEA.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_SEA.txt index 9c51184..5ae0e4b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_SEA.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_SEA.txt @@ -4,18 +4,18 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x1x2; deg = 2, term_n = 3, related_n = 3 -y1 = 1 + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 -y2 = 1 + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + x0 + + + + + x1x2; deg = 2, term_n = 2, related_n = 3 +y1 = + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 +y2 = + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + = 1 + x0 + + + + + x1x2; deg = 2, term_n = 3, related_n = 3 - + y1 + = 1 + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 +y0 + + = + x0 + + + + + x1x2; deg = 2, term_n = 2, related_n = 3 + + y1 + = + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 y0 + y1 + = + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 - + + y2 = 1 + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 5, related_n = 3 + + + y2 = + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 y0 + + y2 = + + x1 + x2 + x0x1 + + x1x2; deg = 2, term_n = 4, related_n = 3 + y1 + y2 = + x0 + + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 5, related_n = 3 -y0 + y1 + y2 = 1 + + + x2 + x0x1 + x0x2 + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 = + + + x2 + x0x1 + x0x2 + ; deg = 2, term_n = 3, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = @@ -128,18 +128,18 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 -y1 = 1 + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 -y2 = 1 + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 +y1 = + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 +y2 = + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + = 1 + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 - + y1 + = 1 + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 +y0 + + = + + x1 + + + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 + + y1 + = + x0 + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 y0 + y1 + = + x0 + + + + + x1x2; deg = 2, term_n = 2, related_n = 3 - + + y2 = 1 + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 5, related_n = 3 + + + y2 = + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 y0 + + y2 = + x0 + + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 5, related_n = 3 + y1 + y2 = + + + x2 + x0x1 + x0x2 + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 = 1 + + x1 + x2 + x0x1 + + x1x2; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 = + + x1 + x2 + x0x1 + + x1x2; deg = 2, term_n = 4, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_ctc2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_ctc2.txt index f3d4995..fe6a18e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_ctc2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_ctc2.txt @@ -4,18 +4,18 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 -y1 = + + x1 + + + x0x2 + ; deg = 2, term_n = 2, related_n = 3 -y2 = + + x1 + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 5, related_n = 3 +y0 = 1 + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 +y2 = 1 + + x1 + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 6, related_n = 3 ANF of components: -y0 + + = + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + = + + x1 + + + x0x2 + ; deg = 2, term_n = 2, related_n = 3 +y0 + + = 1 + x0 + x1 + x2 + x0x1 + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + = 1 + + x1 + + + x0x2 + ; deg = 2, term_n = 3, related_n = 3 y0 + y1 + = + x0 + + x2 + x0x1 + x0x2 + ; deg = 2, term_n = 4, related_n = 3 - + + y2 = + + x1 + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 5, related_n = 3 + + + y2 = 1 + + x1 + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 6, related_n = 3 y0 + + y2 = + x0 + + + + x0x2 + x1x2; deg = 2, term_n = 3, related_n = 3 + y1 + y2 = + + + x2 + x0x1 + + x1x2; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 = + x0 + x1 + + + + x1x2; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 = 1 + x0 + x1 + + + + x1x2; deg = 2, term_n = 4, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = @@ -128,18 +128,18 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 -y1 = + + x1 + + x0x1 + x0x2 + ; deg = 2, term_n = 3, related_n = 3 -y2 = 1 + x0 + x1 + + x0x1 + + x1x2; deg = 2, term_n = 5, related_n = 3 +y0 = + + + x2 + x0x1 + + ; deg = 2, term_n = 2, related_n = 3 +y1 = 1 + + x1 + + x0x1 + x0x2 + ; deg = 2, term_n = 4, related_n = 3 +y2 = + x0 + x1 + + x0x1 + + x1x2; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + = 1 + + + x2 + x0x1 + + ; deg = 2, term_n = 3, related_n = 3 - + y1 + = + + x1 + + x0x1 + x0x2 + ; deg = 2, term_n = 3, related_n = 3 +y0 + + = + + + x2 + x0x1 + + ; deg = 2, term_n = 2, related_n = 3 + + y1 + = 1 + + x1 + + x0x1 + x0x2 + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + = 1 + + x1 + x2 + + x0x2 + ; deg = 2, term_n = 4, related_n = 3 - + + y2 = 1 + x0 + x1 + + x0x1 + + x1x2; deg = 2, term_n = 5, related_n = 3 + + + y2 = + x0 + x1 + + x0x1 + + x1x2; deg = 2, term_n = 4, related_n = 3 y0 + + y2 = + x0 + x1 + x2 + + + x1x2; deg = 2, term_n = 4, related_n = 3 + y1 + y2 = 1 + x0 + + + + x0x2 + x1x2; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + y2 = + x0 + + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 = 1 + x0 + + x2 + x0x1 + x0x2 + x1x2; deg = 2, term_n = 6, related_n = 3 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:7, }; DDT = diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_sboxes3_Part0.csv b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_sboxes3_Part0.csv new file mode 100644 index 0000000..bcc8389 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes3/properties_sboxes3_Part0.csv @@ -0,0 +1,5 @@ +Cipher,LUT,bit_slice,Permutation,Involution,Diff,DiffFreq,Diff1,CardD1,Lin,LinFreq,Lin1,CardL1,max_degree,min_degree,MaxDegreeFreq,MinDegreeFreq,Max_ProductDegrees,LS_number,"max_v (v, w)-linear","max_w (v, w)-linear",Optimal_Class,Cost (GE) TSMC65nm,Cost is Best ,inv_LUT,inv_bit_slice,inv_max_degree,inv_min_degree,inv_MaxDegreeFreq,inv_MinDegreeFreq,inv_Max_ProductDegrees,inv_LS_number,"inv_max_v (v, w)-linear","inv_max_w (v, w)-linear",inv_Optimal_Class +PRINTcipher,0001030607040502,78_9c_56,True,False,2,28,2,3,4,28,4,3,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",-,0,-,0001070205060304,b4_6c_56,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",- +SEA,0005060704030102,1e_ac_6a,True,False,2,28,2,4,4,28,4,4,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",-,0,-,0006070504010203,1e_c6_ac,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",- +ctc2,0706000402050103,2b_93_e1,True,False,2,28,2,5,4,28,4,5,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",-,0,-,0206040703050100,2e_1b_78,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",- +3-way,0702040501060300,2d_63_59,True,False,2,28,2,3,4,28,4,3,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",-,0,-,0704010602030500,4b_39_65,2,2,7,7,[2|2|3],7,"(2, 2)","(2, 2)",- diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_001.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_001.txt new file mode 100644 index 0000000..7d46541 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_001.txt @@ -0,0 +1,406 @@ +001 Sbox: +LUT = { +0x04,0x00,0x01,0x0f,0x02,0x0b,0x06,0x07,0x03,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{8: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{6: 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{a: 0, 0, 2, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 0, 2, 0, }, +{c: 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 4, 2, 2, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 0, 0, 2, 2, 6, 0, 0, 4, 0, 2, 2, }, +{2: 16, 0, 6, 2, 0, 0, 4, 0, 6, 0, 8, 0, 0, 0, 4, 2, }, +{4: 16, 0, 0, 4, 2, 4, 0, 2, 0, 0, 0, 6, 2, 2, 0, 2, }, +{8: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 16, 2, 0, 6, 0, 4, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, }, +{5: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, }, +{6: 16, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{a: 16, 4, 2, 0, 0, 2, 2, 2, 0, 4, 2, 0, 4, 0, 2, 0, }, +{c: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +{7: 16, 0, 0, 4, 0, 6, 0, 2, 2, 2, 0, 4, 2, 2, 0, 0, }, +{b: 16, 6, 4, 0, 6, 0, 2, 0, 0, 8, 2, 0, 4, 0, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 4, 0, 4, 0, 6, 0, 2, 2, 0, 0, }, +{e: 16, 0, 10, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 2, 4, 0, }, +{f: 16, 2, 0, 2, 0, 2, 4, 0, 4, 0, 4, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:78, 4:28, 6:11, 8:2, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:9, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, -8, 8, 0, 8, 0, -8, 0, -8, 0, 0, }, +{2: 16, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, -8, 8, -8, 8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 8, 0, -8, 0, 0, -8, 0, -8, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, 0, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, }, +{9: 16, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 8, -8, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, }, +{7: 16, -8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, -8, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, -8, 8, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 8, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, 0, 8, -8, 0, -8, 0, 8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, , x, x, , x, , , x, , , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, , x, , x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, , , x, , x, , , x, , , x, x, x, }, +{b: , x, x, x, x, , , x, , , x, x, x, x, x, x, }, +{d: , , x, x, , , x, , x, x, , , x, x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x04,}}, +{{0x0a,0x04,}, {0x01,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x08,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +001 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x0b,0x06,0x07,0x0f,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{2: 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{4: 0, 2, 2, 4, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{8: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 4, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, }, +{5: 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{6: 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 4, 0, 0, }, +{a: 0, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 4, 0, 2, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 4, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 6, 2, 0, 2, }, +{2: 16, 0, 6, 0, 0, 0, 4, 2, 0, 2, 4, 0, 4, 0, 10, 0, }, +{4: 16, 2, 2, 4, 0, 6, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{8: 16, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, 0, 6, 2, 4, 0, }, +{3: 16, 0, 0, 4, 0, 4, 0, 2, 2, 2, 0, 6, 0, 2, 0, 2, }, +{5: 16, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 4, 2, 4, }, +{6: 16, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 16, 2, 6, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 4, 0, 4, }, +{a: 16, 6, 0, 0, 2, 0, 4, 0, 0, 4, 0, 2, 8, 0, 6, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 4, 4, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 4, 0, 2, 2, 2, 2, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, }, +{e: 16, 2, 4, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 2, }, +{f: 16, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:78, 4:28, 6:11, 8:2, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 8, 4, 4, 4, 4, 0, }, +{4: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{5: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 8, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:9, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 8, 0, }, +{2: 16, 8, 0, -8, 0, -8, 0, -8, -8, 0, 0, 0, -8, 8, 0, 8, }, +{4: 16, 0, 0, 0, 8, 0, -8, 0, 8, 0, 0, -8, 0, -8, -8, 0, }, +{8: 16, 8, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, }, +{3: 16, -8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, 8, }, +{5: 16, 0, -8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, }, +{a: 16, 0, -8, 8, -8, 0, 0, 0, -8, 8, -8, 0, 0, 0, 8, -8, }, +{c: 16, 0, -8, 0, -8, 0, 8, -8, 8, 0, 8, -8, -8, 0, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{a: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, , x, , , x, , x, x, , x, x, , , x, }, +{b: , , x, x, , x, , x, , , x, x, x, x, x, x, }, +{d: , x, x, x, x, , , x, , , x, x, , , x, x, }, +{e: , , , x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x09,}}, +{{0x02,0x04,}, {0x08,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x05,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x07,}}, +{{0x09,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x0f,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_002.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_002.txt new file mode 100644 index 0000000..4eb1092 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_002.txt @@ -0,0 +1,406 @@ +002 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x05,0x06,0x09,0x04,0x03,0x0a,0x0b,0x07,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{8: 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 2, 2, 0, }, +{9: 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, }, +{a: 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 4, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, }, +{b: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{e: 0, 2, 2, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:4, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 0, 4, 4, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 16, 0, 2, 2, 2, 0, 4, 4, 8, 0, 4, 0, 0, 0, 2, 4, }, +{4: 16, 4, 0, 4, 0, 2, 8, 0, 4, 2, 4, 2, 0, 0, 2, 0, }, +{8: 16, 0, 0, 0, 4, 6, 2, 2, 0, 0, 2, 2, 6, 0, 0, 0, }, +{3: 16, 2, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, }, +{5: 16, 4, 2, 6, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{6: 16, 0, 0, 0, 0, 2, 4, 2, 4, 2, 6, 0, 0, 2, 2, 0, }, +{9: 16, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, }, +{a: 16, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 16, 4, 2, 0, 0, 2, 0, 8, 4, 0, 2, 4, 0, 2, 0, 4, }, +{7: 16, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, }, +{b: 16, 0, 2, 0, 6, 6, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 16, 4, 2, 0, 0, 2, 2, 4, 0, 0, 0, 6, 0, 2, 2, 0, }, +{e: 16, 2, 2, 0, 2, 0, 0, 4, 4, 2, 0, 0, 0, 0, 2, 6, }, +{f: 16, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:80, 4:27, 6:10, 8:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, 8, 0, -8, 0, -8, 0, 0, -8, 0, -8, 0, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 0, 0, -8, -8, 8, -8, 0, 8, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, 0, 8, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, -8, -8, -8, 0, 0, -8, 0, 0, 8, 0, 0, 8, }, +{9: 16, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 0, -8, -8, 0, 0, 0, 0, 8, -8, 8, 0, -8, -8, 0, 8, }, +{7: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, -8, 0, 0, 8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{f: 16, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, , x, x, x, , x, , x, , , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{c: , x, x, , x, x, x, x, x, , x, x, , x, x, x, }, +{7: , x, , x, x, , x, x, x, , x, , , , , x, }, +{b: , x, x, , , , , , x, , x, , x, , , x, }, +{d: , , x, , , , x, x, x, , x, x, , x, , x, }, +{e: , , x, , x, x, x, x, , , x, x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x09,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x0c,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x0e,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +002 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x09,0x08,0x05,0x06,0x0c,0x00,0x07,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{2: 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{4: 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 2, 2, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 2, 2, 4, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{6: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 0, 4, 0, }, +{9: 0, 0, 4, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, }, +{7: 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, }, +{e: 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{f: 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:4, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 0, 2, 4, 2, 0, 4, 2, 0, }, +{2: 16, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{4: 16, 4, 2, 4, 0, 2, 6, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 16, 2, 2, 0, 4, 6, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, }, +{3: 16, 0, 0, 2, 6, 4, 0, 2, 0, 0, 2, 0, 6, 2, 0, 0, }, +{5: 16, 4, 4, 8, 2, 0, 4, 4, 0, 2, 0, 0, 0, 2, 0, 2, }, +{6: 16, 4, 4, 0, 2, 0, 0, 2, 2, 0, 8, 2, 0, 4, 4, 0, }, +{9: 16, 0, 8, 4, 0, 2, 2, 4, 2, 0, 4, 0, 0, 0, 4, 2, }, +{a: 16, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 16, 0, 4, 4, 2, 0, 0, 6, 0, 2, 2, 2, 0, 0, 0, 2, }, +{7: 16, 4, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 6, 0, 2, }, +{b: 16, 0, 0, 0, 6, 6, 0, 0, 2, 2, 0, 2, 4, 0, 0, 2, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, }, +{e: 16, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{f: 16, 2, 4, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 0, 6, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:80, 4:27, 6:10, 8:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{3: 0, 4, 4, 8, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{5: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, 8, -8, 8, -8, }, +{2: 16, 0, 0, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, }, +{4: 16, 0, 0, 0, 8, 0, 0, -8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 0, 0, 8, -8, 0, 8, -8, 0, 0, -8, -8, 0, }, +{6: 16, 8, 0, -8, -8, 0, -8, 8, -8, -8, 0, 0, 0, 8, 0, 0, }, +{9: 16, 0, -8, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 0, -8, 8, }, +{a: 16, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, -8, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, 0, }, +{7: 16, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, -8, 0, 8, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, , x, x, x, , x, x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{7: , x, , , x, , x, x, x, , x, , , , , x, }, +{b: , , , , x, , x, x, , , , x, x, , , x, }, +{d: , x, x, x, , , x, x, x, , x, x, , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0d,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x02,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x03,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x06,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x06,0x09,0x0f,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x09,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_003.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_003.txt new file mode 100644 index 0000000..ac7cdc9 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_003.txt @@ -0,0 +1,406 @@ +003 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x0f,0x05,0x06,0x07,0x04,0x03,0x0a,0x0b,0x09,0x0d,0x0e,0x02, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, }, +{2: 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, }, +{4: 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 2, 0, }, +{8: 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 2, 0, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, }, +{6: 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 4, 0, }, +{9: 0, 0, 2, 4, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, }, +{a: 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 4, }, +{c: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, 2, }, +{7: 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{b: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, }, +{e: 0, 2, 4, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, }, +{f: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 0, 0, 0, 0, 2, 6, 2, 0, 6, 0, 0, }, +{2: 16, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 6, 0, 0, 6, 2, }, +{4: 16, 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 4, 2, 2, 6, 0, }, +{8: 16, 0, 0, 0, 4, 6, 2, 2, 0, 0, 2, 2, 6, 0, 0, 0, }, +{3: 16, 2, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, }, +{5: 16, 0, 0, 0, 2, 0, 6, 2, 2, 4, 0, 0, 0, 2, 0, 6, }, +{6: 16, 2, 0, 0, 0, 2, 0, 2, 6, 2, 0, 6, 0, 0, 4, 0, }, +{9: 16, 0, 6, 4, 0, 0, 0, 6, 2, 2, 2, 0, 2, 0, 0, 0, }, +{a: 16, 2, 2, 0, 0, 0, 6, 0, 0, 6, 0, 2, 2, 0, 0, 4, }, +{c: 16, 6, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 6, 2, 2, }, +{7: 16, 0, 6, 6, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{b: 16, 0, 2, 0, 6, 6, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 16, 6, 2, 0, 0, 2, 2, 0, 2, 0, 6, 0, 0, 4, 0, 0, }, +{e: 16, 2, 4, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 2, 0, }, +{f: 16, 0, 0, 2, 0, 2, 4, 0, 0, 6, 2, 0, 0, 0, 2, 6, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:120, 2:60, 4:15, 6:30, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{4: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{6: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:8, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, -8, 0, 0, 8, 0, -8, 0, -8, 0, 8, -8, 0, }, +{4: 16, -8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 8, 0, -8, }, +{8: 16, 0, 0, 0, 0, 8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, 0, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, }, +{6: 16, 0, -8, 0, 0, -8, -8, 8, -8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 16, 8, 0, 0, 0, 0, -8, -8, 8, 0, -8, -8, 0, 0, 0, 0, }, +{a: 16, -8, -8, 0, 0, 0, 8, 0, 0, 8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, 0, -8, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, -8, }, +{f: 16, 0, 0, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, x, x, , x, x, x, x, , , x, x, x, x, }, +{b: , x, x, , , , , , x, , x, , x, , , x, }, +{d: , x, , , , , x, x, x, x, , x, x, , x, x, }, +{e: , x, , , x, x, x, x, , x, , x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x09,}}, +{{0x02,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x0c,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,}}, +{{0x05,0x08,}, {0x0a,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +003 Inverse Sbox: +LUT = { +0x01,0x02,0x0f,0x09,0x08,0x05,0x06,0x07,0x00,0x0c,0x0a,0x0b,0x03,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{2: 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 4, 0, }, +{4: 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, }, +{8: 0, 2, 2, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{5: 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 4, }, +{6: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 4, 0, 0, 2, 0, }, +{9: 0, 0, 4, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{a: 0, 2, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{c: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 2, 4, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, }, +{f: 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 2, 0, 2, 6, 0, 0, 6, 2, 0, }, +{2: 16, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 6, 2, 2, 4, 0, }, +{4: 16, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 6, 0, 0, 6, 2, }, +{8: 16, 2, 2, 0, 4, 6, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, }, +{3: 16, 0, 0, 0, 6, 4, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, }, +{5: 16, 0, 0, 2, 2, 0, 6, 0, 0, 6, 0, 0, 0, 2, 2, 4, }, +{6: 16, 0, 0, 0, 2, 0, 2, 2, 6, 0, 2, 4, 0, 0, 6, 0, }, +{9: 16, 0, 4, 6, 0, 2, 2, 6, 2, 0, 0, 0, 0, 2, 0, 0, }, +{a: 16, 2, 0, 0, 0, 0, 4, 2, 2, 6, 0, 0, 2, 0, 0, 6, }, +{c: 16, 6, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 6, 0, 2, }, +{7: 16, 2, 6, 4, 2, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, }, +{b: 16, 0, 0, 2, 6, 6, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 6, 0, 2, 0, 0, 2, 0, 0, 0, 6, 2, 2, 4, 0, 0, }, +{e: 16, 0, 6, 6, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, }, +{f: 16, 0, 2, 0, 0, 2, 6, 0, 0, 4, 2, 2, 0, 0, 0, 6, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:120, 2:60, 4:15, 6:30, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{3: 0, 4, 4, 8, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 8, 4, 4, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:8, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, -8, 8, 0, }, +{2: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 0, -8, }, +{4: 16, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 0, 8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, -8, -8, -8, 0, 0, 8, 0, 0, }, +{9: 16, 0, 0, 0, 8, -8, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, -8, 0, 0, 8, }, +{c: 16, 0, 8, 0, -8, 0, 0, 0, 0, -8, 8, -8, -8, 0, 0, 0, }, +{7: 16, 8, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, 0, -8, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{e: 16, 8, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, }, +{f: 16, 0, -8, 0, 0, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{7: , x, , , x, , x, x, , x, x, , x, x, x, x, }, +{b: , , , , x, , x, x, x, x, , x, , x, x, x, }, +{d: , , , x, x, x, , , x, , , , , x, , x, }, +{e: , x, x, x, , , x, x, x, x, , x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x0a,0x04,}, {0x05,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x03,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x0f,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_004.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_004.txt new file mode 100644 index 0000000..d9f2ccf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_004.txt @@ -0,0 +1,406 @@ +004 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0d,0x06,0x07,0x04,0x09,0x0a,0x05,0x0c,0x0b,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{2: 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{4: 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 4, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 0, 2, 4, }, +{6: 0, 0, 2, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 2, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, }, +{7: 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:6, 2:8, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 0, 4, 0, 0, 0, 6, 0, 0, 2, 0, 2, 2, 2, }, +{2: 16, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{4: 16, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, }, +{8: 16, 4, 0, 0, 4, 0, 0, 4, 10, 0, 0, 0, 2, 2, 0, 6, }, +{3: 16, 4, 0, 6, 0, 4, 10, 4, 0, 2, 0, 0, 2, 0, 0, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 10, 4, 0, 0, 0, 2, 0, 2, 4, }, +{6: 16, 0, 2, 2, 0, 4, 6, 4, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 16, 10, 2, 4, 6, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 16, 6, 2, 4, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 16, 0, 2, 2, 0, 0, 0, 0, 0, 0, 6, 4, 6, 0, 2, 2, }, +{7: 16, 2, 0, 0, 0, 0, 2, 2, 2, 0, 6, 6, 4, 0, 0, 0, }, +{b: 16, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, 6, 6, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 2, 0, 6, 4, 2, 2, 0, 0, 2, 2, 4, }, +{e: 16, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:112, 2:72, 4:23, 6:14, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 0, 4, 4, }, +{a: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 8, 4, }, +{f: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, 0, 0, -8, }, +{2: 16, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, -8, 0, }, +{4: 16, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 8, -8, -8, 8, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, -8, 8, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, 8, -8, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 8, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, -8, -8, }, +{a: 16, 0, 8, 0, 0, -8, 8, -8, -8, 0, 0, 0, -8, 0, 0, 0, }, +{c: 16, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, }, +{7: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, 8, 0, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, -8, -8, 0, 0, -8, 0, 0, 8, 0, 0, 8, }, +{e: 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, , x, , x, x, x, x, , x, , x, }, +{5: , , x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{6: , , x, x, x, x, , x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , , x, , , , , x, , x, x, , x, , x, }, +{b: , x, , , x, , x, , x, x, , , , , , x, }, +{d: , , x, x, , , x, , x, x, , , x, x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x05,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x08,}, {0x06,0x09,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x0b,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +004 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0b,0x06,0x07,0x03,0x09,0x0a,0x0d,0x0c,0x05,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 2, 0, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 2, }, +{8: 0, 0, 2, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, }, +{5: 0, 0, 2, 0, 0, 2, 4, 2, 0, 4, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, }, +{a: 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, }, +{c: 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 2, 2, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, }, +{d: 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, }, +{e: 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:6, 2:8, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 4, 0, 0, 10, 6, 0, 2, 0, 0, 0, 0, }, +{2: 16, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, }, +{4: 16, 0, 2, 2, 0, 6, 0, 2, 4, 4, 2, 0, 0, 0, 0, 2, }, +{8: 16, 4, 2, 2, 4, 0, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, }, +{3: 16, 0, 2, 0, 0, 4, 6, 4, 0, 0, 0, 0, 2, 2, 2, 2, }, +{5: 16, 0, 2, 0, 0, 10, 4, 6, 4, 4, 0, 2, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 4, 4, 10, 4, 0, 0, 0, 2, 0, 6, 0, 2, }, +{9: 16, 6, 0, 0, 10, 0, 4, 0, 4, 0, 0, 2, 0, 4, 2, 0, }, +{a: 16, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, }, +{c: 16, 0, 2, 0, 0, 0, 0, 0, 0, 2, 6, 6, 4, 2, 2, 0, }, +{7: 16, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 6, 6, 0, 0, 2, }, +{b: 16, 0, 0, 0, 2, 2, 2, 0, 2, 0, 6, 4, 6, 0, 0, 0, }, +{d: 16, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, }, +{e: 16, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 16, 2, 0, 2, 6, 0, 4, 0, 0, 0, 2, 0, 0, 4, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:112, 2:72, 4:23, 6:14, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 8, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{4: 16, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, -8, 0, 0, -8, 8, }, +{8: 16, 8, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, -8, 0, 0, 0, 0, -8, 0, 0, 8, 8, 0, 0, -8, 0, }, +{5: 16, 0, -8, 0, 8, -8, 8, -8, -8, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, 0, -8, 0, 0, 8, 8, 0, -8, -8, 8, -8, -8, 0, 0, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 0, -8, 0, 0, 8, 0, 0, -8, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 8, -8, }, +{7: 16, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, 8, 0, }, +{b: 16, -8, 0, 0, 0, 8, 0, 0, -8, -8, -8, 0, 0, 8, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, }, +{f: 16, 0, 8, -8, 0, 0, 0, 0, -8, 8, 0, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, , x, x, , x, x, x, x, x, , , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, , x, x, x, , x, x, x, , x, x, , x, }, +{a: , , x, x, x, x, x, , , x, x, , , x, x, x, }, +{c: , x, x, x, , x, x, , , x, x, , x, , x, x, }, +{7: , x, , x, , , x, , x, x, , x, x, , , x, }, +{b: , , x, , x, x, x, , , x, x, , , x, , x, }, +{d: , x, x, , , , x, , , x, x, , x, , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x09,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x0a,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0d,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x09,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_005.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_005.txt new file mode 100644 index 0000000..41c9efc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_005.txt @@ -0,0 +1,406 @@ +005 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0f,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{2: 0, 2, 4, 0, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{4: 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, }, +{8: 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 4, 2, 0, 4, 0, }, +{b: 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 2, }, +{e: 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{f: 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:8, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 4, 2, 2, 0, }, +{2: 16, 2, 4, 0, 4, 2, 6, 0, 0, 0, 0, 10, 0, 0, 0, 4, }, +{4: 16, 4, 0, 2, 10, 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, 4, }, +{8: 16, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{3: 16, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{5: 16, 0, 4, 0, 0, 2, 4, 2, 2, 0, 0, 4, 0, 2, 2, 2, }, +{6: 16, 0, 2, 2, 4, 2, 0, 2, 2, 2, 0, 4, 0, 0, 0, 4, }, +{9: 16, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{a: 16, 6, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 10, 2, 4, 0, }, +{c: 16, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 16, 0, 4, 0, 2, 0, 10, 2, 0, 0, 0, 4, 6, 0, 4, 0, }, +{b: 16, 10, 0, 0, 6, 0, 2, 0, 4, 4, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 4, 2, 4, 2, }, +{e: 16, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{f: 16, 4, 0, 2, 4, 2, 0, 0, 4, 2, 2, 0, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:80, 4:30, 6:5, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{9: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, -8, 0, 0, 0, 8, -8, 0, 0, 0, -8, }, +{2: 16, 0, 0, 8, 8, 0, 8, 0, -8, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, -8, 0, 0, 0, 8, 0, 8, 0, 8, 0, -8, -8, -8, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, }, +{6: 16, 0, -8, 0, 8, 0, 0, 0, 0, -8, -8, -8, 8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{a: 16, -8, 0, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, -8, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, -8, 0, -8, 8, 0, 8, 0, -8, }, +{b: 16, -8, 8, 8, -8, 0, -8, 0, 0, 0, -8, 0, -8, 8, 0, 0, }, +{d: 16, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 8, 0, }, +{e: 16, 8, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 8, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , , x, x, , x, , x, x, x, x, , x, x, x, x, }, +{b: , , , , x, x, x, , , x, , , x, , , x, }, +{d: , , x, , , , , x, x, x, x, x, x, , x, x, }, +{e: , x, , x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x06,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0d,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,0x09,0x0e,}}, +{{0x09,0x02,}, {0x04,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +005 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0a,0x06,0x07,0x03,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{2: 0, 2, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, }, +{4: 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, }, +{8: 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, }, +{3: 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{6: 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +{9: 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 2, 2, }, +{c: 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, }, +{7: 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 4, 4, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 2, 2, }, +{f: 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:8, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 0, 2, 0, 0, 0, 6, 0, 0, 10, 0, 0, 4, }, +{2: 16, 2, 4, 0, 2, 0, 4, 2, 0, 0, 2, 4, 0, 2, 2, 0, }, +{4: 16, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, }, +{8: 16, 0, 4, 10, 2, 0, 0, 4, 0, 0, 0, 2, 6, 0, 0, 4, }, +{3: 16, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{5: 16, 0, 6, 0, 0, 0, 4, 0, 0, 4, 0, 10, 2, 4, 2, 0, }, +{6: 16, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +{9: 16, 2, 0, 4, 2, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, }, +{a: 16, 4, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 4, 2, 2, 2, }, +{c: 16, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, }, +{7: 16, 0, 10, 6, 0, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 16, 4, 0, 2, 0, 0, 0, 0, 2, 10, 0, 6, 4, 4, 0, 0, }, +{d: 16, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 2, 0, 0, 0, 0, 2, 0, 2, 4, 2, 4, 0, 4, 2, 2, }, +{f: 16, 0, 4, 4, 2, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:80, 4:30, 6:5, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{2: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{b: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, 0, -8, -8, 0, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, }, +{4: 16, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, -8, -8, 0, }, +{8: 16, 0, -8, 0, 0, 8, 8, 0, 8, 0, 0, -8, -8, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, }, +{5: 16, 0, -8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, 8, 0, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, }, +{9: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, -8, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 8, }, +{c: 16, -8, 0, 0, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, -8, 0, 0, -8, 0, 0, -8, 8, 0, -8, 0, 8, 0, 8, -8, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, -8, 0, -8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 8, 0, 0, }, +{f: 16, 0, 8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, , x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, , , x, x, x, x, x, , x, x, , x, x, x, }, +{d: , , x, , x, x, x, , , x, , , , x, , x, }, +{e: , x, , , , , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x0c,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x0a,}}, +{{0x03,0x04,}, {0x0a,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x08,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_006.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_006.txt new file mode 100644 index 0000000..db1cede --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_006.txt @@ -0,0 +1,406 @@ +006 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0b,0x06,0x07,0x04,0x09,0x0a,0x0f,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{2: 0, 0, 2, 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, }, +{8: 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 2, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 2, 2, }, +{6: 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, }, +{9: 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 2, }, +{c: 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, 2, }, +{7: 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 4, }, +{e: 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{f: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:6, 2:7, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 0, 2, 0, 2, 0, 2, 4, 0, 0, 6, 2, 0, 0, }, +{2: 16, 0, 2, 0, 4, 2, 6, 2, 0, 0, 2, 0, 0, 4, 2, 0, }, +{4: 16, 2, 0, 4, 2, 4, 0, 0, 0, 2, 0, 6, 2, 0, 0, 2, }, +{8: 16, 0, 2, 0, 2, 0, 0, 4, 6, 0, 0, 2, 2, 0, 0, 6, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 2, 2, 0, 4, 2, 2, 0, 0, }, +{5: 16, 2, 0, 0, 0, 2, 2, 6, 4, 0, 0, 0, 0, 0, 2, 6, }, +{6: 16, 0, 4, 2, 0, 2, 0, 2, 0, 2, 6, 2, 0, 0, 4, 0, }, +{9: 16, 0, 6, 2, 0, 2, 0, 0, 2, 0, 4, 2, 2, 0, 4, 0, }, +{a: 16, 6, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 4, 2, 2, 2, }, +{c: 16, 0, 2, 0, 6, 0, 4, 0, 0, 0, 2, 2, 0, 4, 2, 2, }, +{7: 16, 2, 0, 4, 0, 6, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, }, +{b: 16, 4, 0, 0, 2, 0, 2, 2, 0, 6, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 0, 6, 6, 2, 2, 0, 0, 2, 0, 4, }, +{e: 16, 0, 2, 2, 4, 0, 4, 0, 2, 0, 2, 0, 0, 6, 2, 0, }, +{f: 16, 2, 4, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 6, 2, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:108, 2:72, 4:27, 6:18, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 8, }, +{6: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{9: 0, 8, 0, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, }, +{2: 16, 8, 0, 0, 0, 0, 0, 0, -8, -8, 0, 8, -8, 0, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, -8, 0, -8, }, +{8: 16, 0, -8, 0, 0, 0, 0, 8, 8, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, -8, 8, }, +{6: 16, 8, -8, 0, 8, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{9: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 8, -8, -8, }, +{a: 16, 0, 0, 0, -8, -8, 8, 0, -8, 8, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, }, +{7: 16, -8, -8, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, -8, 0, -8, 0, 8, }, +{e: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, -8, 0, -8, 0, 8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, , , x, x, , x, x, , x, x, , , x, }, +{b: , x, x, , , x, x, x, , , x, x, x, x, x, x, }, +{d: , , x, x, , , x, , x, x, , , x, x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x09,}}, +{{0x09,0x02,}, {0x07,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x08,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x0d,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x0d,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +006 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0f,0x06,0x07,0x03,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0b, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 2, 2, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{8: 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, }, +{3: 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{5: 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 4, 0, }, +{6: 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 4, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:6, 2:7, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 2, 2, 0, 0, 6, 0, 2, 4, 0, 0, 2, }, +{2: 16, 2, 2, 0, 2, 0, 0, 4, 6, 0, 2, 0, 0, 0, 2, 4, }, +{4: 16, 0, 0, 4, 0, 6, 0, 2, 2, 0, 0, 4, 0, 2, 2, 2, }, +{8: 16, 2, 4, 2, 2, 0, 0, 0, 0, 2, 6, 0, 2, 0, 4, 0, }, +{3: 16, 0, 2, 4, 0, 4, 2, 2, 2, 0, 0, 6, 0, 0, 0, 2, }, +{5: 16, 2, 6, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 4, 0, }, +{6: 16, 0, 2, 0, 4, 0, 6, 2, 0, 0, 0, 2, 2, 6, 0, 0, }, +{9: 16, 2, 0, 0, 6, 2, 4, 0, 2, 0, 0, 0, 0, 6, 2, 0, }, +{a: 16, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 6, 2, 0, 0, }, +{c: 16, 0, 2, 0, 0, 0, 0, 6, 4, 0, 2, 0, 2, 2, 2, 4, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 6, 0, 2, 2, 2, 0, 0, 2, 4, 0, 2, 4, 0, 0, 0, }, +{d: 16, 2, 4, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 6, 0, }, +{e: 16, 0, 2, 0, 0, 0, 2, 4, 4, 2, 2, 0, 0, 0, 2, 6, }, +{f: 16, 0, 0, 2, 6, 0, 6, 0, 0, 2, 2, 0, 0, 4, 0, 2, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:108, 2:72, 4:27, 6:18, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{6: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{9: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, -8, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 0, }, +{8: 16, 8, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, 0, -8, }, +{6: 16, 0, 0, 0, 0, 0, 8, 0, 0, -8, -8, 8, -8, 0, 0, -8, }, +{9: 16, -8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, -8, -8, -8, 0, 0, 0, 8, 0, 8, 0, -8, 0, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, -8, 0, 8, -8, 8, }, +{f: 16, 0, 8, -8, -8, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{7: , x, , , , , , x, x, x, x, , x, x, x, x, }, +{b: , , x, , , x, x, , x, x, , , , , , x, }, +{d: , x, x, x, x, , , x, x, x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x0a,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x05,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_007.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_007.txt new file mode 100644 index 0000000..077f0f2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_007.txt @@ -0,0 +1,406 @@ +007 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x0b,0x06,0x07,0x00,0x09,0x0a,0x0e,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 2, 0, 0, 0, 4, 0, 2, 4, 2, 2, 0, 0, 0, 0, }, +{4: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +{8: 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 4, 2, 0, 2, }, +{6: 0, 0, 4, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, }, +{9: 0, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{a: 0, 2, 0, 2, 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{7: 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, }, +{d: 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:7, 2:8, 4:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 2, 0, 0, 2, 6, 2, 0, 4, 0, 0, 0, }, +{2: 16, 0, 10, 0, 4, 0, 4, 0, 2, 4, 2, 6, 0, 0, 0, 0, }, +{4: 16, 2, 4, 2, 0, 2, 6, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +{8: 16, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, }, +{3: 16, 0, 0, 2, 2, 4, 4, 6, 2, 0, 0, 0, 0, 2, 2, 0, }, +{5: 16, 0, 0, 2, 0, 4, 4, 10, 0, 0, 0, 0, 4, 6, 0, 2, }, +{6: 16, 0, 4, 0, 0, 6, 10, 4, 2, 0, 0, 4, 0, 0, 0, 2, }, +{9: 16, 0, 6, 0, 4, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 2, }, +{a: 16, 6, 0, 2, 0, 0, 0, 4, 0, 4, 0, 0, 10, 4, 2, 0, }, +{c: 16, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{7: 16, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{b: 16, 4, 4, 0, 6, 0, 0, 0, 0, 10, 2, 0, 4, 0, 2, 0, }, +{d: 16, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, }, +{e: 16, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 6, 4, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:110, 2:75, 4:25, 6:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 8, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, -8, 0, -8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 0, 0, 0, 0, -8, 8, -8, -8, 0, -8, -8, 0, 8, 0, 8, }, +{4: 16, -8, 0, -8, 8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, 8, -8, -8, 0, }, +{5: 16, -8, 0, -8, 0, 0, 0, -8, 8, 8, -8, 8, -8, 0, 0, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 0, -8, 8, }, +{9: 16, 0, 0, 0, -8, 0, 8, 8, 0, -8, 0, 0, 0, 0, -8, -8, }, +{a: 16, 8, -8, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, }, +{b: 16, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, }, +{e: 16, -8, 0, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, -8, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, , , x, }, +{9: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , , , x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, , x, x, , x, }, +{7: , , x, x, , x, x, , x, x, , x, x, , , x, }, +{b: , , x, , , , , x, x, , x, , , , x, x, }, +{d: , , , x, x, , x, , x, x, , , x, x, , x, }, +{e: , x, x, , , x, x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x0c,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +007 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x0e,0x06,0x07,0x01,0x09,0x0a,0x05,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, }, +{2: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 2, 4, 0, 0, 0, }, +{4: 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, }, +{3: 0, 2, 0, 2, 2, 4, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 2, 2, 2, 4, 0, 4, 0, 0, 0, 0, 2, 0, }, +{9: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{a: 0, 2, 4, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, }, +{7: 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 4, }, +{e: 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:7, 2:8, 4:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, 2, }, +{2: 16, 0, 10, 4, 0, 0, 0, 4, 6, 0, 2, 2, 4, 0, 0, 0, }, +{4: 16, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{8: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 2, 0, 6, 2, 0, 0, }, +{3: 16, 2, 0, 2, 2, 4, 4, 6, 0, 0, 2, 2, 0, 0, 0, 0, }, +{5: 16, 0, 4, 6, 0, 4, 4, 10, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 16, 0, 0, 0, 2, 6, 10, 4, 0, 4, 0, 0, 0, 0, 2, 4, }, +{9: 16, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{a: 16, 6, 4, 0, 0, 0, 0, 0, 4, 4, 0, 2, 10, 2, 0, 0, }, +{c: 16, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, }, +{7: 16, 0, 6, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{b: 16, 4, 0, 0, 2, 0, 4, 0, 0, 10, 0, 0, 4, 2, 0, 6, }, +{d: 16, 0, 0, 0, 0, 2, 6, 0, 2, 4, 2, 0, 0, 2, 2, 4, }, +{e: 16, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{f: 16, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:110, 2:75, 4:25, 6:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{f: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, 0, 8, -8, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 0, -8, 0, 0, 0, -8, 0, 8, -8, -8, 0, -8, 8, 8, 0, }, +{4: 16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{8: 16, -8, 8, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 8, 8, -8, 0, -8, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 8, 0, -8, 8, -8, 0, -8, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 8, -8, 0, 0, -8, 0, 0, -8, 0, -8, 8, 0, -8, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, 0, 8, -8, }, +{c: 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{7: 16, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, 0, -8, -8, }, +{b: 16, -8, 0, 0, -8, 0, 8, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, -8, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 8, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, , , x, x, x, }, +{a: , x, x, , x, x, x, x, x, x, x, , x, , , x, }, +{c: , x, , x, x, , x, x, x, x, x, , x, x, x, x, }, +{7: , , x, , , , x, x, , x, x, x, , , x, x, }, +{b: , , x, , x, x, x, , x, x, , , , , , x, }, +{d: , x, , x, x, , x, x, , x, x, , , x, x, x, }, +{e: , x, , , , , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x0c,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x03,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_008.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_008.txt new file mode 100644 index 0000000..bdc911f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_008.txt @@ -0,0 +1,406 @@ +008 Sbox: +LUT = { +0x08,0x00,0x01,0x09,0x02,0x05,0x0d,0x07,0x04,0x06,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{8: 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, }, +{9: 0, 2, 2, 2, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 0, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, }, +{b: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:4, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 2, 4, 4, 0, 4, 0, 4, 2, 0, 2, 0, 0, 0, 2, }, +{2: 16, 4, 4, 0, 4, 0, 0, 0, 8, 0, 2, 0, 4, 2, 2, 2, }, +{4: 16, 4, 0, 4, 2, 4, 8, 4, 0, 2, 2, 0, 0, 0, 2, 0, }, +{8: 16, 0, 2, 0, 2, 6, 4, 4, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 16, 4, 0, 0, 6, 2, 2, 0, 4, 0, 2, 0, 0, 2, 0, 2, }, +{5: 16, 4, 2, 6, 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{6: 16, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, }, +{9: 16, 2, 6, 2, 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 2, 0, }, +{a: 16, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 16, 0, 0, 2, 0, 4, 4, 8, 0, 0, 2, 2, 4, 4, 0, 2, }, +{7: 16, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 2, 4, 6, 0, 2, }, +{b: 16, 0, 4, 0, 0, 2, 0, 4, 4, 2, 0, 2, 8, 4, 2, 0, }, +{d: 16, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 16, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:100, 2:85, 4:30, 6:5, 8:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 8, 8, -8, 0, 0, -8, -8, -8, 0, -8, }, +{2: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, 8, -8, 0, }, +{4: 16, 8, 8, -8, 0, 0, 0, -8, -8, 8, -8, 0, 0, 0, -8, 0, }, +{8: 16, 8, -8, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, 0, 0, }, +{3: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, }, +{9: 16, 0, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 0, -8, -8, 8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 0, 8, }, +{7: 16, -8, 0, 0, -8, 8, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 8, 8, 0, 8, -8, }, +{d: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{f: 16, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, , x, x, x, x, , , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , , x, , x, x, x, x, x, , x, , , x, x, x, }, +{7: , x, , x, x, x, x, x, , , x, x, , x, , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , , x, , , x, x, x, , , x, , , , , x, }, +{e: , , x, , x, , x, x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x01,0x04,0x05,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x01,0x02,0x03,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x02,}, {0x09,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +008 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0d,0x08,0x05,0x09,0x07,0x00,0x03,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 4, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 0, 4, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 4, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, }, +{9: 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 2, }, +{a: 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 2, }, +{d: 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, }, +{e: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{f: 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:150, 2:90, 4:15, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:4, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 0, 4, 4, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{2: 16, 2, 4, 0, 2, 0, 2, 0, 6, 2, 0, 0, 4, 0, 0, 2, }, +{4: 16, 4, 0, 4, 0, 0, 6, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 16, 4, 4, 2, 2, 6, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, }, +{3: 16, 0, 0, 4, 6, 2, 0, 2, 2, 0, 4, 0, 2, 0, 0, 2, }, +{5: 16, 4, 0, 8, 4, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 2, }, +{6: 16, 0, 0, 4, 4, 0, 2, 2, 0, 0, 8, 4, 4, 2, 2, 0, }, +{9: 16, 4, 8, 0, 0, 4, 0, 2, 4, 0, 0, 2, 4, 0, 2, 2, }, +{a: 16, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 16, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, }, +{7: 16, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{d: 16, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 6, 4, 2, 2, 0, }, +{e: 16, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{f: 16, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:100, 2:85, 4:30, 6:5, 8:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{2: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, 8, -8, 0, 0, }, +{2: 16, 0, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, -8, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 8, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, -8, }, +{3: 16, 0, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, -8, 0, 0, 8, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, 0, 8, -8, 0, 0, -8, -8, 8, }, +{6: 16, 8, 8, -8, -8, 0, 0, 0, -8, -8, 0, 8, -8, 0, 0, 0, }, +{9: 16, 0, -8, 0, 0, -8, 0, 8, 8, -8, 0, -8, 0, 8, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, }, +{7: 16, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, }, +{b: 16, -8, -8, 0, -8, 8, 8, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 8, 0, -8, }, +{e: 16, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, , , x, , x, x, , x, }, +{a: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , x, , , x, x, x, x, , , x, x, , x, , x, }, +{b: , , , , x, , x, , , , x, , x, x, , x, }, +{d: , x, x, x, , x, x, x, , , x, , , , , x, }, +{e: , , , x, x, , , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x06,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,}}, +{{0x03,0x08,}, {0x03,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x0b,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x04,0x0b,0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x09,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_009.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_009.txt new file mode 100644 index 0000000..1ea1643 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_009.txt @@ -0,0 +1,418 @@ +009 Sbox: +LUT = { +0x08,0x0e,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x0c,0x0a,0x0b,0x09,0x0d,0x00,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{4: 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, }, +{3: 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 0, 2, 4, 0, 0, }, +{6: 0, 0, 2, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 2, 2, }, +{c: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 2, 0, 0, }, +{7: 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{d: 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 2, 2, }, +{e: 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:5, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 2, 0, 4, 0, 0, 4, 0, 4, 8, 0, 2, }, +{2: 16, 4, 4, 0, 8, 0, 2, 0, 4, 4, 2, 2, 0, 0, 2, 0, }, +{4: 16, 2, 0, 2, 0, 0, 2, 4, 0, 2, 0, 2, 4, 6, 0, 0, }, +{8: 16, 0, 6, 0, 4, 0, 0, 2, 2, 6, 2, 0, 2, 0, 0, 0, }, +{3: 16, 0, 0, 2, 0, 6, 8, 4, 0, 6, 0, 0, 0, 2, 0, 4, }, +{5: 16, 0, 0, 2, 0, 4, 4, 10, 2, 0, 0, 0, 6, 4, 0, 0, }, +{6: 16, 0, 2, 2, 0, 4, 4, 6, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 16, 0, 0, 2, 2, 0, 4, 0, 2, 4, 2, 2, 0, 0, 2, 4, }, +{a: 16, 0, 6, 0, 4, 2, 4, 0, 0, 8, 0, 0, 0, 0, 2, 6, }, +{c: 16, 8, 0, 0, 4, 2, 0, 0, 6, 0, 4, 2, 0, 6, 0, 0, }, +{7: 16, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, }, +{b: 16, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{d: 16, 6, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 4, 2, 2, }, +{e: 16, 6, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 2, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:69, 4:28, 6:14, 8:5, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, -16, 0, 0, }, +{2: 16, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, 0, 16, -8, 0, }, +{4: 16, -8, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, 8, -8, }, +{8: 16, 8, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, -16, 0, 8, }, +{5: 16, -8, 8, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, }, +{9: 16, 8, 0, 0, -8, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, 0, }, +{a: 16, 0, -8, 0, 0, -8, 8, -8, -8, 8, 0, 0, 0, 0, -8, 8, }, +{c: 16, -8, 8, 0, 0, 0, -8, 0, -8, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{b: 16, 0, 0, -8, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{d: 16, -8, 0, -8, 0, -8, 8, 0, 0, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, 0, -8, -8, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, x, , , x, x, }, +{9: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , , x, x, x, }, +{7: , , x, , , , , x, , x, x, x, , , x, x, }, +{b: , , , x, x, x, , x, x, x, , , x, , x, x, }, +{d: , , , x, x, x, , x, , x, x, , , x, x, x, }, +{e: , x, x, , x, x, , x, x, x, , , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x04,}, {0x0d,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x09,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x04,0x09,0x0d,}}, +{{0x09,0x06,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +009 Inverse Sbox: +LUT = { +0x0e,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x0c,0x0a,0x0b,0x09,0x0d,0x01,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, }, +{2: 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{4: 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, }, +{3: 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 4, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, }, +{9: 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 2, }, +{c: 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 2, }, +{7: 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, }, +{d: 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 4, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:5, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 2, 0, 0, 0, 0, 0, 0, 8, 2, 0, 6, 6, 0, }, +{2: 16, 0, 4, 0, 6, 0, 0, 2, 0, 6, 0, 2, 0, 2, 2, 0, }, +{4: 16, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 16, 2, 8, 0, 4, 0, 0, 0, 2, 4, 4, 2, 0, 0, 4, 2, }, +{3: 16, 2, 0, 0, 0, 6, 4, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 16, 0, 2, 2, 0, 8, 4, 4, 4, 4, 0, 0, 2, 2, 0, 0, }, +{6: 16, 4, 0, 4, 2, 4, 10, 6, 0, 0, 0, 0, 2, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 6, 0, 0, 0, 6, 0, }, +{a: 16, 0, 4, 2, 6, 6, 0, 0, 4, 8, 0, 0, 0, 0, 0, 2, }, +{c: 16, 4, 2, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 4, 0, 2, }, +{7: 16, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, }, +{b: 16, 4, 0, 4, 2, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 2, }, +{d: 16, 8, 0, 6, 0, 2, 4, 0, 0, 0, 6, 0, 2, 4, 0, 0, }, +{e: 16, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 2, 0, 0, 0, 4, 0, 0, 4, 6, 0, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:69, 4:28, 6:14, 8:5, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{4: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, -8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 0, 8, -8, }, +{2: 16, 8, -8, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, }, +{4: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, }, +{3: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, -8, 0, 8, 8, 0, -8, 0, -8, 0, 0, 8, -8, -8, 0, 0, }, +{9: 16, 8, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, 0, 0, 0, -8, -8, 8, -8, -8, 8, }, +{c: 16, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, }, +{7: 16, 0, 0, -8, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, }, +{d: 16, -8, 8, -8, 0, 0, 0, -16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, -8, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, , x, , x, x, x, x, x, , , x, x, }, +{9: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, , x, , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , , x, x, x, }, +{7: , x, x, x, , , , x, , x, x, x, , , x, x, }, +{b: , , x, x, , , , x, x, x, , , x, , x, x, }, +{d: , x, , , x, , , x, , x, x, , , x, x, x, }, +{e: , x, , , , x, , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0110,0101,1,}, +{0110,1000,0,}, +{0110,1101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x05,0x06,0x08,}, {0x06,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x08,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x06,0x09,0x0f,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x01,0x06,0x07,}}, +{{0x01,0x0a,}, {0x07,}}, +{{0x05,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_010.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_010.txt new file mode 100644 index 0000000..23fcb76 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_010.txt @@ -0,0 +1,418 @@ +010 Sbox: +LUT = { +0x08,0x0e,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0f,0x0b,0x0c,0x0d,0x00,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 0, }, +{4: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, }, +{8: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +{3: 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 0, 2, 4, 0, 0, }, +{6: 0, 0, 2, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 2, 0, 0, 2, }, +{c: 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, 0, }, +{7: 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, }, +{b: 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, 0, }, +{d: 0, 2, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{e: 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 2, 0, 4, 0, 6, 0, 0, 8, 6, 0, 0, }, +{2: 16, 0, 8, 0, 0, 0, 2, 0, 2, 0, 8, 2, 2, 0, 8, 0, }, +{4: 16, 2, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 4, 4, 0, 2, }, +{8: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +{3: 16, 0, 0, 2, 0, 6, 8, 4, 0, 6, 0, 0, 0, 2, 0, 4, }, +{5: 16, 0, 0, 2, 0, 4, 4, 10, 2, 0, 0, 0, 6, 4, 0, 0, }, +{6: 16, 0, 2, 2, 0, 4, 4, 6, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 16, 2, 0, 0, 0, 0, 4, 0, 2, 4, 2, 2, 0, 2, 2, 4, }, +{a: 16, 4, 0, 0, 0, 2, 4, 0, 0, 8, 0, 2, 6, 0, 0, 6, }, +{c: 16, 2, 4, 2, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, 4, 0, }, +{7: 16, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, }, +{b: 16, 6, 0, 0, 2, 2, 2, 2, 2, 4, 0, 0, 4, 0, 0, 0, }, +{d: 16, 2, 4, 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 4, 0, }, +{e: 16, 0, 6, 2, 2, 0, 0, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 6, 0, 2, 2, 0, 0, 0, 2, 6, 0, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:70, 4:27, 6:13, 8:6, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{9: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:8, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, -16, 8, 0, }, +{2: 16, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, -8, 16, 0, 0, }, +{4: 16, -8, 0, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, 0, 0, -8, }, +{8: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{3: 16, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, -16, 0, 8, }, +{5: 16, -8, 8, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 8, 0, }, +{a: 16, -8, -8, 0, 0, 0, 8, -8, -8, 8, -8, 0, 0, 0, 0, 8, }, +{c: 16, 0, 8, 0, 0, 8, -8, 0, -8, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{b: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 8, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, }, +{e: 16, 8, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, -8, }, +{f: 16, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, , , , , x, , x, x, x, , , x, x, }, +{b: , , , x, x, , x, , x, x, , x, , x, , x, }, +{d: , , , x, x, x, , x, , x, x, , , x, x, x, }, +{e: , x, x, , x, , x, , x, x, , x, x, x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x0d,}}, +{{0x06,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x04,}, {0x0d,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x09,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x04,0x09,0x0d,}}, +{{0x09,0x06,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +010 Inverse Sbox: +LUT = { +0x0e,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0f,0x0b,0x0c,0x0d,0x01,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, }, +{4: 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, }, +{3: 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 4, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 2, }, +{c: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 2, }, +{7: 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, }, +{b: 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 6, 2, 0, 0, }, +{2: 16, 0, 8, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 6, 6, }, +{4: 16, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, }, +{8: 16, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, }, +{3: 16, 2, 0, 0, 0, 6, 4, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 16, 0, 2, 2, 0, 8, 4, 4, 4, 4, 0, 0, 2, 2, 0, 0, }, +{6: 16, 4, 0, 4, 2, 4, 10, 6, 0, 0, 0, 0, 2, 0, 0, 0, }, +{9: 16, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{a: 16, 6, 0, 0, 0, 6, 0, 0, 4, 8, 0, 0, 4, 2, 0, 2, }, +{c: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, }, +{b: 16, 8, 2, 4, 0, 0, 6, 0, 0, 6, 0, 0, 4, 2, 0, 0, }, +{d: 16, 6, 0, 4, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{e: 16, 0, 8, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 0, 2, 2, 4, 0, 0, 4, 6, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:70, 4:27, 6:13, 8:6, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{4: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 8, 0, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:8, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 0, -8, -8, 0, -8, 8, 0, 8, -8, 8, 0, 0, 0, 0, -8, }, +{4: 16, 0, 0, -8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, }, +{3: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, -8, 0, 8, 8, 0, -8, 0, -8, 0, 0, 8, -8, -8, 0, 0, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, 8, 0, 0, }, +{a: 16, -8, 0, 8, -8, -8, 0, 0, 0, 0, 0, -8, 8, -8, 0, 8, }, +{c: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, -8, 8, -8, 0, }, +{7: 16, 8, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 0, 0, -16, 8, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, , x, , x, x, x, x, x, x, x, x, x, x, }, +{7: , x, x, x, , , , x, , x, x, x, , , x, x, }, +{b: , , x, x, , x, x, , x, x, , x, , x, , x, }, +{d: , x, , , x, , , x, , x, x, , , x, x, x, }, +{e: , x, , , , , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0110,0101,1,}, +{0110,1011,1,}, +{0110,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x08,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x08,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x0b,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x01,0x06,0x07,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_011.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_011.txt new file mode 100644 index 0000000..2c7af86 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_011.txt @@ -0,0 +1,418 @@ +011 Sbox: +LUT = { +0x08,0x0f,0x01,0x02,0x03,0x05,0x0c,0x07,0x04,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x00, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, }, +{2: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 2, }, +{4: 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{8: 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, }, +{6: 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, }, +{7: 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, }, +{b: 0, 4, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 4, 2, 2, 0, }, +{2: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 6, 6, }, +{4: 16, 0, 2, 4, 4, 8, 2, 0, 0, 2, 0, 4, 4, 2, 0, 0, }, +{8: 16, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{3: 16, 0, 0, 6, 0, 4, 0, 2, 2, 2, 0, 4, 0, 0, 2, 2, }, +{5: 16, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, }, +{6: 16, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, }, +{9: 16, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, }, +{a: 16, 8, 2, 6, 0, 0, 4, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 6, 6, }, +{7: 16, 6, 0, 8, 0, 6, 4, 0, 0, 0, 0, 4, 0, 2, 0, 2, }, +{b: 16, 4, 0, 0, 6, 4, 2, 2, 0, 4, 0, 0, 10, 0, 0, 0, }, +{d: 16, 4, 0, 4, 0, 0, 6, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{e: 16, 0, 8, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +{f: 16, 2, 0, 2, 4, 6, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:70, 4:27, 6:13, 8:6, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 8, 0, 4, 0, }, +{3: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:6, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, }, +{2: 16, 0, 0, 0, -8, -8, 8, 0, 8, -8, 8, 0, 0, 0, -8, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, -16, 8, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, 8, 0, 0, }, +{3: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, -8, 8, }, +{5: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +{6: 16, 8, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, -8, -8, 0, 0, 0, 0, 0, -8, 8, -8, -8, 8, 0, 0, }, +{7: 16, -8, 0, -8, 8, 8, 0, 0, 0, 0, 0, -8, 8, -8, 0, -8, }, +{b: 16, -8, 0, 8, 8, 0, -8, 0, -8, 0, 0, 8, -8, -8, 0, 0, }, +{d: 16, -8, 8, 0, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 8, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{7: , x, , , x, x, x, , x, x, , , x, x, x, x, }, +{b: , , , , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, x, x, , , x, , x, x, , x, x, , x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0110,0100,1,}, +{0110,1010,1,}, +{0110,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x04,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x06,0x09,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x04,}}, +{{0x09,0x02,}, {0x04,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +011 Inverse Sbox: +LUT = { +0x0f,0x02,0x03,0x04,0x08,0x05,0x0c,0x07,0x00,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x01, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 2, }, +{2: 0, 0, 4, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, }, +{8: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 4, }, +{3: 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, }, +{5: 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, }, +{6: 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, }, +{b: 0, 4, 0, 4, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, }, +{e: 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, }, +{f: 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 0, 0, 0, 2, 8, 0, 6, 4, 4, 0, 2, }, +{2: 16, 0, 8, 2, 2, 0, 0, 2, 0, 2, 8, 0, 0, 0, 8, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 2, 0, 6, 0, 8, 0, 4, 0, 2, }, +{8: 16, 0, 2, 4, 2, 0, 0, 2, 2, 0, 0, 0, 6, 0, 2, 4, }, +{3: 16, 2, 0, 8, 0, 4, 0, 0, 2, 0, 0, 6, 4, 0, 0, 6, }, +{5: 16, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 4, 2, 6, 0, 2, }, +{6: 16, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{9: 16, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, }, +{a: 16, 4, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +{7: 16, 2, 0, 4, 2, 4, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 0, 2, 6, 0, 0, 10, 0, 0, 4, }, +{d: 16, 2, 4, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 0, }, +{e: 16, 2, 6, 0, 0, 2, 2, 0, 2, 0, 6, 0, 0, 0, 4, 0, }, +{f: 16, 0, 6, 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:70, 4:27, 6:13, 8:6, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 0, 4, 0, 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 8, 0, 0, }, +{9: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{b: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:6, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, -8, 0, 0, 0, }, +{4: 16, 0, -8, -8, 8, 8, 0, 0, 0, 0, -8, -8, 8, -8, 0, 0, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, -8, 0, }, +{3: 16, -16, -8, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, -8, 0, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, }, +{6: 16, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, }, +{7: 16, 0, 0, -8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, 8, -8, }, +{b: 16, 0, 8, 8, 0, 0, -8, 0, 0, 8, -8, -8, 0, -8, 0, -8, }, +{d: 16, 0, 0, 0, 8, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, }, +{e: 16, 0, 0, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , x, x, x, x, , x, x, , , x, x, x, x, }, +{b: , , x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , x, , , x, x, , x, x, , x, x, , x, x, }, +{e: , , x, , x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,}}, +{{0x09,0x02,}, {0x01,}}, +{{0x0d,0x02,}, {0x01,0x06,0x07,}}, +{{0x01,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_012.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_012.txt new file mode 100644 index 0000000..0bd461b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_012.txt @@ -0,0 +1,418 @@ +012 Sbox: +LUT = { +0x08,0x0f,0x01,0x02,0x03,0x05,0x06,0x0d,0x04,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x00, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, }, +{2: 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{4: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, }, +{8: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, }, +{3: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 4, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, }, +{7: 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, 0, }, +{b: 0, 4, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{e: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:6, 4:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 4, 2, 2, 0, }, +{2: 16, 0, 4, 0, 2, 0, 6, 0, 2, 0, 0, 6, 0, 2, 2, 0, }, +{4: 16, 0, 0, 2, 6, 4, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, }, +{8: 16, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, }, +{3: 16, 0, 4, 0, 0, 4, 0, 0, 2, 2, 10, 0, 0, 0, 4, 6, }, +{5: 16, 0, 8, 2, 0, 2, 4, 0, 0, 2, 4, 4, 0, 2, 4, 0, }, +{6: 16, 0, 4, 0, 0, 0, 0, 2, 2, 2, 6, 2, 0, 0, 6, 0, }, +{9: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 16, 8, 2, 6, 0, 0, 4, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 2, 2, 2, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 6, }, +{7: 16, 6, 4, 4, 0, 0, 10, 0, 2, 0, 0, 4, 0, 2, 0, 0, }, +{b: 16, 4, 0, 0, 6, 4, 2, 2, 0, 4, 0, 0, 10, 0, 0, 0, }, +{d: 16, 4, 0, 4, 0, 2, 4, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{e: 16, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 2, 0, 0, 4, 8, 0, 2, 2, 0, 4, 0, 4, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:69, 4:30, 6:12, 8:3, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 8, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:6, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, }, +{2: 16, 0, 0, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 8, -8, -8, }, +{4: 16, 0, -8, 0, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, 0, -8, 0, -8, 0, -8, 0, -8, 0, 8, 0, 8, 0, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, }, +{9: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, -8, 0, 8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, }, +{7: 16, -8, 8, -8, 8, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, -8, 0, 8, 8, 0, -8, 0, -8, 0, 0, 8, -8, -8, 0, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, -8, 8, 0, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 16, 0, 0, 0, 0, -8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, , x, x, x, x, x, , x, , x, x, , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, , x, x, , , x, x, , x, x, x, x, }, +{7: , x, , , x, , x, , , x, , x, x, , x, x, }, +{b: , , , , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, x, x, , x, x, , , x, , , x, x, x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0110,0101,1,}, +{0110,1010,1,}, +{0110,1111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x04,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +012 Inverse Sbox: +LUT = { +0x0f,0x02,0x03,0x04,0x08,0x05,0x06,0x0d,0x00,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x01, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 2, }, +{2: 0, 0, 4, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 4, 0, 0, 2, 0, }, +{8: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 4, 2, 0, 0, }, +{5: 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{6: 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +{9: 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +{a: 0, 0, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 4, 0, 0, 2, 0, 0, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, }, +{b: 0, 4, 0, 4, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{e: 0, 2, 2, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 4, DDT_spectrum: {0:153, 2:84, 4:18, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:6, 4:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 0, 0, 0, 2, 8, 0, 6, 4, 4, 0, 2, }, +{2: 16, 0, 4, 0, 2, 4, 8, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{4: 16, 0, 0, 2, 0, 0, 2, 0, 2, 6, 2, 4, 0, 4, 2, 0, }, +{8: 16, 0, 2, 6, 2, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 4, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 2, 0, 4, 0, 4, 2, 0, 8, }, +{5: 16, 0, 6, 0, 0, 0, 4, 0, 0, 4, 0, 10, 2, 4, 2, 0, }, +{6: 16, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +{9: 16, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +{a: 16, 4, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 0, 0, 2, 10, 4, 6, 0, 0, 4, 0, 0, 2, 0, 4, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 0, 2, 4, 0, 2, 0, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 0, 2, 6, 0, 0, 10, 0, 0, 4, }, +{d: 16, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{e: 16, 2, 2, 2, 0, 4, 4, 6, 0, 0, 0, 0, 0, 0, 2, 2, }, +{f: 16, 0, 0, 2, 2, 6, 0, 0, 0, 0, 6, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:69, 4:30, 6:12, 8:3, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 8, 0, 0, 4, 4, }, +{7: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{b: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:6, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, -8, 8, 8, 0, 0, }, +{8: 16, 0, 0, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, 0, -8, 0, }, +{3: 16, -16, 0, 8, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 0, -8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, 8, 0, 0, }, +{6: 16, 0, 0, 0, -8, 0, -8, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, 0, 0, 0, -8, -8, -8, 0, 8, -8, 0, 0, 8, }, +{7: 16, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, 8, 8, 0, 0, -8, 0, 0, 8, -8, -8, 0, -8, 0, -8, }, +{d: 16, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, 8, 0, -8, 0, 0, 0, 8, 0, 0, -8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, , x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , x, x, , x, , , x, , x, x, , x, x, }, +{b: , , x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , x, , , , x, , , x, , , x, x, x, x, }, +{e: , , x, , x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x09,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_013.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_013.txt new file mode 100644 index 0000000..43be59d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_013.txt @@ -0,0 +1,438 @@ +013 Sbox: +LUT = { +0x0c,0x00,0x01,0x09,0x03,0x05,0x04,0x07,0x06,0x02,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 4, }, +{d: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{e: 0, 0, 4, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{f: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:2, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 2, 2, 6, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{2: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{4: 16, 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 4, 0, 6, 2, 2, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{5: 16, 4, 0, 4, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{9: 16, 4, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 4, 4, }, +{a: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{c: 16, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 16, 4, 0, 4, 0, 2, 4, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{b: 16, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 4, 4, }, +{d: 16, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 6, 6, }, +{e: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{f: 16, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 6, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:64, 4:32, 6:8, 8:12, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:5, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -8, 0, -8, 0, 0, 0, -8, -8, 0, 0, }, +{2: 16, 0, 0, 0, 0, -8, 0, 0, 8, -16, 0, -8, 0, 8, 0, 0, }, +{4: 16, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -16, 0, }, +{8: 16, 8, -8, 16, -8, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, -8, }, +{3: 16, -8, 8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 8, 0, 0, 0, 0, 8, 0, 0, -16, 0, 0, -8, 0, 0, -8, }, +{9: 16, 0, -8, 0, -8, -8, -8, 0, 0, 0, 0, 8, 8, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{b: 16, -8, -8, 0, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, }, +{d: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +{e: 16, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, 8, -16, 0, }, +{f: 16, 0, 0, 0, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, x, , x, x, x, , , x, }, +{5: , x, x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, , x, x, , x, x, , x, x, , , x, x, }, +{9: , x, x, , x, x, , x, x, , x, , x, x, , x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, , x, x, , x, x, , x, , , x, x, x, }, +{7: , x, , , , , , x, x, , x, x, , , , x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , x, x, , x, x, , x, x, , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1110,0100,1,}, +{1110,1010,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x02,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +013 Inverse Sbox: +LUT = { +0x01,0x02,0x09,0x04,0x06,0x05,0x08,0x07,0x0c,0x03,0x0a,0x0b,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, }, +{2: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{5: 0, 2, 0, 4, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, }, +{a: 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{c: 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, }, +{7: 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{e: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:2, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 0, 8, 0, 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{4: 16, 6, 0, 8, 0, 6, 4, 0, 0, 0, 2, 4, 0, 0, 2, 0, }, +{8: 16, 2, 4, 0, 8, 2, 0, 4, 0, 4, 0, 0, 0, 2, 4, 2, }, +{3: 16, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{5: 16, 6, 0, 8, 0, 6, 4, 0, 0, 0, 2, 4, 0, 0, 2, 0, }, +{6: 16, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{a: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{c: 16, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, }, +{7: 16, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{b: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{d: 16, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{e: 16, 0, 0, 8, 0, 0, 0, 0, 4, 0, 2, 0, 4, 6, 2, 6, }, +{f: 16, 0, 0, 8, 0, 0, 0, 0, 4, 0, 2, 0, 4, 6, 2, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:64, 4:32, 6:8, 8:12, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 4, 4, }, +{2: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 8, 4, 4, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 8, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:5, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 16, -8, 0, 0, -8, 0, 8, 0, -8, 0, 8, -8, 0, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, 0, -8, 0, 0, -8, 8, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, 8, -8, -16, 0, 0, }, +{3: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 8, -8, 8, 0, -8, -8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, }, +{9: 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 16, -8, -8, }, +{a: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -16, 0, 0, 0, 0, 0, }, +{c: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, 8, -8, -8, 0, -8, 0, 8, 0, 0, -8, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, -8, 8, 8, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , x, , x, x, x, , , x, }, +{5: , , x, , , x, x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , , x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , , x, x, x, , , , x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , x, , , x, , , x, , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , x, , , x, , x, x, , , , , x, , x, }, +{e: , , x, x, x, , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1100,0001,0,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1101,0001,1,}, +{1101,1000,1,}, +{1101,1001,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0d,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x01,0x06,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x01,}}, +{{0x0a,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,}, {0x01,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x0d,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_014.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_014.txt new file mode 100644 index 0000000..403e45e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_014.txt @@ -0,0 +1,438 @@ +014 Sbox: +LUT = { +0x0c,0x0b,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x00,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, }, +{5: 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{6: 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, }, +{d: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 4, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{f: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:11, 2:1, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 0, 4, 6, 6, 0, 2, 0, 2, 0, 0, 0, 2, }, +{2: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{4: 16, 0, 0, 4, 0, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 2, 0, 6, 0, 4, 0, 2, 0, 2, 0, 6, 0, 0, 2, 0, }, +{5: 16, 2, 0, 0, 2, 4, 6, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{6: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{9: 16, 2, 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 2, 4, 6, 0, }, +{a: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{c: 16, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 16, 2, 0, 6, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 2, 0, 2, 2, 4, 0, 0, 2, 0, 4, 0, 2, 0, 0, 6, }, +{d: 16, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 6, 6, 0, }, +{e: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{f: 16, 2, 0, 0, 0, 4, 2, 0, 0, 2, 6, 0, 0, 2, 0, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:60, 4:36, 6:12, 8:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, }, +{7: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, }, +{2: 16, 0, 0, 0, 0, -8, 0, 0, 8, -16, 0, -8, 0, 8, 0, 0, }, +{4: 16, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -16, 0, }, +{8: 16, 8, -8, 16, -8, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, -8, }, +{3: 16, 0, -8, 0, 8, 0, -8, 0, -8, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{6: 16, 8, 0, 0, 0, 0, 8, 0, 0, -16, 0, 0, -8, 0, 0, -8, }, +{9: 16, -8, 8, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, 8, 0, -8, 8, -8, 0, 0, 0, 0, -8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, -8, -8, -8, 0, 8, 0, 8, -8, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, 8, -16, 0, }, +{f: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, x, x, x, x, x, , , x, }, +{5: , x, x, , x, x, x, x, x, x, x, x, x, x, , x, }, +{6: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{9: , x, x, , x, x, , x, x, x, x, , x, x, , x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , , , x, , x, x, x, x, x, x, , , x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , x, x, , x, , , x, x, x, , , x, x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1110,0100,1,}, +{1110,1010,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x02,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +014 Inverse Sbox: +LUT = { +0x0b,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x0c,0x09,0x0a,0x01,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{2: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, }, +{5: 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, }, +{6: 0, 2, 2, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, 0, 0, }, +{9: 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, }, +{a: 0, 2, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 2, }, +{7: 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, 2, }, +{e: 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{f: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:11, 2:1, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{2: 16, 0, 8, 0, 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 0, 0, 2, 6, 2, 2, 2, 0, }, +{8: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{3: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 6, 0, 4, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 2, 2, }, +{6: 16, 6, 2, 4, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{a: 16, 2, 4, 0, 8, 2, 0, 4, 0, 4, 0, 0, 0, 2, 4, 2, }, +{c: 16, 0, 2, 4, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 6, }, +{7: 16, 2, 2, 4, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{d: 16, 0, 2, 4, 0, 0, 0, 2, 4, 2, 2, 0, 0, 6, 0, 2, }, +{e: 16, 0, 0, 4, 0, 2, 2, 0, 6, 0, 2, 0, 0, 6, 2, 0, }, +{f: 16, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 6, 0, 2, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:60, 4:36, 6:12, 8:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +{2: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 4, 4, }, +{6: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 8, 0, 0, 0, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -8, 0, 0, -8, 0, 8, 0, -8, 0, 8, -8, 0, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, -8, -16, 8, -8, 0, 0, 0, }, +{3: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 8, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 8, -8, 0, -8, -8, 0, 0, 0, -8, 0, 0, 8, }, +{9: 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 16, -8, -8, }, +{a: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, 0, 0, 0, -16, 0, 0, }, +{c: 16, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, 0, 8, 0, 0, 0, -8, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{e: 16, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , x, x, x, x, x, , , x, }, +{5: , , x, , x, x, x, x, x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , , x, x, x, x, , x, x, x, x, , x, x, , x, }, +{a: , , x, x, x, , , , x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , x, , , x, , , x, x, , x, x, , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , x, , , x, , x, x, x, , , x, x, , x, }, +{e: , , x, x, x, , , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1100,0011,0,}, +{1100,1000,1,}, +{1100,1011,1,}, +{1101,0011,1,}, +{1101,1001,0,}, +{1101,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x09,0x0a,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x0a,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x01,}}, +{{0x0a,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,}, {0x01,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x0d,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_015.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_015.txt new file mode 100644 index 0000000..5f6d260 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_015.txt @@ -0,0 +1,438 @@ +015 Sbox: +LUT = { +0x0c,0x09,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x00,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{5: 0, 0, 0, 0, 2, 0, 4, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 0, 0, 4, 0, 0, 0, 0, 2, 0, 4, 2, 2, 0, 2, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{b: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{d: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 2, }, +{f: 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:12, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{4: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{5: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{6: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 0, 2, 4, 0, 2, 2, }, +{9: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{c: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{7: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{b: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{d: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 0, 2, 4, 0, 2, 2, }, +{f: 16, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:72, 4:32, 8:16, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{c: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{d: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{e: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{f: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:9, 4:3, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, -8, -8, 0, -8, 0, 0, 8, -8, -8, 0, 8, }, +{2: 16, 0, -8, 0, 0, 0, 0, -8, 8, -8, 0, 0, -8, 8, 8, -8, }, +{4: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, -8, }, +{5: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, 0, 8, 8, 0, -8, 0, 0, -8, 0, -8, -8, }, +{9: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 8, -8, 0, 0, -8, 8, -8, 0, -8, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{7: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, }, +{b: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{d: 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, 16, 0, 0, -8, 0, 0, }, +{e: 16, 0, -8, 0, 0, -8, 0, 8, 8, -8, 0, -8, 0, 8, -8, 0, }, +{f: 16, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, -8, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, x, , x, x, x, , , x, }, +{5: , x, x, , , x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, , x, x, , x, x, , x, x, , , x, x, }, +{9: , x, x, , , x, , x, x, , x, , x, x, , x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , x, x, , , , , x, x, , x, x, , , , x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1000,0001,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1100,0101,1,}, +{1100,1000,1,}, +{1100,1101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x04,0x07,}}, +{{0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0a,0x0c,}, {0x01,0x04,0x05,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x01,0x04,0x05,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x0c,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x08,}}, +{{0x05,0x06,}, {0x0c,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +015 Inverse Sbox: +LUT = { +0x09,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x0c,0x01,0x0a,0x0b,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, }, +{5: 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, }, +{6: 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, }, +{a: 0, 0, 0, 0, 4, 2, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, }, +{c: 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, }, +{b: 0, 0, 4, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{e: 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:12, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 0, 0, 4, 2, 2, 4, 0, 2, }, +{2: 16, 0, 8, 0, 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{4: 16, 8, 0, 4, 0, 2, 4, 0, 0, 0, 4, 2, 2, 4, 0, 2, }, +{8: 16, 0, 4, 0, 8, 2, 2, 4, 2, 4, 0, 0, 0, 0, 4, 2, }, +{3: 16, 8, 0, 4, 0, 2, 4, 0, 0, 0, 4, 2, 2, 4, 0, 2, }, +{5: 16, 16, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{6: 16, 8, 2, 4, 0, 0, 4, 2, 0, 2, 4, 0, 0, 4, 2, 0, }, +{9: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{a: 16, 0, 4, 0, 8, 2, 2, 4, 2, 4, 0, 0, 0, 0, 4, 2, }, +{c: 16, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, }, +{7: 16, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, }, +{b: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{d: 16, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{e: 16, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:72, 4:32, 8:16, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{6: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, }, +{7: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:9, 4:3, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 16, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 16, 0, 0, -8, 0, 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, -8, -8, 8, -8, -8, -8, 8, }, +{3: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -8, }, +{5: 16, 0, 16, -8, 8, 0, -8, -8, -8, 8, 0, -8, -8, 0, 0, 0, }, +{6: 16, 0, 0, 0, 8, -16, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, 8, 0, 8, -8, -8, }, +{a: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, 0, -8, -8, 8, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, }, +{7: 16, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{b: 16, 0, 0, 8, 0, 0, 8, 0, 0, -8, -8, 0, -8, 8, -8, -8, }, +{d: 16, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , x, , x, x, x, , , x, }, +{5: , , , , x, , x, x, x, , , x, , x, , x, }, +{6: , , , x, x, x, , x, x, , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, , , x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , , , , , , , x, , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, x, x, , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_016.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_016.txt new file mode 100644 index 0000000..d1a6b6f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_016.txt @@ -0,0 +1,438 @@ +016 Sbox: +LUT = { +0x08,0x0e,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x00,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, }, +{4: 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, }, +{3: 0, 2, 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 4, 0, 0, }, +{9: 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 0, 4, 0, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{c: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{7: 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{d: 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{e: 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 2, 0, 4, 4, 8, 0, 2, 0, 0, 4, 4, 0, 2, }, +{2: 16, 4, 4, 4, 16, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{4: 16, 2, 0, 2, 0, 4, 4, 8, 0, 2, 0, 0, 4, 4, 0, 2, }, +{8: 16, 0, 6, 0, 8, 0, 0, 0, 0, 4, 0, 6, 2, 0, 2, 4, }, +{3: 16, 2, 0, 2, 0, 4, 4, 8, 0, 2, 0, 0, 4, 4, 0, 2, }, +{5: 16, 0, 0, 0, 0, 8, 8, 16, 0, 0, 0, 0, 8, 8, 0, 0, }, +{6: 16, 0, 2, 0, 0, 4, 4, 8, 2, 0, 2, 2, 4, 4, 0, 0, }, +{9: 16, 4, 0, 4, 8, 0, 0, 0, 6, 0, 6, 0, 2, 0, 2, 0, }, +{a: 16, 0, 6, 0, 8, 0, 0, 0, 0, 4, 0, 6, 2, 0, 2, 4, }, +{c: 16, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{7: 16, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, }, +{b: 16, 4, 0, 4, 8, 0, 0, 0, 6, 0, 6, 0, 2, 0, 2, 0, }, +{d: 16, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{e: 16, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:64, 4:32, 6:8, 8:12, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{4: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 4, 8, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 0, 4, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -16, 0, 8, }, +{2: 16, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, -16, 0, 16, 0, 0, }, +{4: 16, -8, 0, 0, 0, 0, 0, -8, 0, 16, -8, 0, -8, 0, 0, 0, }, +{8: 16, 0, -8, 0, -8, 8, 8, 8, 0, 0, 0, 0, -8, 0, -8, -8, }, +{3: 16, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -16, 0, 8, }, +{5: 16, -8, 0, -8, 0, -8, 0, -8, 8, 0, -8, 16, -8, 0, 8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 0, 8, -16, 0, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, 0, -8, 8, -8, 0, 0, 0, -8, 0, 0, -8, }, +{a: 16, 8, -8, 8, -8, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, -8, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, }, +{7: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, 8, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, -8, }, +{d: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{e: 16, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , , , x, x, x, x, x, , , x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{9: , x, x, x, x, x, , , x, x, x, , , x, x, x, }, +{a: , x, , x, , , , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , , , , , , , , x, x, x, , , x, x, }, +{b: , , , , , , , , x, , x, , , , x, x, }, +{d: , , x, x, x, x, , , , x, x, , , x, x, x, }, +{e: , x, , x, , , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +016 Inverse Sbox: +LUT = { +0x0b,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0e,0x0c,0x0d,0x01,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, }, +{2: 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{4: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, }, +{a: 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{7: 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 4, 2, 0, 2, 0, 0, 4, 0, 0, 2, 4, 0, 2, 2, }, +{2: 16, 0, 4, 0, 6, 0, 0, 2, 0, 6, 0, 2, 0, 2, 2, 0, }, +{4: 16, 2, 4, 2, 0, 2, 0, 0, 4, 0, 2, 2, 4, 2, 0, 0, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{5: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 0, 0, 0, 2, 6, 0, 0, 2, 6, 2, 2, 0, }, +{a: 16, 2, 4, 2, 4, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 0, 2, 6, 0, 2, 2, 6, 0, 0, 2, }, +{7: 16, 0, 4, 0, 6, 0, 0, 2, 0, 6, 2, 2, 0, 0, 0, 2, }, +{b: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 16, 2, 4, 2, 4, 2, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:64, 4:32, 6:8, 8:12, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{2: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{5: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, 0, }, +{2: 16, 8, -8, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, }, +{4: 16, -8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, 16, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, -8, 0, 0, 16, -8, -8, 0, -8, 0, 0, 8, -8, -8, 0, 8, }, +{9: 16, 0, -8, 0, 0, -8, 0, 0, 8, -8, 0, 0, 0, 8, 0, -8, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, }, +{c: 16, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, -8, -8, 8, 0, 0, }, +{7: 16, 8, -8, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, 0, }, +{b: 16, 0, 8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{d: 16, 0, 0, -16, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 8, }, +{e: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, 0, 8, 0, 8, -8, 0, 0, 0, 0, -8, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{5: , , x, , x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, , x, , x, x, x, x, x, x, , , x, }, +{9: , x, x, , , x, , x, x, x, x, , x, x, x, x, }, +{a: , x, x, , , , , x, x, x, x, , x, , x, x, }, +{c: , x, x, , , x, , x, x, x, x, , x, x, , x, }, +{7: , , x, , , x, , , x, x, , x, x, , , x, }, +{b: , x, x, , , , , x, , x, x, , x, , x, x, }, +{d: , , x, , , x, , x, x, x, , , x, x, , x, }, +{e: , x, , , , , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0100,0101,1,}, +{0100,1000,0,}, +{0100,1101,1,}, +{1000,0110,0,}, +{1000,1000,1,}, +{1000,1110,1,}, +{1100,0011,0,}, +{1100,1000,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x08,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0b,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x08,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_017.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_017.txt new file mode 100644 index 0000000..ad0c433 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_017.txt @@ -0,0 +1,406 @@ +017 Sbox: +LUT = { +0x08,0x0a,0x01,0x02,0x03,0x0b,0x06,0x07,0x04,0x09,0x00,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 2, 0, 2, 2, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{6: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, }, +{9: 0, 2, 2, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 4, 0, }, +{a: 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:149, 2:93, 4:12, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:8, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 0, 6, 6, 2, 0, 4, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 4, 8, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, }, +{4: 16, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, }, +{8: 16, 6, 0, 0, 4, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, }, +{3: 16, 6, 4, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 16, 0, 0, 2, 0, 2, 2, 2, 4, 0, 0, 4, 2, 0, 4, 2, }, +{6: 16, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, }, +{9: 16, 6, 2, 2, 4, 0, 0, 0, 8, 0, 0, 6, 0, 0, 4, 0, }, +{a: 16, 4, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 6, 2, 0, 2, }, +{c: 16, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 4, 0, 2, 8, 2, }, +{7: 16, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, }, +{b: 16, 4, 0, 0, 2, 0, 2, 2, 0, 6, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:102, 2:83, 4:26, 6:11, 8:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:7, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, 0, 0, -8, 0, 8, 0, -8, -8, 0, -8, }, +{2: 16, 8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, -8, -8, 0, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, -8, 8, }, +{6: 16, 8, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, -8, 8, 8, -8, -8, }, +{a: 16, 0, 0, 0, -8, 0, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, -8, 0, 0, 0, -8, }, +{7: 16, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , , x, x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, , , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , , , x, x, x, , x, , , x, x, , , x, }, +{b: , x, , , x, , x, , x, x, , , , , , x, }, +{d: , , x, x, , , x, , x, , , , x, x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x06,0x09,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +017 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x08,0x0b,0x06,0x07,0x00,0x09,0x01,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{8: 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{5: 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, }, +{9: 0, 0, 2, 0, 0, 2, 4, 2, 4, 0, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:149, 2:93, 4:12, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:8, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 2, 6, 6, 0, 0, 6, 4, 0, 2, 4, 0, 0, 0, }, +{2: 16, 6, 8, 0, 0, 4, 0, 2, 2, 0, 4, 0, 0, 0, 6, 0, }, +{4: 16, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{8: 16, 6, 2, 2, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 6, 4, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{5: 16, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, }, +{6: 16, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, }, +{9: 16, 4, 2, 0, 4, 2, 4, 2, 8, 0, 4, 2, 0, 0, 0, 0, }, +{a: 16, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 6, 2, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{7: 16, 0, 0, 2, 2, 0, 4, 0, 6, 0, 4, 2, 0, 2, 0, 2, }, +{b: 16, 4, 0, 2, 0, 2, 2, 0, 0, 6, 0, 2, 4, 0, 0, 2, }, +{d: 16, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, }, +{e: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:102, 2:83, 4:26, 6:11, 8:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{6: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:7, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -8, 8, -8, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, }, +{8: 16, 8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, }, +{6: 16, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, }, +{9: 16, -8, 0, 0, 8, -8, 0, 0, 0, -8, -8, 0, 0, 8, -8, 8, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, -8, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, -8, }, +{7: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, -8, 0, 0, 8, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, , , x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , x, , x, x, x, x, , x, , , x, x, , , x, }, +{b: , , x, , , x, x, , x, x, , , , , , x, }, +{d: , x, x, , , x, x, , x, , , , x, x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x0e,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x05,0x09,0x0c,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_018.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_018.txt new file mode 100644 index 0000000..aeee6aa --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_018.txt @@ -0,0 +1,418 @@ +018 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x0c,0x03,0x07,0x06,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{8: 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, 2, 0, 4, 0, 0, 0, }, +{6: 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{9: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, }, +{c: 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 4, 0, 2, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{d: 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:7, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{2: 16, 2, 8, 4, 2, 0, 2, 4, 4, 0, 2, 0, 4, 0, 0, 0, }, +{4: 16, 4, 6, 6, 0, 6, 4, 6, 0, 0, 2, 4, 0, 0, 0, 2, }, +{8: 16, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{5: 16, 4, 2, 4, 2, 0, 8, 2, 0, 0, 2, 0, 4, 0, 4, 0, }, +{6: 16, 0, 4, 10, 2, 6, 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{9: 16, 0, 6, 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 2, 0, 2, }, +{a: 16, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, }, +{c: 16, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, }, +{7: 16, 0, 0, 8, 0, 8, 0, 0, 2, 2, 0, 8, 0, 2, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, }, +{e: 16, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 2, 4, 0, 6, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:80, 4:29, 6:7, 8:7, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{5: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, -8, 8, 0, 8, 0, -8, 0, -8, -8, -8, }, +{2: 16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -16, 8, 0, -8, }, +{4: 16, 8, 0, -8, 8, 8, -8, -8, 8, 0, 0, -8, 0, -8, -8, 0, }, +{8: 16, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, -16, 8, 0, 0, }, +{6: 16, 0, -8, -8, 8, 8, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 16, 0, 0, 0, }, +{b: 16, 8, -8, 0, -8, -8, 8, 0, 0, 0, 8, 0, 0, 0, -8, -8, }, +{d: 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, x, x, , , x, }, +{5: , x, x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , x, x, x, , x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, , x, x, x, x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , , x, , , x, x, x, }, +{7: , x, x, x, , , x, x, , , x, x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , x, x, , , x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x06,}, {0x0b,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +018 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x0c,0x08,0x07,0x03,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 4, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{8: 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 2, 2, 4, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{c: 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{d: 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 2, 2, }, +{f: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:7, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 0, 2, }, +{2: 16, 0, 8, 6, 2, 0, 2, 4, 6, 0, 0, 0, 4, 0, 0, 0, }, +{4: 16, 8, 4, 6, 0, 4, 4, 10, 0, 0, 2, 8, 0, 0, 2, 0, }, +{8: 16, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 16, 4, 0, 6, 2, 4, 0, 6, 0, 2, 0, 8, 0, 0, 0, 0, }, +{5: 16, 4, 2, 4, 0, 2, 8, 0, 0, 0, 2, 0, 4, 2, 4, 0, }, +{6: 16, 0, 4, 6, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, }, +{9: 16, 2, 4, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 2, 0, 2, }, +{a: 16, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{c: 16, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{7: 16, 4, 0, 4, 2, 4, 0, 4, 0, 2, 2, 8, 0, 0, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, }, +{e: 16, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 4, 2, 6, 2, }, +{f: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:80, 4:29, 6:7, 8:7, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 0, 8, 8, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 8, 4, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 0, -8, 0, 8, -8, -8, -8, 0, 0, }, +{2: 16, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, -8, 8, -8, -8, }, +{4: 16, 8, 8, -8, 8, 0, -16, 0, 0, 8, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{3: 16, 0, -8, 0, 8, 8, 0, 0, -8, -8, -8, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, 0, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{a: 16, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, }, +{7: 16, 8, -8, -8, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{d: 16, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, -8, }, +{f: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, x, , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , , x, , , x, x, x, }, +{7: , , x, , , x, x, , , , x, x, , , , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, x, x, x, x, x, x, , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0101,0100,1,}, +{0101,1011,0,}, +{0101,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x05,}}, +{{0x09,0x02,0x04,}, {0x05,}}, +{{0x01,0x0a,0x04,}, {0x05,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0a,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x05,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x02,0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_019.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_019.txt new file mode 100644 index 0000000..ded3a24 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_019.txt @@ -0,0 +1,418 @@ +019 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x03,0x0b,0x06,0x09,0x0a,0x07,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, }, +{4: 0, 0, 2, 4, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{3: 0, 4, 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, 0, }, +{9: 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 2, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 4, 0, }, +{d: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{f: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:9, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 16, 6, 8, 0, 2, 4, 2, 0, 0, 0, 6, 0, 0, 0, 4, 0, }, +{4: 16, 0, 2, 4, 2, 6, 2, 2, 0, 2, 0, 4, 0, 0, 0, 0, }, +{8: 16, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{3: 16, 8, 4, 4, 0, 6, 4, 10, 2, 0, 2, 8, 0, 0, 0, 0, }, +{5: 16, 2, 2, 0, 0, 4, 8, 4, 2, 2, 0, 0, 4, 0, 4, 0, }, +{6: 16, 0, 0, 0, 2, 6, 4, 4, 0, 2, 0, 2, 2, 2, 0, 0, }, +{9: 16, 4, 2, 0, 0, 0, 2, 4, 2, 0, 2, 4, 0, 2, 0, 2, }, +{a: 16, 6, 0, 0, 0, 0, 0, 6, 0, 2, 2, 4, 0, 0, 2, 2, }, +{c: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 0, 0, 6, 0, 6, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, 6, 2, 4, 0, }, +{d: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:77, 4:30, 6:10, 8:5, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 4, 0, 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, -8, 8, -8, -8, }, +{4: 16, 8, 0, 0, 8, 0, 0, -8, 0, 0, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 8, 8, 0, -16, 0, -8, -8, 8, 0, 0, -8, 0, 8, }, +{5: 16, -8, 0, 8, 0, -8, 0, -8, 0, 8, -8, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, -8, 8, 0, }, +{9: 16, 0, 0, -8, 0, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, 8, }, +{a: 16, 0, -8, -8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, -8, 0, 0, 8, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, 0, 0, -8, }, +{d: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, x, , , x, x, , x, }, +{6: , , x, x, x, x, x, , x, x, , , x, , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, , x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , x, , , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , , , x, , x, x, , , x, , , x, }, +{b: , x, x, x, x, x, x, , x, x, , x, , , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0101,0011,1,}, +{0101,1101,1,}, +{0101,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x05,}}, +{{0x09,0x0a,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x05,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x05,0x09,0x0c,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +019 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x05,0x08,0x0b,0x03,0x09,0x0a,0x07,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 2, 0, 6, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 2, }, +{6: 0, 0, 0, 2, 0, 2, 0, 4, 4, 2, 0, 0, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, }, +{a: 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, }, +{c: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{d: 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:9, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 6, 0, 0, 8, 2, 0, 4, 6, 0, 0, 0, 2, 0, 0, }, +{2: 16, 4, 8, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, }, +{4: 16, 2, 0, 4, 2, 4, 0, 0, 0, 0, 2, 6, 0, 2, 0, 2, }, +{8: 16, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 16, 4, 4, 6, 0, 6, 4, 6, 0, 0, 0, 6, 2, 2, 0, 0, }, +{5: 16, 0, 2, 2, 0, 4, 8, 4, 2, 0, 0, 0, 4, 0, 4, 2, }, +{6: 16, 0, 0, 2, 0, 10, 4, 4, 4, 6, 0, 0, 0, 2, 0, 0, }, +{9: 16, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, }, +{a: 16, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 2, }, +{c: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{7: 16, 2, 0, 4, 0, 8, 0, 2, 4, 4, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, 6, 2, 4, 2, }, +{d: 16, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:77, 4:30, 6:10, 8:5, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{9: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, 0, -8, -8, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -16, -8, }, +{4: 16, 0, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 8, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, 8, -16, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 0, 8, -8, -8, 0, 8, -8, 0, 8, }, +{9: 16, -8, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, 0, 0, 0, 8, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, 0, -8, 0, 0, 8, 0, 0, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{e: 16, 0, -8, 8, -8, 0, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, }, +{f: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , , x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , , x, , x, x, }, +{9: , x, x, x, x, x, x, , x, x, , x, , x, , x, }, +{a: , , x, x, x, x, x, x, x, x, , x, , , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , x, x, x, x, x, , , x, , , x, }, +{b: , , x, x, , , x, , x, x, , x, , , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x09,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x07,0x08,}, {0x07,0x09,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_020.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_020.txt new file mode 100644 index 0000000..bebc602 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_020.txt @@ -0,0 +1,418 @@ +020 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x03,0x0e,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x07,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, }, +{4: 0, 0, 2, 4, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{8: 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 2, }, +{6: 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, 0, 2, 2, 0, }, +{9: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{d: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:9, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 0, 0, 4, 2, 0, 0, 6, 0, 2, 0, 2, }, +{2: 16, 2, 8, 4, 2, 0, 2, 4, 4, 0, 2, 0, 4, 0, 0, 0, }, +{4: 16, 0, 6, 4, 0, 0, 2, 8, 0, 6, 4, 0, 0, 2, 0, 0, }, +{8: 16, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, }, +{3: 16, 2, 0, 0, 0, 4, 4, 10, 0, 6, 4, 0, 0, 2, 0, 0, }, +{5: 16, 2, 2, 0, 0, 4, 8, 4, 0, 0, 2, 0, 4, 0, 4, 2, }, +{6: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{9: 16, 0, 6, 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 2, 0, 2, }, +{a: 16, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, }, +{c: 16, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, }, +{7: 16, 4, 0, 2, 0, 2, 0, 8, 2, 4, 4, 4, 0, 0, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 16, 0, 0, 0, 2, 2, 4, 0, 0, 0, 0, 2, 4, 2, 6, 2, }, +{f: 16, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:77, 4:30, 6:10, 8:5, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 0, 4, 4, }, +{5: 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -16, 8, 0, -8, }, +{4: 16, 8, 0, -8, 8, -8, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -8, -8, 8, 0, 0, -8, 8, 8, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, -16, 8, 0, 0, }, +{6: 16, 0, -8, -8, 8, -8, -8, 8, 0, -8, 0, 8, 0, -8, 8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{a: 16, -8, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 8, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 16, 0, 0, 0, }, +{b: 16, 8, -8, 0, -8, -8, 8, 0, 0, 0, 8, 0, 0, 0, -8, -8, }, +{d: 16, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{e: 16, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, x, x, x, , x, x, , x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{6: , x, x, x, , x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, , x, x, x, x, , x, x, x, x, , , x, }, +{c: , x, x, x, x, , x, x, , x, x, x, , x, , x, }, +{7: , x, x, x, , x, x, x, , x, x, , , , x, x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , x, x, , , , x, , , x, x, x, , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0b,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x07,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +020 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x05,0x08,0x0e,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x07,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 4, 0, 2, 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, }, +{a: 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, }, +{c: 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 2, 2, }, +{b: 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{d: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 2, 2, 0, }, +{f: 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:9, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 0, 2, 2, 2, 6, 0, 2, 0, 4, 0, 0, 0, 0, }, +{2: 16, 0, 8, 6, 2, 0, 2, 4, 6, 0, 0, 0, 4, 0, 0, 0, }, +{4: 16, 2, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 16, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, }, +{3: 16, 0, 0, 0, 2, 4, 4, 6, 0, 2, 0, 2, 0, 2, 2, 0, }, +{5: 16, 0, 2, 2, 0, 4, 8, 4, 0, 2, 2, 0, 4, 0, 4, 0, }, +{6: 16, 4, 4, 8, 0, 10, 4, 6, 2, 0, 2, 8, 0, 0, 0, 0, }, +{9: 16, 2, 4, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 2, 0, 2, }, +{a: 16, 0, 0, 6, 0, 6, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, }, +{c: 16, 0, 2, 4, 0, 4, 2, 0, 2, 0, 2, 4, 0, 2, 0, 2, }, +{7: 16, 6, 0, 0, 0, 0, 0, 6, 0, 2, 2, 4, 0, 0, 2, 2, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 16, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, 4, 2, 6, 0, }, +{f: 16, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:77, 4:30, 6:10, 8:5, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 8, 0, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -8, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, }, +{2: 16, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, -8, }, +{3: 16, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 8, -8, 0, 0, }, +{5: 16, 8, 0, -8, 0, -8, 0, -8, -8, 8, 0, 0, 0, 8, -8, 0, }, +{6: 16, 8, 0, -8, 8, 0, -16, 0, 8, -8, -8, 0, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, 0, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{a: 16, -8, -8, 0, 0, 8, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, }, +{c: 16, -8, 0, 0, 0, 0, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{d: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, -8, }, +{f: 16, -8, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{3: , x, x, , x, , x, x, , x, x, , x, , x, x, }, +{5: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{6: , x, x, x, x, , x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , , x, }, +{c: , x, x, x, x, x, x, x, , x, x, x, , x, , x, }, +{7: , , x, , , , x, , , x, x, , , , x, x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, x, x, x, , x, x, , x, x, x, , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0101,0110,1,}, +{0101,1011,0,}, +{0101,1101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x05,}}, +{{0x09,0x02,0x04,}, {0x05,}}, +{{0x01,0x0a,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0a,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x05,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_021.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_021.txt new file mode 100644 index 0000000..64cd30d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_021.txt @@ -0,0 +1,418 @@ +021 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x05,0x04,0x0b,0x00,0x09,0x0a,0x07,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:4, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 6, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 16, 0, 4, 4, 2, 4, 4, 0, 2, 0, 2, 8, 0, 2, 0, 0, }, +{8: 16, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, }, +{3: 16, 6, 4, 6, 2, 6, 4, 4, 2, 0, 0, 6, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 0, 4, 0, 0, 6, 8, 4, 0, 2, 0, 6, 0, 0, 2, 0, }, +{9: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, }, +{a: 16, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 2, 0, 6, 0, 4, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 16, 2, 4, 0, 6, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 0, }, +{d: 16, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:76, 4:32, 6:12, 8:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 8, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 0, 0, -8, 8, 0, -8, 0, 0, -8, 8, 8, 0, -8, }, +{4: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 8, -8, 0, -8, -8, 0, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 8, 0, -8, }, +{d: 16, 0, 0, 0, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, 0, 8, 0, 8, -8, 0, -8, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, , x, x, , , x, }, +{5: , , , x, x, x, x, x, x, x, , , x, x, , x, }, +{6: , , , x, x, x, x, x, x, x, , , x, , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, , x, , x, }, +{a: , x, , x, x, x, x, x, x, x, , x, , , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , , x, , , x, x, x, x, , , x, , , x, }, +{b: , x, , , x, x, x, , x, x, , x, , , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +021 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x05,0x00,0x0b,0x01,0x09,0x0a,0x07,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{8: 0, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 4, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:4, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 6, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 0, 0, 4, 2, 6, 0, 0, 0, 0, 0, 6, 0, 2, 2, 2, }, +{8: 16, 0, 4, 2, 2, 2, 0, 0, 4, 2, 0, 0, 6, 0, 2, 0, }, +{3: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 2, 4, 0, 2, 0, 0, }, +{5: 16, 0, 4, 4, 2, 4, 4, 8, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 2, 4, 6, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 16, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{a: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 0, 4, 8, 0, 6, 0, 6, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 16, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, }, +{d: 16, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:76, 4:32, 6:12, 8:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 8, -16, 0, 0, -8, -8, 0, 8, 0, 0, 8, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, -8, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, -8, 0, 8, }, +{9: 16, -8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, 0, 0, 0, -8, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -16, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, }, +{b: 16, -8, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, 0, 0, 8, -8, 8, -8, -8, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, , x, x, , , x, }, +{5: , x, , x, x, , x, x, x, x, , , x, x, , x, }, +{6: , x, , x, x, x, x, x, x, x, , , x, , x, x, }, +{9: , , x, , x, , x, x, x, x, , x, , x, , x, }, +{a: , , , x, x, x, x, x, x, x, , x, , , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , , x, x, x, x, , , x, , , x, }, +{b: , , , , x, , x, x, x, x, , x, , , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_022.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_022.txt new file mode 100644 index 0000000..5ab244f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_022.txt @@ -0,0 +1,418 @@ +022 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x09,0x03,0x07,0x06,0x05,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, }, +{2: 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, }, +{4: 0, 0, 2, 4, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, }, +{8: 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, }, +{9: 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 4, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +{e: 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{f: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:7, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 0, 10, 4, 4, 2, 0, 0, 8, 2, 0, 0, 0, }, +{2: 16, 6, 8, 0, 2, 4, 2, 0, 0, 0, 6, 0, 0, 0, 4, 0, }, +{4: 16, 4, 2, 4, 2, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 2, }, +{8: 16, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 16, 6, 4, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 0, 0, 0, 4, 2, 4, 0, }, +{6: 16, 6, 0, 4, 2, 6, 0, 4, 0, 2, 0, 8, 0, 0, 0, 0, }, +{9: 16, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 16, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{c: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 4, 0, 4, 2, 4, 0, 4, 2, 2, 0, 8, 2, 0, 0, 0, }, +{b: 16, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 6, 2, 4, 2, }, +{d: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:80, 4:29, 6:7, 8:7, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 8, 4, 0, }, +{6: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 8, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -16, 0, 0, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, -8, 8, -8, -8, }, +{4: 16, 8, 0, 0, 0, 0, 0, 0, 8, 0, -8, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 8, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, 0, 8, -8, -8, -8, 0, 0, -8, 8, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, }, +{a: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, -8, 8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, }, +{b: 16, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , , x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , , , x, x, x, , , x, , , , x, }, +{b: , x, x, x, x, x, x, x, x, , , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0101,0001,1,}, +{0101,1110,0,}, +{0101,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x06,0x08,}, {0x05,}}, +{{0x01,0x0a,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x05,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x05,}}, +{{0x01,0x02,}, {0x05,0x09,0x0c,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,}}, +{{0x01,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +022 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x09,0x08,0x07,0x03,0x05,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{8: 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, }, +{9: 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, }, +{c: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 4, 0, 0, 2, 0, 2, 2, 0, 0, 2, }, +{d: 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:152, 2:87, 4:15, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:7, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 4, 0, 6, 4, 6, 2, 0, 0, 4, 0, 0, 0, 2, }, +{2: 16, 4, 8, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, }, +{4: 16, 8, 0, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{8: 16, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +{3: 16, 10, 4, 0, 2, 4, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, }, +{5: 16, 4, 2, 4, 2, 2, 8, 0, 2, 0, 0, 0, 4, 0, 4, 0, }, +{6: 16, 4, 0, 2, 0, 0, 2, 4, 2, 2, 0, 4, 0, 2, 0, 2, }, +{9: 16, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, }, +{a: 16, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, }, +{c: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{7: 16, 8, 0, 0, 0, 0, 0, 8, 0, 2, 2, 8, 2, 2, 0, 0, }, +{b: 16, 2, 0, 0, 2, 0, 4, 0, 0, 2, 0, 2, 6, 0, 4, 2, }, +{d: 16, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:80, 4:29, 6:7, 8:7, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 8, 4, }, +{9: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:111, 4:112, 8:32, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 8, 0, 0, 8, -8, -8, -8, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -16, -8, }, +{4: 16, 0, 8, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, -8, 0, -8, }, +{8: 16, 8, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 8, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, }, +{9: 16, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, 0, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, 0, 0, 0, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 16, 0, }, +{b: 16, -8, 0, 0, 0, 0, 8, 0, -8, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, -8, 8, -8, 0, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, }, +{f: 16, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , , x, x, , x, }, +{a: , , x, x, x, x, x, x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , x, x, , x, , , x, , , , x, }, +{b: , , x, x, , , x, x, x, , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x09,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x07,0x09,0x0e,}}, +{{0x07,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_023.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_023.txt new file mode 100644 index 0000000..ffba551 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_023.txt @@ -0,0 +1,406 @@ +023 Sbox: +LUT = { +0x08,0x0f,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x00,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{4: 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, }, +{9: 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 6, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:148, 2:96, 4:9, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 6, 2, 0, 0, }, +{2: 16, 0, 6, 2, 0, 0, 6, 0, 6, 0, 4, 6, 4, 2, 4, 0, }, +{4: 16, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, }, +{8: 16, 2, 0, 0, 4, 4, 0, 2, 2, 0, 2, 0, 4, 2, 0, 2, }, +{3: 16, 0, 0, 2, 4, 4, 0, 2, 2, 2, 0, 0, 4, 0, 2, 2, }, +{5: 16, 0, 4, 2, 0, 0, 4, 2, 2, 2, 2, 4, 0, 2, 0, 0, }, +{6: 16, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, }, +{9: 16, 2, 6, 0, 0, 0, 0, 0, 4, 2, 2, 0, 6, 0, 2, 0, }, +{a: 16, 4, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 6, 2, 0, 2, }, +{c: 16, 0, 6, 2, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 2, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 6, 4, 0, 0, 6, 0, 0, 2, }, +{d: 16, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, }, +{e: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:100, 2:84, 4:27, 6:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, 8, -8, 8, -8, 8, -8, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, -8, 0, 0, }, +{3: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, -8, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, }, +{a: 16, 0, 0, 0, -8, 0, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, 8, 0, -8, 0, 8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, -8, 0, 8, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , x, x, , , x, x, x, x, x, x, , x, x, x, x, }, +{b: , , x, , , , x, x, x, , x, x, , x, x, x, }, +{d: , x, , x, x, , x, x, x, x, x, x, x, , x, x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +023 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x01, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, }, +{4: 0, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, }, +{b: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 6, 2, 0, 0, }, +{d: 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{e: 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:148, 2:96, 4:9, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 0, 0, 0, 2, 4, 0, 2, 4, 2, 0, 2, }, +{2: 16, 0, 6, 0, 0, 0, 4, 2, 6, 0, 6, 4, 4, 0, 6, 2, }, +{4: 16, 2, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{8: 16, 0, 0, 2, 4, 4, 0, 2, 0, 2, 2, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 0, 4, 4, 0, 2, 0, 0, 0, 0, 6, 2, 2, 2, }, +{5: 16, 0, 6, 2, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 2, }, +{6: 16, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 2, 2, 0, 4, 0, 0, 2, 6, 0, 0, 0, }, +{a: 16, 4, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 0, 2, 4, 0, 2, 0, 0, }, +{b: 16, 6, 4, 2, 4, 4, 0, 0, 6, 6, 0, 0, 6, 2, 0, 0, }, +{d: 16, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{e: 16, 0, 4, 2, 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 4, 2, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:100, 2:84, 4:27, 6:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 0, -8, 0, 0, 8, -8, 8, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, -8, 0, 0, 0, }, +{9: 16, -8, 0, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, }, +{7: 16, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, -8, }, +{b: 16, -8, 0, 8, -8, 0, -8, -8, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, , x, x, x, x, x, x, x, x, , x, }, +{7: , x, x, , , , , , , x, , x, , , , x, }, +{b: , , x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, x, , , , , x, , , , x, , x, }, +{e: , , x, , x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x08,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0c,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_024.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_024.txt new file mode 100644 index 0000000..4e123c1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_024.txt @@ -0,0 +1,406 @@ +024 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x0f,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, }, +{8: 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, 2, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, 0, }, +{9: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, }, +{c: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, }, +{d: 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:148, 2:96, 4:9, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:8, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 0, 0, 4, 2, 0, 0, 6, 0, 2, 0, 2, }, +{2: 16, 0, 6, 0, 2, 0, 6, 0, 4, 0, 6, 4, 4, 2, 6, 0, }, +{4: 16, 0, 0, 4, 2, 4, 2, 2, 0, 2, 0, 4, 0, 0, 2, 2, }, +{8: 16, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{5: 16, 2, 6, 0, 0, 0, 4, 2, 2, 0, 0, 6, 2, 0, 0, 0, }, +{6: 16, 4, 0, 0, 2, 2, 0, 4, 0, 2, 0, 6, 2, 2, 0, 0, }, +{9: 16, 0, 6, 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 2, 0, 2, }, +{a: 16, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, }, +{c: 16, 0, 4, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 2, }, +{7: 16, 4, 4, 6, 0, 6, 6, 4, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 16, 2, 6, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 0, 2, 2, }, +{d: 16, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{e: 16, 0, 4, 0, 2, 2, 2, 0, 2, 2, 4, 0, 0, 2, 4, 0, }, +{f: 16, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:100, 2:84, 4:27, 6:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 0, 8, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, 8, -8, 0, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, -8, 8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{7: 16, -8, -8, -8, 8, 8, 8, 0, -8, 0, -8, -8, 8, 0, 0, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, -8, }, +{d: 16, 0, 0, 0, 0, 0, -8, -8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , , x, , , , x, , x, x, x, , x, x, x, x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x09,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +024 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0f,0x00,0x05,0x08,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{5: 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 2, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, }, +{c: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 2, }, +{f: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:148, 2:96, 4:9, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:8, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 2, 2, 4, 0, 2, 0, 4, 2, 0, 0, 2, }, +{2: 16, 0, 6, 0, 2, 0, 6, 0, 6, 0, 4, 4, 6, 2, 4, 0, }, +{4: 16, 2, 0, 4, 2, 4, 0, 0, 0, 0, 2, 6, 0, 2, 0, 2, }, +{8: 16, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 16, 0, 0, 4, 2, 4, 0, 2, 0, 2, 0, 6, 0, 2, 2, 0, }, +{5: 16, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 4, 0, 2, 0, 0, 2, 4, 2, 2, 0, 4, 0, 2, 0, 2, }, +{9: 16, 2, 4, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 2, 2, 2, }, +{a: 16, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, }, +{c: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{7: 16, 6, 4, 4, 0, 4, 6, 6, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 2, 0, 4, 2, 0, 0, }, +{d: 16, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 6, 2, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 4, 2, }, +{f: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +}; +BCT_uniformity: 6, BCT_spectrum: {0:100, 2:84, 4:27, 6:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 8, 0, 0, 0, 0, 4, 4, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:105, 4:120, 8:30, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, }, +{2: 16, 0, 0, 8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, }, +{3: 16, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, 0, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 8, 0, 8, 8, -8, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, -8, }, +{f: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , , , x, , x, x, x, , x, x, x, x, }, +{b: , x, x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 0 */ +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 5, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x01,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_025.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_025.txt new file mode 100644 index 0000000..20cb91e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_025.txt @@ -0,0 +1,438 @@ +025 Sbox: +LUT = { +0x0d,0x00,0x01,0x02,0x03,0x05,0x0e,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x08,0x04,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, }, +{4: 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 4, 2, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +{6: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 6, 4, 0, 0, 2, }, +{c: 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, }, +{7: 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, }, +{b: 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:6, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, }, +{2: 16, 0, 6, 0, 2, 0, 4, 0, 4, 0, 8, 10, 8, 2, 4, 0, }, +{4: 16, 2, 4, 2, 0, 0, 4, 0, 4, 2, 0, 8, 0, 0, 4, 2, }, +{8: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{3: 16, 2, 0, 2, 0, 4, 4, 4, 0, 0, 2, 0, 2, 2, 0, 2, }, +{5: 16, 0, 0, 0, 2, 6, 4, 6, 0, 0, 2, 0, 0, 0, 2, 2, }, +{6: 16, 0, 8, 0, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 16, 0, 10, 0, 0, 0, 4, 0, 8, 2, 4, 6, 8, 0, 4, 2, }, +{c: 16, 2, 8, 2, 2, 0, 4, 0, 0, 0, 4, 4, 0, 2, 4, 0, }, +{7: 16, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, }, +{b: 16, 2, 0, 2, 2, 4, 4, 4, 0, 2, 2, 0, 2, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 6, 4, 6, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 0, 2, 8, 2, }, +{f: 16, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:72, 4:30, 6:6, 8:12, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:10, 4:3, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, 0, 0, 0, 0, 8, -8, 0, -16, 8, -8, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, -8, 0, 0, -8, 16, 0, 0, 0, 0, -8, 0, }, +{8: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 0, 8, -8, -8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, 8, }, +{6: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{a: 16, -8, -16, 0, 0, 8, 8, 0, 0, 0, -8, -8, 0, 8, 8, -8, }, +{c: 16, 0, 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, }, +{7: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 8, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, -8, 8, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 8, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, , x, x, x, x, x, x, x, x, , x, x, x, }, +{6: , x, , x, , x, x, x, x, x, x, x, , x, x, x, }, +{9: , , x, , , x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, , x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , x, , x, x, x, x, , x, , , x, x, x, }, +{7: , x, , , , , x, , x, x, , x, , x, x, x, }, +{b: , , , , , x, x, x, x, , x, , x, x, , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , x, , x, , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0110,1,}, +{0010,1010,1,}, +{0010,1100,0,}, +{1000,0110,0,}, +{1000,1000,1,}, +{1000,1110,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x02,}}, +{{0x09,0x0a,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x03,0x04,}, {0x0a,}}, +{{0x09,0x04,}, {0x03,0x09,0x0a,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +025 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x0e,0x05,0x08,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x00,0x06,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, }, +{4: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{8: 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 4, 2, 0, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 4, 2, 0, 0, }, +{9: 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, }, +{a: 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, }, +{c: 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, }, +{7: 0, 0, 2, 0, 0, 0, 0, 4, 0, 6, 0, 2, 0, 0, 0, 2, }, +{b: 0, 2, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, }, +{d: 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:6, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{2: 16, 0, 6, 4, 4, 0, 0, 8, 0, 10, 8, 2, 0, 0, 4, 2, }, +{4: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{8: 16, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 8, 2, 0, 0, 0, 4, 6, 0, 0, }, +{5: 16, 0, 4, 4, 0, 4, 4, 16, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 6, 8, 2, 0, 0, 0, 4, 6, 0, 0, }, +{9: 16, 2, 4, 4, 4, 0, 0, 0, 2, 8, 0, 2, 0, 0, 4, 2, }, +{a: 16, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, }, +{c: 16, 0, 8, 0, 4, 2, 2, 0, 0, 4, 4, 0, 2, 2, 4, 0, }, +{7: 16, 0, 10, 8, 4, 0, 0, 8, 0, 6, 4, 2, 0, 0, 4, 2, }, +{b: 16, 2, 8, 0, 8, 2, 0, 0, 2, 8, 0, 0, 2, 0, 0, 0, }, +{d: 16, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 8, 2, }, +{f: 16, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:72, 4:30, 6:6, 8:12, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, }, +{3: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:10, 4:3, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 8, -8, 0, -8, -8, 0, 0, 0, }, +{4: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, }, +{3: 16, -8, 0, 0, 8, -8, -8, 0, 0, -8, 0, 8, 0, -8, 0, 8, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, -8, 0, 0, 0, -8, -8, 0, 8, 0, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, }, +{a: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, }, +{c: 16, 0, 0, 0, 0, 0, 0, -16, 0, -8, 8, 0, -8, 8, 0, 0, }, +{7: 16, 8, -16, 0, 0, -8, 8, 0, 0, 0, -8, -8, 0, -8, 8, 8, }, +{b: 16, 0, 0, 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, -16, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, , x, x, x, x, x, x, x, x, }, +{5: , , , , x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, x, x, , , x, x, x, x, x, , x, x, x, x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, , , x, x, x, }, +{7: , , , , , , , , , x, x, x, , , x, x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , , , , , , , x, , x, x, , , x, x, x, }, +{e: , x, , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0100,1011,0,}, +{0100,1110,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x05,0x06,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x01,0x0a,0x04,}, {0x04,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x06,0x09,0x0f,}}, +{{0x0b,0x04,}, {0x04,0x09,0x0d,}}, +{{0x01,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_026.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_026.txt new file mode 100644 index 0000000..18869cd --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_026.txt @@ -0,0 +1,438 @@ +026 Sbox: +LUT = { +0x0c,0x0a,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x00,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{5: 0, 2, 0, 0, 0, 0, 2, 4, 4, 0, 0, 0, 2, 0, 0, 2, }, +{6: 0, 0, 2, 0, 6, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 2, 2, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, }, +{d: 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 0, 4, 6, 8, 4, 0, 0, 0, 2, 0, 0, 6, }, +{2: 16, 0, 6, 4, 10, 0, 0, 8, 0, 4, 4, 2, 0, 2, 8, 0, }, +{4: 16, 0, 4, 4, 4, 4, 4, 16, 4, 0, 0, 0, 0, 0, 4, 4, }, +{8: 16, 2, 8, 0, 8, 2, 0, 0, 2, 8, 0, 0, 2, 0, 0, 0, }, +{3: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{5: 16, 2, 0, 0, 0, 4, 6, 8, 4, 0, 0, 0, 2, 0, 0, 6, }, +{6: 16, 0, 10, 8, 6, 0, 0, 8, 0, 4, 4, 2, 0, 2, 4, 0, }, +{9: 16, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{a: 16, 2, 4, 4, 8, 0, 0, 0, 0, 4, 4, 2, 2, 2, 0, 0, }, +{c: 16, 0, 4, 4, 4, 0, 2, 0, 0, 0, 8, 2, 0, 2, 4, 2, }, +{7: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{b: 16, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, }, +{d: 16, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 16, 0, 8, 0, 4, 2, 2, 0, 2, 4, 4, 0, 0, 0, 4, 2, }, +{f: 16, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:72, 4:30, 6:6, 8:12, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{6: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 8, -8, -8, 0, 8, }, +{2: 16, 8, -8, 0, 8, -8, 8, 0, 8, -16, 0, 0, -8, 0, 0, -8, }, +{4: 16, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, }, +{5: 16, -8, 0, 0, 0, -8, -8, 8, 8, 0, -8, 0, -8, 0, 0, 8, }, +{6: 16, 8, 0, 0, 0, 0, 8, 8, 0, -16, -8, 8, -8, -8, 0, -8, }, +{9: 16, 0, 0, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 16, 0, }, +{c: 16, 0, 8, -16, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, }, +{d: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 8, -16, 0, }, +{f: 16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, , x, x, x, x, , , x, }, +{5: , , x, , x, x, x, x, , x, x, x, , x, , x, }, +{6: , , x, , x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, , x, x, , x, x, x, x, , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, , x, x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , x, , x, x, x, , , , x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , , x, , x, x, , x, , x, , , , x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1110,0100,1,}, +{1110,1010,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x06,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x04,0x09,0x0d,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x03,0x09,0x0a,}}, +{{0x09,0x02,}, {0x0a,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +026 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x0c,0x09,0x01,0x0b,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{5: 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, }, +{6: 0, 4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 2, 4, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{b: 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, }, +{e: 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, }, +{f: 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, }, +{2: 16, 0, 6, 4, 8, 0, 0, 10, 2, 4, 4, 0, 0, 2, 8, 0, }, +{4: 16, 0, 4, 4, 0, 2, 0, 8, 0, 4, 4, 2, 2, 0, 0, 2, }, +{8: 16, 0, 10, 4, 8, 0, 0, 6, 0, 8, 4, 0, 2, 0, 4, 2, }, +{3: 16, 4, 0, 4, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{5: 16, 6, 0, 4, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 2, 2, }, +{6: 16, 8, 8, 16, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 4, 0, 4, 2, 2, 4, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{7: 16, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{b: 16, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 16, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, }, +{e: 16, 0, 8, 4, 0, 2, 0, 4, 2, 0, 4, 2, 0, 2, 4, 0, }, +{f: 16, 6, 0, 4, 0, 0, 6, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:72, 4:30, 6:6, 8:12, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{9: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{7: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{e: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 0, -16, 0, 0, 8, -8, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 8, -8, 0, 0, 0, 0, 8, 8, -8, -8, 8, -16, -8, 0, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +{5: 16, 0, 8, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{9: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 8, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, -16, 0, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{7: 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{b: 16, -8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, -8, -8, }, +{f: 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , x, x, x, x, , , x, }, +{5: , x, x, , x, , x, x, , x, , x, , x, , x, }, +{6: , x, x, x, , x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, x, x, , x, x, , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , x, , x, x, , , x, x, x, }, +{7: , x, x, , , , , , , x, , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , x, x, , , , , x, , x, , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{1000,0110,0,}, +{1000,1010,1,}, +{1000,1100,1,}, +{1011,0110,1,}, +{1011,1000,1,}, +{1011,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x0b,}}, +{{0x05,0x06,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x05,0x06,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x03,0x08,0x0b,}}, +{{0x05,0x06,}, {0x03,0x08,0x0b,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_027.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_027.txt new file mode 100644 index 0000000..d4b3f1e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_027.txt @@ -0,0 +1,438 @@ +027 Sbox: +LUT = { +0x0c,0x00,0x01,0x02,0x03,0x05,0x0f,0x07,0x06,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{8: 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{5: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 4, 2, 0, 0, 2, }, +{d: 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:4, 4:1, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{2: 16, 0, 6, 0, 0, 0, 8, 2, 10, 0, 8, 4, 4, 2, 4, 0, }, +{4: 16, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 16, 0, 0, 4, 4, }, +{8: 16, 2, 8, 0, 2, 2, 0, 0, 8, 2, 0, 0, 8, 0, 0, 0, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, }, +{5: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{6: 16, 0, 8, 0, 2, 2, 4, 2, 4, 0, 0, 4, 4, 2, 0, 0, }, +{9: 16, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, }, +{a: 16, 2, 4, 0, 0, 0, 0, 2, 8, 2, 0, 4, 4, 2, 4, 0, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{7: 16, 2, 2, 6, 0, 6, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 2, 2, 6, 0, 0, 0, 0, 2, 0, 4, 2, 0, 0, 6, }, +{d: 16, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{e: 16, 0, 10, 2, 0, 0, 4, 0, 6, 0, 8, 4, 4, 0, 8, 2, }, +{f: 16, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 4, 0, 0, 2, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:70, 4:32, 6:8, 8:10, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, }, +{7: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 8, }, +{2: 16, 8, 0, 0, 0, -8, 0, -8, 8, -16, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -16, 0, }, +{8: 16, -8, 0, 16, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -8, 0, 8, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, 8, 0, 0, -16, 0, 0, 0, 0, 0, -8, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, }, +{a: 16, -8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, -8, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, -8, -8, 0, 8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, -8, 0, 0, 0, -8, }, +{d: 16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, -8, 8, 8, 0, 0, -8, 8, 8, -16, 0, }, +{f: 16, 8, 0, 0, -8, 0, 0, 8, -8, 0, 0, 0, -8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, , x, x, x, x, x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, , x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, , , x, , x, x, , x, , x, x, , x, }, +{a: , x, x, , x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , x, , , , x, x, , x, x, , , x, x, x, x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , x, x, , x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1110,0100,1,}, +{1110,1010,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x06,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x0a,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +027 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x0f,0x05,0x08,0x07,0x0c,0x09,0x0a,0x0b,0x00,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 4, }, +{3: 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, }, +{5: 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 6, 0, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, }, +{c: 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{e: 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:4, 4:1, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, }, +{2: 16, 0, 6, 4, 8, 0, 0, 8, 0, 4, 4, 2, 2, 0, 10, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 0, 0, 2, 6, 2, 2, 2, 0, }, +{8: 16, 2, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 4, }, +{3: 16, 2, 0, 4, 2, 4, 2, 2, 0, 0, 0, 6, 0, 2, 0, 0, }, +{5: 16, 2, 8, 4, 0, 0, 2, 4, 2, 0, 4, 0, 0, 2, 4, 0, }, +{6: 16, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 16, 0, 10, 4, 8, 0, 2, 4, 2, 8, 4, 0, 0, 0, 6, 0, }, +{a: 16, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, }, +{c: 16, 2, 8, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 8, 2, }, +{7: 16, 0, 4, 16, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{d: 16, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{e: 16, 0, 4, 4, 0, 2, 2, 0, 2, 4, 4, 0, 0, 0, 8, 2, }, +{f: 16, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 6, 0, 2, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:70, 4:32, 6:8, 8:10, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 8, 0, 0, 4, 0, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 8, 4, 0, 4, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:5, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{8: 16, -8, 0, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 0, 8, 0, 0, 0, -8, -8, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 16, -8, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, }, +{9: 16, 8, 0, 0, -8, -8, 0, 8, -8, 0, 0, 8, 0, 8, -16, -8, }, +{a: 16, -8, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, 0, 0, 0, 0, -8, 0, -8, 16, -8, -8, 0, 0, 0, }, +{7: 16, 0, -16, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 16, 0, }, +{b: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, 8, 0, -16, 0, }, +{f: 16, 0, 0, -8, 0, 8, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, , x, x, , x, x, x, , x, x, x, x, }, +{5: , x, , , x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, , x, x, x, x, , x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, , , , x, x, , x, x, x, , x, x, x, x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, , x, x, , x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{1100,0111,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1110,0111,0,}, +{1110,1001,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x05,0x07,}}, +{{0x09,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_028.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_028.txt new file mode 100644 index 0000000..61ce436 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_028.txt @@ -0,0 +1,438 @@ +028 Sbox: +LUT = { +0x08,0x0a,0x01,0x02,0x03,0x00,0x04,0x07,0x06,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 6, 0, 2, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 2, 0, 4, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 2, }, +{c: 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{d: 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 2, 2, 2, }, +{f: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 10, 4, 0, 10, 4, 4, 0, 0, 0, 4, 0, 0, 2, 2, }, +{2: 16, 4, 6, 8, 2, 10, 4, 4, 2, 0, 0, 8, 0, 0, 0, 0, }, +{4: 16, 0, 4, 4, 0, 4, 4, 16, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 16, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, }, +{3: 16, 4, 4, 4, 0, 8, 0, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{5: 16, 0, 4, 0, 2, 4, 8, 4, 2, 2, 0, 4, 2, 0, 0, 0, }, +{6: 16, 4, 8, 4, 2, 4, 0, 4, 2, 0, 2, 0, 0, 2, 0, 0, }, +{9: 16, 2, 0, 0, 0, 0, 0, 4, 2, 6, 4, 2, 2, 0, 2, 0, }, +{a: 16, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 6, 4, 0, 2, }, +{c: 16, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, }, +{7: 16, 4, 8, 0, 2, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{d: 16, 0, 2, 0, 0, 0, 2, 4, 0, 6, 6, 0, 0, 0, 2, 2, }, +{e: 16, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 6, 6, 2, 2, }, +{f: 16, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:70, 4:37, 6:7, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{8: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{f: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -8, -8, 0, }, +{2: 16, 0, -8, 8, 8, 0, 8, 0, 0, -16, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, -16, 0, 16, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, 0, }, +{3: 16, 0, 0, 0, 0, 8, -8, -16, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, 8, -8, 0, 0, 8, }, +{6: 16, 8, 0, 0, 0, -8, 0, 0, 8, -16, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 0, 8, 8, 0, }, +{a: 16, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 8, -8, }, +{c: 16, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 16, -8, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{d: 16, 8, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 8, 0, 0, 8, -8, 0, 0, 0, }, +{f: 16, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , , , x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, , , , , x, x, , x, , x, , , , x, }, +{b: , , , , , x, x, x, , , , , x, , , x, }, +{d: , x, x, x, x, x, x, x, , x, , , , x, , x, }, +{e: , x, x, x, x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0111,0,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0001,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x08,}, {0x05,0x09,0x0c,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +028 Inverse Sbox: +LUT = { +0x05,0x02,0x03,0x04,0x06,0x0a,0x08,0x07,0x00,0x09,0x01,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{2: 0, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{8: 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, }, +{3: 0, 6, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 4, 4, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{a: 0, 0, 0, 4, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, }, +{e: 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 4, 0, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{2: 16, 10, 6, 4, 0, 4, 4, 8, 0, 0, 0, 8, 0, 2, 2, 0, }, +{4: 16, 4, 8, 4, 2, 4, 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, }, +{8: 16, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, }, +{3: 16, 10, 10, 4, 2, 8, 4, 4, 0, 0, 0, 4, 2, 0, 0, 0, }, +{5: 16, 4, 4, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{6: 16, 4, 4, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 16, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{a: 16, 0, 0, 4, 2, 2, 2, 0, 6, 2, 0, 0, 0, 6, 0, 0, }, +{c: 16, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 0, 2, 6, 0, 2, }, +{7: 16, 4, 8, 0, 0, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 0, 4, 0, 2, 2, 0, 2, 6, 0, 0, 2, 0, 6, 0, }, +{d: 16, 0, 0, 4, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 6, 2, }, +{e: 16, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:70, 4:37, 6:7, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{2: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{9: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 4, 8, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -16, 0, 0, 8, 0, }, +{2: 16, 8, -8, 0, 8, -16, 0, 0, 8, -8, 8, 0, -8, 0, 0, -8, }, +{4: 16, 0, 0, 0, 0, 16, -8, -8, 0, 0, 0, 0, 0, -8, -8, 0, }, +{8: 16, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 16, 8, 0, -8, 0, -8, 0, 8, 0, -8, -8, 0, -8, }, +{5: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -16, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, 8, 0, 0, }, +{a: 16, 0, 8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{c: 16, -8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, 8, }, +{7: 16, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, -16, 0, 8, 0, 0, }, +{b: 16, 0, 0, 0, 0, 0, -8, -8, 0, 8, -8, 0, 8, 0, -8, 0, }, +{d: 16, 8, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, }, +{e: 16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, }, +{f: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, x, , , x, , x, x, , , x, }, +{5: , x, x, , x, , x, x, , x, , x, , x, , x, }, +{6: , x, x, , x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , x, x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, x, , , , , , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , x, x, , , , , x, , x, , , , x, , x, }, +{e: , x, x, , x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0011,0,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0111,0001,1,}, +{0111,0110,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x06,0x08,}, {0x07,}}, +{{0x05,0x06,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x0a,0x0c,}, {0x07,}}, +{{0x09,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x05,0x06,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x02,0x05,0x07,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x04,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x0e,}, {0x04,0x09,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_029.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_029.txt new file mode 100644 index 0000000..a7696a2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_029.txt @@ -0,0 +1,438 @@ +029 Sbox: +LUT = { +0x08,0x0d,0x01,0x02,0x03,0x00,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x05,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 2, 2, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 4, 0, 0, 0, }, +{a: 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{c: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{7: 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, }, +{b: 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, }, +{f: 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:11, 2:2, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 8, 0, 6, 10, 4, 2, 0, 0, 4, 0, 0, 0, 2, }, +{2: 16, 0, 4, 4, 0, 4, 4, 0, 2, 2, 2, 8, 0, 0, 0, 2, }, +{4: 16, 4, 0, 4, 0, 4, 8, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 16, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{3: 16, 0, 0, 4, 0, 8, 4, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{5: 16, 4, 4, 4, 2, 10, 10, 8, 0, 0, 0, 4, 0, 0, 2, 0, }, +{6: 16, 4, 4, 0, 2, 8, 4, 4, 0, 2, 2, 0, 0, 0, 2, 0, }, +{9: 16, 2, 4, 0, 2, 0, 0, 2, 6, 2, 2, 0, 4, 0, 0, 0, }, +{a: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 6, 0, 6, }, +{c: 16, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{7: 16, 4, 16, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 16, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, }, +{d: 16, 2, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 6, }, +{e: 16, 0, 4, 0, 0, 0, 0, 2, 6, 0, 0, 2, 6, 2, 2, 0, }, +{f: 16, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:70, 4:37, 6:7, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 0, 0, 0, 4, 0, 8, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{a: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{f: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:9, 4:3, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -8, -8, 8, }, +{2: 16, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, -16, 0, 8, 0, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 8, -8, -16, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, -8, 16, -8, 0, -8, 8, }, +{6: 16, 16, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{7: 16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, -8, 0, 0, -8, 0, 0, 8, -8, 0, 0, 0, 8, 0, -8, }, +{f: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , x, x, , x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , x, x, , x, x, x, }, +{9: , , x, , x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, x, , x, x, , x, , x, }, +{b: , , , , x, x, x, x, x, , x, , x, x, , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0001,0001,1,}, +{0001,0110,0,}, +{0001,0111,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0111,0,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x06,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x01,0x0a,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x09,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x07,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x01,0x06,0x07,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x01,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +029 Inverse Sbox: +LUT = { +0x05,0x02,0x03,0x04,0x06,0x0d,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{8: 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, }, +{3: 0, 6, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 2, 0, 4, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, }, +{a: 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{c: 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{7: 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, }, +{d: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, }, +{f: 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 2, 0, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:11, 2:2, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 0, 4, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{2: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 16, 0, 4, 4, 0, }, +{4: 16, 8, 4, 4, 2, 4, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{8: 16, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, }, +{3: 16, 6, 4, 4, 0, 8, 10, 8, 0, 0, 0, 4, 2, 0, 0, 2, }, +{5: 16, 10, 4, 8, 2, 4, 10, 4, 0, 0, 2, 4, 0, 0, 0, 0, }, +{6: 16, 4, 0, 4, 0, 4, 8, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{9: 16, 2, 2, 0, 2, 0, 0, 0, 6, 0, 2, 4, 0, 0, 6, 0, }, +{a: 16, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{c: 16, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{7: 16, 4, 8, 0, 0, 4, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 4, 2, 0, 6, 0, }, +{d: 16, 0, 0, 2, 0, 2, 0, 0, 0, 6, 2, 4, 0, 4, 2, 2, }, +{e: 16, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, }, +{f: 16, 2, 2, 0, 2, 0, 0, 0, 0, 6, 2, 4, 0, 6, 0, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:70, 4:37, 6:7, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{a: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{c: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{f: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:9, 4:3, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 16, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 16, 0, 0, 0, 0, 16, -8, -8, 0, 0, 0, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, }, +{3: 16, -16, 0, 8, 8, 0, -8, 0, -8, 8, 8, 0, -8, -8, 0, 0, }, +{5: 16, 0, 16, -8, 8, 0, 0, -8, -8, 8, -8, 0, -8, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, -16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 8, 0, -8, }, +{a: 16, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, 0, }, +{c: 16, 0, 0, 0, 0, 0, -8, -8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{7: 16, 0, -16, 0, 0, 0, 8, 0, 0, 0, 0, -8, 0, 8, 0, -8, }, +{b: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 0, 8, -8, 0, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, }, +{f: 16, 0, 0, 0, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , , x, x, , x, x, x, , x, x, , x, , x, }, +{6: , , , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, x, x, , x, x, x, , , , x, x, , x, }, +{a: , , , x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , , x, , , x, x, x, }, +{7: , , , x, , , x, , x, , x, x, , x, , x, }, +{b: , , , , x, , x, , , , , , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , , , x, x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,0x05,0x07,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_030.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_030.txt new file mode 100644 index 0000000..203c5a4 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_030.txt @@ -0,0 +1,438 @@ +030 Sbox: +LUT = { +0x06,0x08,0x01,0x0e,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x02,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 2, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, }, +{f: 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:156, 2:81, 4:15, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 6, 2, 0, 0, 4, 0, 2, 2, 2, }, +{2: 16, 0, 10, 4, 4, 0, 4, 6, 0, 6, 4, 4, 0, 0, 6, 0, }, +{4: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 2, 8, 4, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 2, 2, 4, 4, 4, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 8, 10, 8, 0, 8, 8, 10, 0, 0, 0, 8, 2, 0, 0, 2, }, +{9: 16, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{a: 16, 4, 8, 0, 6, 6, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, }, +{c: 16, 6, 8, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 6, 0, }, +{7: 16, 6, 0, 2, 0, 0, 0, 4, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 16, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, }, +{d: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 8, 4, 0, 2, 0, 4, 2, 0, 4, 2, 0, 2, 4, 0, }, +{f: 16, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:70, 4:29, 6:11, 8:10, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 8, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:4, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 0, -8, 0, -8, 0, 8, 0, -8, }, +{4: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -16, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 8, -16, 0, 8, -8, 0, 0, 16, -8, 0, 0, -16, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, -8, 0, -8, 8, 0, }, +{c: 16, 0, 0, 0, 0, 0, -8, -8, -16, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, -8, -8, }, +{f: 16, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, , x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , , x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , , x, , x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , x, x, , , x, , x, }, +{7: , , , x, , , , x, , x, x, x, , , x, x, }, +{b: , x, , , x, x, , , , x, x, , x, , x, x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , x, , x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{1001,0110,0,}, +{1001,1010,1,}, +{1001,1100,1,}, +{1011,0110,1,}, +{1011,1000,1,}, +{1011,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,0x08,}, {0x0b,}}, +{{0x05,0x06,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x0a,0x0c,}, {0x09,}}, +{{0x09,0x0a,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x02,0x09,0x0b,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x02,0x09,0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x02,0x09,0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x0b,0x0c,}, {0x09,}}, +{{0x01,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x08,}, {0x0b,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x02,0x09,0x0b,}}, +{{0x05,0x06,}, {0x02,0x09,0x0b,}}, +{{0x09,0x06,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +030 Inverse Sbox: +LUT = { +0x08,0x02,0x0e,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x03,0x0f, +}; + +ANF of coordinates: +y0 = + + + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, }, +{8: 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 2, 0, 4, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, 2, 0, 2, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:156, 2:81, 4:15, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 2, 0, 8, 0, 4, 6, 6, 0, 0, 0, 0, }, +{2: 16, 0, 10, 8, 8, 0, 0, 10, 0, 8, 8, 0, 2, 0, 8, 2, }, +{4: 16, 0, 4, 4, 4, 2, 0, 8, 2, 0, 0, 2, 0, 2, 4, 0, }, +{8: 16, 0, 4, 2, 4, 2, 0, 0, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 8, 0, 6, 4, 0, 0, 0, 2, 0, }, +{5: 16, 0, 4, 4, 2, 4, 4, 8, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 16, 6, 6, 4, 4, 4, 6, 10, 0, 0, 0, 4, 0, 0, 4, 0, }, +{9: 16, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{a: 16, 0, 6, 0, 4, 0, 2, 0, 2, 4, 2, 0, 0, 2, 0, 2, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 4, 4, 4, 0, 0, 0, 8, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, }, +{d: 16, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 16, 2, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 2, 2, 4, 0, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:70, 4:29, 6:11, 8:10, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{6: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:4, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, -8, 0, -8, 8, 0, }, +{2: 16, 8, -16, 0, 8, -8, 0, 0, 16, -8, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 8, 0, 0, 0, 0, -8, 0, 0, -8, -8, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -16, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 8, 0, 0, 8, -8, 0, 8, 0, -8, -8, 8, -16, -8, 0, 0, }, +{9: 16, -8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, 8, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -16, 0, 0, 0, 8, 0, 0, 0, 0, -8, 0, 8, 0, -8, }, +{b: 16, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, 0, -8, -8, -8, 0, 0, 0, 8, 0, 0, 8, 0, -8, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, , x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , , x, , x, , x, , x, x, x, , , x, x, }, +{9: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , x, , x, , x, , x, x, x, , , x, x, }, +{b: , x, , , x, x, , x, , x, x, , x, , x, x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 2, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x02,0x09,0x0b,}}, +{{0x03,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0b,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x02,0x09,0x0b,}}, +{{0x05,0x06,}, {0x02,0x09,0x0b,}}, +{{0x09,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_031.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_031.txt new file mode 100644 index 0000000..099c18a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_031.txt @@ -0,0 +1,438 @@ +031 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x0a,0x07,0x06,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, }, +{8: 0, 0, 4, 2, 4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 2, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 2, 2, 2, }, +{9: 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, }, +{d: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:156, 2:80, 4:18, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:3, 4:5, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 0, 4, 4, 0, 0, 2, 6, 0, 2, 0, 0, 2, 2, 0, 2, }, +{8: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{3: 16, 6, 4, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{6: 16, 0, 4, 4, 2, 2, 0, 4, 0, 0, 0, 2, 0, 2, 2, 2, }, +{9: 16, 0, 4, 0, 0, 0, 2, 2, 4, 2, 0, 0, 6, 2, 0, 2, }, +{a: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{c: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{b: 16, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, 2, 2, }, +{d: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 16, 2, 4, 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:76, 4:44, 6:4, 8:8, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 8, 8, -8, 16, -8, 0, -8, 0, 0, -16, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 8, 8, -8, 0, 0, -8, 0, 0, }, +{8: 16, 8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, -8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -16, 8, 0, 0, }, +{6: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, 8, 0, -8, 0, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 16, 0, 0, 0, }, +{b: 16, -8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, -8, 8, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , x, , x, , x, , x, , , , x, }, +{b: , , x, , x, , , x, , x, , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0101,0010,0,}, +{0101,1101,1,}, +{0101,1111,1,}, +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0e,}}, +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x05,0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x0b,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x07,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x06,}, {0x0b,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +031 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0a,0x00,0x05,0x08,0x07,0x03,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 8, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 0, 2, 4, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, }, +{a: 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:156, 2:80, 4:18, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:3, 4:5, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 2, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{3: 16, 4, 4, 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{5: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 4, 6, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, }, +{9: 16, 2, 4, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 2, 0, 2, }, +{a: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 2, 0, 0, 2, 0, 6, 2, 0, 0, 4, 2, 0, 2, }, +{d: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{f: 16, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:76, 4:44, 6:4, 8:8, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, 0, 0, -8, 8, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, 0, 8, 8, -8, 16, -8, 0, -8, 0, 0, -16, 8, -16, -8, }, +{4: 16, 0, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -16, 0, 0, -8, }, +{3: 16, -8, -8, 0, 0, 8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, 0, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 16, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, 0, 0, -8, 0, 0, -8, 8, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , , x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, x, x, , x, , x, , x, , x, , , , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0101,0010,0,}, +{0101,1101,1,}, +{0101,1111,1,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x0b,}}, +{{0x05,0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x0b,}}, +{{0x05,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x07,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x05,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_032.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_032.txt new file mode 100644 index 0000000..920fece --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_032.txt @@ -0,0 +1,470 @@ +032 Sbox: +LUT = { +0x0c,0x00,0x0a,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x01,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + +ANF of components: +y0 + + + = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{5: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{b: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{d: 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{e: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:165, 2:64, 4:24, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:2, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{5: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{6: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{b: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{d: 16, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{e: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 8, 8, }, +{f: 16, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:64, 4:48, 8:12, 16:38, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{c: 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{d: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{e: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +}; +Lin: 8, LAT_spectrum: {0:147, 4:64, 8:44, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:10, 4:2, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 8, }, +{2: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{4: 16, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, -8, }, +{5: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, 0, 0, 16, 0, -16, -16, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 8, }, +{e: 16, 8, -16, 0, 0, -8, 8, 0, 8, 0, 16, -8, -8, 8, -16, -8, }, +{f: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, , x, x, x, x, , , x, }, +{5: , x, x, , x, x, x, x, , x, x, x, , x, , x, }, +{6: , x, , , , x, , x, , x, x, x, , , x, x, }, +{9: , x, x, , , x, , x, x, , x, , x, x, , x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , x, , , , , , x, , x, x, x, , , , x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0010,0010,1,}, +{0010,1100,0,}, +{0010,1110,1,}, +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{0110,0110,0,}, +{0110,1010,1,}, +{0110,1100,1,}, +{1000,0010,0,}, +{1000,1000,1,}, +{1000,1010,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0110,1,}, +{1100,1000,1,}, +{1100,1110,0,}, +{1110,0100,1,}, +{1110,1010,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 11, +v=3 15, 1, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x01,0x02,0x0c,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x01,0x0a,0x0c,}, {0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0b,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x02,0x08,0x0a,}}, +{{0x09,0x02,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x02,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +032 Inverse Sbox: +LUT = { +0x01,0x0a,0x03,0x04,0x06,0x05,0x08,0x07,0x0c,0x09,0x02,0x0b,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, }, +{8: 0, 2, 0, 0, 4, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{5: 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, 0, }, +{6: 0, 2, 4, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 0, 2, 2, 0, 0, 0, }, +{a: 0, 2, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 2, 2, 0, 0, }, +{7: 0, 0, 4, 0, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 4, 0, 0, 0, 0, 2, }, +{e: 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, }, +}; +Diff: 8, DDT_spectrum: {0:165, 2:64, 4:24, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:2, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{2: 16, 0, 16, 16, 16, 0, 0, 16, 0, 16, 16, 0, 0, 0, 16, 0, }, +{4: 16, 0, 8, 4, 0, 2, 0, 4, 0, 0, 4, 2, 2, 0, 4, 2, }, +{8: 16, 2, 4, 0, 8, 2, 0, 4, 0, 4, 0, 0, 0, 2, 4, 2, }, +{3: 16, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, }, +{5: 16, 2, 8, 4, 0, 0, 2, 4, 2, 0, 4, 0, 0, 2, 4, 0, }, +{6: 16, 2, 8, 4, 0, 0, 2, 4, 2, 0, 4, 0, 0, 2, 4, 0, }, +{9: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{a: 16, 2, 4, 0, 8, 2, 0, 4, 0, 4, 0, 0, 0, 2, 4, 2, }, +{c: 16, 2, 4, 4, 0, 0, 0, 0, 0, 4, 4, 2, 2, 2, 8, 0, }, +{7: 16, 0, 8, 4, 0, 2, 0, 4, 0, 0, 4, 2, 2, 0, 4, 2, }, +{b: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{d: 16, 0, 4, 4, 0, 2, 2, 0, 2, 4, 4, 0, 0, 0, 8, 2, }, +{e: 16, 0, 4, 4, 0, 2, 2, 0, 2, 4, 4, 0, 0, 0, 8, 2, }, +{f: 16, 2, 4, 4, 0, 0, 0, 0, 0, 4, 4, 2, 2, 2, 8, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:64, 4:48, 8:12, 16:38, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{6: 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +}; +Lin: 8, LAT_spectrum: {0:147, 4:64, 8:44, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:10, 4:2, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -16, 0, 0, -16, 0, 0, 0, 0, 16, 0, 0, 16, -16, -16, }, +{4: 16, 0, 0, -8, 0, 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, 8, -8, -16, 0, 0, }, +{3: 16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 16, -8, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 8, -16, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, 0, 0, 8, 0, -8, -16, 8, -8, 0, 0, 0, }, +{a: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, 0, 0, 0, -16, 0, 0, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 16, 0, }, +{7: 16, 0, -16, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{b: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 16, }, +{e: 16, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, 8, 0, -16, 0, }, +{f: 16, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, 8, 0, 0, -16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , x, x, x, x, , , x, }, +{5: , , , , x, , x, x, , x, , x, , x, , x, }, +{6: , , , x, x, x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, x, , x, x, , x, }, +{a: , , , x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , x, , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , , , , , x, , x, , , , x, , x, }, +{e: , , , x, x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{1100,0010,0,}, +{1100,1001,1,}, +{1100,1011,1,}, +{1101,0010,0,}, +{1101,1000,1,}, +{1101,1010,1,}, +{1110,0010,1,}, +{1110,1100,0,}, +{1110,1110,1,}, +{1111,0010,1,}, +{1111,1101,0,}, +{1111,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 13, +v=3 7, 7, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x04,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x07,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_033.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_033.txt new file mode 100644 index 0000000..e17ea62 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_033.txt @@ -0,0 +1,470 @@ +033 Sbox: +LUT = { +0x0d,0x00,0x0a,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x01,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 4, 2, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{3: 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 2, 4, 0, }, +{6: 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 4, 0, 2, 0, 0, }, +{9: 0, 2, 0, 2, 0, 2, 0, 2, 4, 0, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{c: 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 2, }, +{e: 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, }, +}; +Diff: 8, DDT_spectrum: {0:165, 2:64, 4:24, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:6, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, }, +{2: 16, 0, 16, 0, 0, 0, 16, 0, 16, 0, 16, 16, 16, 0, 16, 0, }, +{4: 16, 2, 4, 2, 0, 0, 4, 0, 4, 2, 0, 8, 0, 0, 4, 2, }, +{8: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{3: 16, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, }, +{5: 16, 0, 4, 0, 2, 2, 4, 2, 4, 0, 0, 8, 0, 2, 4, 0, }, +{6: 16, 0, 4, 0, 2, 2, 4, 2, 4, 0, 0, 8, 0, 2, 4, 0, }, +{9: 16, 2, 4, 2, 0, 2, 0, 2, 4, 0, 4, 4, 8, 0, 0, 0, }, +{a: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{c: 16, 2, 8, 2, 2, 0, 4, 0, 0, 0, 4, 4, 0, 2, 4, 0, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 4, 2, 0, 8, 0, 0, 4, 2, }, +{b: 16, 2, 4, 2, 0, 2, 0, 2, 4, 0, 4, 4, 8, 0, 0, 0, }, +{d: 16, 0, 8, 0, 0, 2, 4, 2, 0, 2, 4, 4, 0, 0, 4, 2, }, +{e: 16, 0, 8, 0, 0, 2, 4, 2, 0, 2, 4, 4, 0, 0, 4, 2, }, +{f: 16, 2, 8, 2, 2, 0, 4, 0, 0, 0, 4, 4, 0, 2, 4, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:64, 4:48, 8:12, 16:38, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{8: 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{3: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, }, +{c: 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{d: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +}; +Lin: 8, LAT_spectrum: {0:147, 4:64, 8:44, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:11, 4:2, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{2: 16, 0, -16, 0, 16, 0, 16, 0, 0, -16, 0, -16, 0, 16, 0, -16, }, +{4: 16, 0, 0, -8, 0, -8, 0, 0, -8, 16, 0, 0, 0, 0, -8, 0, }, +{8: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 16, 0, 0, -8, 0, }, +{6: 16, -8, 0, 0, 0, 0, 0, 8, 0, -16, -8, 0, 8, 0, 0, 0, }, +{9: 16, -8, 0, 8, 0, 0, -16, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{c: 16, 0, 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 8, -16, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 16, }, +{e: 16, 8, -16, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, -16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, x, x, x, x, x, x, x, , x, }, +{5: , x, x, , x, x, x, x, x, x, x, x, , x, , x, }, +{6: , x, , x, , x, x, x, x, x, x, x, , x, x, x, }, +{9: , , x, , , x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, , x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , x, , x, x, x, x, , x, , , x, x, x, }, +{7: , , , , , , x, x, x, x, x, x, , x, , x, }, +{b: , , , , , x, x, x, x, , x, , x, x, , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , x, , x, , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0010,0010,1,}, +{0010,1100,0,}, +{0010,1110,1,}, +{0101,0010,0,}, +{0101,1001,1,}, +{0101,1011,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,0010,0,}, +{1000,1000,1,}, +{1000,1010,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1111,0010,1,}, +{1111,1101,0,}, +{1111,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 13, +v=3 7, 7, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x02,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x0b,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0b,0x0c,}, {0x02,0x05,0x07,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x05,0x07,}}, +{{0x09,0x0e,}, {0x02,0x05,0x07,}}, +{{0x0d,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +033 Inverse Sbox: +LUT = { +0x01,0x0a,0x03,0x04,0x06,0x05,0x08,0x07,0x0d,0x09,0x02,0x0b,0x0c,0x00,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{4: 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{8: 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, }, +{a: 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{e: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:165, 2:64, 4:24, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:6, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 8, 8, }, +{4: 16, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, }, +{8: 16, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{5: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{a: 16, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, }, +{e: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:64, 4:48, 8:12, 16:38, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{3: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{5: 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +}; +Lin: 8, LAT_spectrum: {0:147, 4:64, 8:44, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:11, 4:2, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{2: 16, 8, -16, 0, 0, -8, 8, 0, 8, 0, 16, -8, -8, 8, -16, -8, }, +{4: 16, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 8, }, +{3: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, 0, 0, 16, 0, -16, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, -8, }, +{c: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{7: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 8, }, +{e: 16, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , , , , x, , x, x, , x, , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, , , x, x, x, }, +{7: , , , , , , , , , x, , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , , , , , , , x, , x, , , , x, , x, }, +{e: , x, , , , x, x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0100,1011,0,}, +{0100,1110,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,0111,0,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1010,0111,1,}, +{1010,1001,1,}, +{1010,1110,0,}, +{1100,0010,0,}, +{1100,1001,1,}, +{1100,1011,1,}, +{1110,0010,1,}, +{1110,1100,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 11, +v=3 15, 1, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0e,}}, +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x06,0x08,}, {0x0a,}}, +{{0x05,0x06,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,}}, +{{0x09,0x0a,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_034.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_034.txt new file mode 100644 index 0000000..03b21e3 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_034.txt @@ -0,0 +1,408 @@ +034 Sbox: +LUT = { +0x08,0x0f,0x01,0x02,0x03,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x00, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{2: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 4, 2, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 0, 0, 2, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 4, 0, 0, 2, 2, 2, 2, 4, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 4, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 0, 4, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 4, }, +{f: 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 4, DDT_spectrum: {0:156, 2:78, 4:21, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 0, 6, 2, 2, }, +{2: 16, 0, 10, 0, 0, 0, 2, 0, 6, 0, 0, 0, 4, 4, 2, 4, }, +{4: 16, 2, 0, 4, 4, 10, 2, 0, 0, 0, 0, 6, 4, 0, 0, 0, }, +{8: 16, 2, 0, 0, 2, 0, 0, 4, 2, 4, 6, 2, 2, 0, 0, 0, }, +{3: 16, 0, 0, 10, 0, 4, 2, 0, 0, 4, 0, 4, 0, 0, 6, 2, }, +{5: 16, 0, 0, 4, 0, 0, 2, 6, 2, 10, 4, 0, 0, 0, 4, 0, }, +{6: 16, 0, 2, 4, 2, 0, 0, 2, 2, 6, 0, 0, 0, 0, 4, 2, }, +{9: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{c: 16, 4, 4, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 10, 0, 6, }, +{7: 16, 2, 0, 6, 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 0, 4, 0, 6, 4, 2, 2, 4, 0, 0, 0, 10, 0, 0, 0, }, +{d: 16, 6, 0, 0, 2, 0, 2, 4, 0, 4, 10, 0, 0, 4, 0, 0, }, +{e: 16, 0, 6, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 2, 4, }, +{f: 16, 2, 0, 0, 4, 6, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:112, 2:57, 4:35, 6:14, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{3: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{c: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{f: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:8, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +{2: 16, -8, 0, 0, -8, -8, 0, -8, 8, 0, 0, 8, 0, 8, 0, -8, }, +{4: 16, -8, 0, 0, 8, 8, -8, -8, 0, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, -8, 8, 0, -8, -8, 0, -8, 0, 8, 0, }, +{3: 16, 0, -8, 0, 0, 0, 0, -8, -8, 8, 0, 0, 8, -8, -8, 8, }, +{5: 16, 8, 8, -8, 0, 0, -8, -8, 0, 0, -8, -8, 0, 0, 0, 8, }, +{6: 16, 8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 0, 8, -8, 0, -8, 8, -8, -8, 8, 0, 0, }, +{7: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, 8, 0, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 8, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 8, 8, 0, 0, -8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 8, 0, 8, -8, -8, 0, 0, -8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , , x, , x, x, , x, x, x, , , x, x, x, x, }, +{b: , , , , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, x, , x, x, x, x, x, x, x, , x, x, }, +{e: , x, , , x, x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0110,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x05,}}, +{{0x03,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x04,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +034 Inverse Sbox: +LUT = { +0x0f,0x02,0x03,0x04,0x08,0x0c,0x06,0x07,0x00,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x01, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 4, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 4, 2, 2, 2, 2, 0, 0, 0, 4, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 0, 0, 4, 4, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, }, +{e: 0, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, }, +{f: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 4, DDT_spectrum: {0:156, 2:78, 4:21, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:5, 4:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 6, 0, 2, }, +{2: 16, 0, 10, 0, 0, 0, 0, 2, 4, 2, 4, 0, 4, 0, 6, 0, }, +{4: 16, 0, 0, 4, 0, 10, 4, 4, 0, 2, 0, 6, 0, 0, 2, 0, }, +{8: 16, 2, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 4, }, +{3: 16, 2, 0, 10, 0, 4, 0, 0, 0, 2, 0, 4, 4, 0, 0, 6, }, +{5: 16, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 0, 0, 0, 4, 0, 6, 2, 2, 0, 0, 0, 2, 4, 2, 2, }, +{9: 16, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, 2, 4, 0, 2, 0, }, +{a: 16, 0, 0, 0, 4, 4, 10, 6, 2, 2, 0, 0, 0, 4, 0, 0, }, +{c: 16, 4, 0, 0, 6, 0, 4, 0, 0, 2, 4, 0, 0, 10, 0, 2, }, +{7: 16, 2, 0, 6, 2, 4, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 16, 0, 4, 4, 2, 0, 0, 0, 6, 2, 0, 0, 10, 0, 0, 4, }, +{d: 16, 6, 4, 0, 0, 0, 0, 0, 0, 2, 10, 2, 0, 4, 4, 0, }, +{e: 16, 2, 2, 0, 0, 6, 4, 4, 2, 0, 0, 2, 0, 0, 2, 0, }, +{f: 16, 2, 4, 0, 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:112, 2:57, 4:35, 6:14, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{2: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{b: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:8, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 8, 8, 0, }, +{4: 16, 0, 0, -8, 8, 0, 0, -8, -8, 8, -8, 0, 8, 0, -8, 0, }, +{8: 16, -8, 0, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, -8, 0, 0, }, +{3: 16, -8, -8, 8, 0, 8, -8, -8, 0, 8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, -8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 8, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, 8, 0, 8, 0, 0, 0, -8, 8, 0, -8, -8, 0, 0, -8, -8, }, +{d: 16, 0, 0, 0, 0, -8, 8, -8, 0, -8, 8, -8, 0, 0, 8, -8, }, +{e: 16, 0, -8, 0, 8, -8, -8, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, x, x, x, x, , x, x, x, , , x, x, x, x, }, +{b: , , x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , , x, x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, x, , , , , x, x, x, , x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x08,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0c,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x03,0x09,0x0a,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_035.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_035.txt new file mode 100644 index 0000000..cc66a7e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_035.txt @@ -0,0 +1,408 @@ +035 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x05,0x0b,0x07,0x04,0x09,0x0a,0x06,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, }, +{3: 0, 2, 2, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, }, +{5: 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 2, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 2, 0, 4, 2, 0, 4, 2, 0, 0, 0, 0, 0, }, +{c: 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 4, 4, 0, 2, 2, }, +{b: 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, }, +{d: 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, }, +{e: 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, }, +{f: 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, }, +}; +Diff: 4, DDT_spectrum: {0:156, 2:78, 4:21, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:3, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 6, 0, 4, 0, 0, 0, 4, 2, 0, 8, 2, 0, }, +{2: 16, 0, 4, 0, 4, 4, 0, 0, 4, 8, 2, 0, 0, 2, 2, 2, }, +{4: 16, 0, 0, 4, 0, 8, 2, 0, 6, 4, 0, 6, 2, 0, 0, 0, }, +{8: 16, 2, 4, 0, 4, 0, 2, 0, 2, 6, 2, 0, 2, 0, 0, 0, }, +{3: 16, 2, 2, 6, 0, 4, 2, 0, 0, 0, 2, 4, 0, 0, 2, 0, }, +{5: 16, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, }, +{6: 16, 0, 0, 0, 0, 4, 0, 6, 8, 6, 0, 2, 2, 0, 0, 4, }, +{9: 16, 2, 0, 4, 0, 0, 0, 4, 6, 0, 0, 2, 4, 0, 0, 10, }, +{a: 16, 0, 6, 0, 10, 0, 4, 2, 0, 4, 2, 0, 0, 4, 0, 0, }, +{c: 16, 4, 0, 0, 0, 2, 0, 2, 0, 0, 6, 0, 2, 6, 0, 2, }, +{7: 16, 0, 0, 10, 0, 4, 2, 0, 0, 0, 0, 4, 4, 0, 2, 6, }, +{b: 16, 0, 0, 2, 4, 0, 4, 2, 0, 2, 0, 0, 2, 6, 2, 0, }, +{d: 16, 6, 2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 0, }, +{e: 16, 2, 2, 4, 2, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 4, }, +{f: 16, 0, 2, 2, 0, 2, 0, 4, 4, 0, 2, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:109, 2:60, 4:34, 6:15, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 8, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 8, 8, 4, 4, 4, 0, 0, 4, 0, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, -8, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 8, -8, }, +{2: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, 8, -8, 0, }, +{4: 16, 0, 0, 0, 0, 0, 0, -8, 0, 8, -16, -8, 8, 0, 0, 0, }, +{8: 16, 0, 8, 8, -8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, 0, 0, 8, 0, -8, -8, -8, 0, 8, 0, 0, 0, -8, 0, }, +{5: 16, 0, 0, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{6: 16, -8, -8, 8, 0, 0, -8, 0, 0, -8, -8, 0, 8, 0, 0, 8, }, +{9: 16, 0, 0, -8, 8, 0, -8, 8, 8, 0, -8, -8, 0, -8, 0, 0, }, +{a: 16, 8, 0, 0, 0, -8, 8, -8, -8, 0, -8, 0, -8, 0, 0, 8, }, +{c: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 8, 0, }, +{7: 16, -8, -8, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, 8, 0, -8, }, +{b: 16, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, -8, 0, -8, }, +{d: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, 0, 0, 0, 8, 0, 0, 8, 0, -8, -8, -8, 0, }, +{f: 16, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, , , x, x, x, x, x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{9: , x, , x, x, x, , x, x, x, x, , , x, , x, }, +{a: , x, x, x, , , , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , x, x, x, , , x, x, x, x, x, x, , , x, }, +{b: , , , x, , , , x, x, x, x, , , , , x, }, +{d: , , , x, x, x, , , , , x, , , x, , x, }, +{e: , x, x, , , , , x, x, x, x, , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x02,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +035 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0c,0x08,0x05,0x0b,0x07,0x00,0x09,0x0a,0x06,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 4, 0, 0, 2, 2, 0, }, +{2: 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{8: 0, 2, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{5: 0, 0, 0, 2, 2, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 0, 2, 0, 2, 0, }, +{9: 0, 0, 4, 2, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 4, 2, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 4, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, }, +{d: 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, }, +{e: 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{f: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 4, DDT_spectrum: {0:156, 2:78, 4:21, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:3, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 2, 2, 0, 0, 2, 0, 4, 0, 0, 6, 2, 0, }, +{2: 16, 0, 4, 0, 4, 2, 2, 0, 0, 6, 0, 0, 0, 2, 2, 2, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 4, 0, 0, 10, 2, 0, 4, 2, }, +{8: 16, 6, 4, 0, 4, 0, 2, 0, 0, 10, 0, 0, 4, 0, 2, 0, }, +{3: 16, 0, 4, 8, 0, 4, 0, 4, 0, 0, 2, 4, 0, 2, 2, 2, }, +{5: 16, 4, 0, 2, 2, 2, 2, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{6: 16, 0, 0, 0, 0, 0, 2, 6, 4, 2, 2, 0, 2, 0, 2, 4, }, +{9: 16, 0, 4, 6, 2, 0, 2, 8, 6, 0, 0, 0, 0, 0, 0, 4, }, +{a: 16, 0, 8, 4, 6, 0, 2, 6, 0, 4, 0, 0, 2, 0, 0, 0, }, +{c: 16, 4, 2, 0, 2, 2, 0, 0, 0, 2, 6, 0, 0, 4, 0, 2, }, +{7: 16, 2, 0, 6, 0, 4, 2, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 0, 2, 2, 0, 0, 2, 4, 0, 2, 4, 2, 2, 4, 0, }, +{d: 16, 8, 2, 0, 0, 0, 2, 0, 0, 4, 6, 0, 6, 4, 0, 0, }, +{e: 16, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{f: 16, 0, 2, 0, 0, 0, 0, 4, 10, 0, 2, 6, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:109, 2:60, 4:34, 6:15, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +{8: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, -8, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, 0, }, +{2: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{4: 16, -8, 0, 0, 0, 8, -8, 0, 8, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, -8, 8, -8, 8, -8, 0, 0, -8, }, +{3: 16, 0, -8, -8, 0, 0, -8, 0, 0, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 8, -8, 0, 0, }, +{6: 16, 0, 0, 0, -8, -8, -8, 0, 0, 0, -8, 0, 0, 8, 0, 8, }, +{9: 16, 8, 0, 0, 8, -8, 0, 0, 8, -8, -8, 0, -8, 0, -8, 0, }, +{a: 16, 8, 0, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, 8, 0, 0, 0, 0, -8, 0, 8, -8, -8, -8, 0, 0, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 8, -8, }, +{e: 16, -8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 8, -8, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, , , x, x, x, x, x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, , , x, , x, }, +{a: , x, x, x, x, , , x, x, x, x, , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , x, , x, , , x, x, x, x, x, x, , , x, }, +{b: , , x, x, x, , , x, x, x, x, , , , , x, }, +{d: , x, , , x, x, , , , , x, , , x, , x, }, +{e: , x, , , , , , x, x, x, x, , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{1100,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x02,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x0b,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x0a,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_036.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_036.txt new file mode 100644 index 0000000..6cccf25 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_036.txt @@ -0,0 +1,408 @@ +036 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x05,0x0d,0x07,0x04,0x09,0x0a,0x0b,0x03,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, }, +{8: 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 2, 4, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 2, 4, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{a: 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 4, 2, 2, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, }, +{b: 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, }, +}; +Diff: 4, DDT_spectrum: {0:156, 2:78, 4:21, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:3, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 6, 0, 10, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{2: 16, 0, 4, 0, 0, 0, 0, 0, 4, 0, 6, 4, 0, 2, 10, 2, }, +{4: 16, 4, 0, 4, 0, 0, 6, 0, 0, 2, 2, 2, 2, 0, 0, 2, }, +{8: 16, 2, 0, 0, 6, 4, 0, 0, 2, 0, 2, 2, 6, 0, 0, 0, }, +{3: 16, 2, 0, 2, 4, 6, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, }, +{5: 16, 6, 4, 8, 0, 0, 4, 6, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 16, 0, 0, 0, 0, 2, 2, 6, 4, 2, 0, 2, 0, 2, 0, 4, }, +{9: 16, 2, 6, 4, 0, 0, 0, 8, 6, 2, 0, 0, 0, 0, 0, 4, }, +{a: 16, 2, 2, 0, 4, 0, 4, 0, 0, 2, 2, 0, 2, 4, 2, 0, }, +{c: 16, 0, 8, 4, 0, 2, 0, 4, 0, 0, 4, 2, 2, 0, 4, 2, }, +{7: 16, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, }, +{b: 16, 0, 0, 2, 8, 6, 4, 0, 0, 2, 0, 0, 4, 6, 0, 0, }, +{d: 16, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 2, 4, 0, }, +{e: 16, 0, 6, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 0, 4, 2, }, +{f: 16, 0, 0, 2, 0, 2, 0, 4, 10, 0, 0, 4, 0, 0, 6, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:109, 2:60, 4:34, 6:15, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{2: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, 8, -8, 0, }, +{4: 16, 0, 0, -8, 0, 8, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, }, +{8: 16, -8, 0, 8, 0, 8, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{3: 16, 0, 8, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, -8, 0, }, +{5: 16, 0, 0, 0, 8, -16, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{6: 16, -8, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 8, 0, 0, 8, }, +{9: 16, 8, 0, 0, 8, -8, -8, 0, 8, 0, -8, -8, 0, -8, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, -8, 8, 0, 0, }, +{c: 16, 0, -8, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, 0, -8, 0, 0, -8, 8, 0, -8, 0, -8, }, +{d: 16, 0, -8, 0, 0, -8, -8, 0, 0, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, -8, -8, -8, 0, 8, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , , , , x, x, x, }, +{7: , , , , x, x, x, x, x, , , x, , x, , x, }, +{b: , x, , , x, x, , , , , x, , x, , , x, }, +{d: , x, x, x, , x, x, x, x, , , , , , , x, }, +{e: , x, , x, , x, x, x, x, , , , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0011,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +036 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0c,0x08,0x05,0x0d,0x07,0x00,0x09,0x0a,0x0b,0x03,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{8: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, }, +{3: 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{5: 0, 2, 0, 2, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 4, 0, 0, 2, 2, 0, }, +{9: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 0, 4, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 4, 2, }, +{f: 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, }, +}; +Diff: 4, DDT_spectrum: {0:156, 2:78, 4:21, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:3, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 6, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{2: 16, 0, 4, 0, 0, 0, 4, 0, 6, 2, 8, 0, 0, 2, 6, 0, }, +{4: 16, 4, 0, 4, 0, 2, 8, 0, 4, 0, 4, 2, 2, 0, 0, 2, }, +{8: 16, 6, 0, 0, 6, 4, 0, 0, 0, 4, 0, 2, 8, 0, 2, 0, }, +{3: 16, 0, 0, 0, 4, 6, 0, 2, 0, 0, 2, 0, 6, 2, 0, 2, }, +{5: 16, 10, 0, 6, 0, 2, 4, 2, 0, 4, 0, 0, 4, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, 0, 6, 6, 8, 0, 4, 0, 0, 2, 2, 4, }, +{9: 16, 0, 4, 0, 2, 0, 0, 4, 6, 0, 0, 0, 0, 4, 2, 10, }, +{a: 16, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 16, 0, 6, 2, 2, 2, 0, 0, 0, 2, 4, 2, 0, 0, 4, 0, }, +{7: 16, 2, 4, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 4, }, +{b: 16, 0, 0, 2, 6, 4, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 16, 4, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 6, 2, 0, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 4, 4, 6, }, +{f: 16, 0, 2, 2, 0, 2, 0, 4, 4, 0, 2, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:109, 2:60, 4:34, 6:15, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{2: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 8, 4, 4, 4, 0, 0, 4, 0, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{4: 16, -8, 0, 0, 0, 8, -8, 0, 8, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, -8, -8, 8, 0, 8, -8, 0, -8, 0, 0, 8, 0, 0, 0, -8, }, +{3: 16, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 8, -8, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, -8, 8, -8, 0, 0, -8, 0, 8, }, +{6: 16, 0, 8, -8, -8, -8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 8, }, +{9: 16, 8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, 0, 0, 8, 0, -8, -8, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, 0, 0, -8, -8, -8, 0, 0, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, -8, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 0, 0, 8, 0, 8, 0, 0, -8, }, +{f: 16, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, , x, x, x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , , , , x, x, x, }, +{7: , , , x, x, x, x, x, x, , , x, , x, , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , x, , , x, x, x, x, , , , , , , x, }, +{e: , x, x, x, , x, x, x, x, , , , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x0b,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_037.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_037.txt new file mode 100644 index 0000000..1a89021 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_037.txt @@ -0,0 +1,420 @@ +037 Sbox: +LUT = { +0x0c,0x00,0x01,0x02,0x03,0x0f,0x06,0x07,0x04,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, }, +{2: 0, 0, 4, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 4, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, }, +{5: 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{6: 0, 0, 4, 0, 0, 0, 0, 2, 0, 4, 2, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, }, +{d: 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, }, +{e: 0, 0, 4, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 4:6, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 6, 2, 0, 0, 0, 8, 0, 2, 6, 0, 4, }, +{2: 16, 0, 8, 0, 4, 0, 2, 2, 4, 4, 0, 0, 4, 2, 2, 0, }, +{4: 16, 0, 0, 4, 0, 8, 2, 0, 0, 0, 6, 6, 0, 0, 2, 4, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{5: 16, 2, 0, 2, 0, 4, 2, 2, 2, 0, 4, 0, 0, 0, 0, 6, }, +{6: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{9: 16, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, }, +{a: 16, 0, 8, 0, 4, 0, 2, 2, 4, 4, 0, 0, 4, 2, 2, 0, }, +{c: 16, 8, 0, 2, 0, 0, 0, 6, 0, 0, 4, 4, 0, 6, 0, 2, }, +{7: 16, 4, 0, 4, 0, 6, 0, 6, 0, 0, 0, 8, 2, 0, 2, 0, }, +{b: 16, 6, 0, 0, 2, 0, 0, 4, 0, 2, 0, 6, 2, 0, 0, 2, }, +{d: 16, 6, 0, 2, 2, 0, 0, 0, 0, 2, 6, 0, 2, 4, 0, 0, }, +{e: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{f: 16, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:110, 2:58, 4:30, 6:14, 8:12, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{6: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{9: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, -8, -8, -8, 0, 8, 0, -8, 0, 8, 0, }, +{2: 16, 8, 0, 0, 0, -8, 8, 0, 0, -8, 0, 8, -8, 0, -8, -8, }, +{4: 16, 0, 0, -16, 0, 8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, }, +{8: 16, 0, 0, 16, -8, 0, 0, 0, 8, -8, -8, 0, -8, 8, -8, -8, }, +{3: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, -8, 8, }, +{6: 16, 8, -8, 0, 0, -8, 8, -8, 0, -8, 0, -8, 0, 0, 8, 0, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, -8, 0, 8, -8, 8, 0, 0, 8, 0, }, +{c: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, 0, 8, 0, -8, 8, -8, 0, 0, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{d: 16, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, -8, }, +{e: 16, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, 8, -16, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , , x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, , x, x, , x, x, x, x, , x, x, x, x, }, +{9: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{a: , x, x, , , x, , , , x, x, , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, , , x, , x, x, x, , , x, x, x, x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , , , x, , , x, x, x, x, x, x, , x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x08,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x0d,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x0f,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +037 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x0f,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x00,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, }, +{2: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{5: 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{6: 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 4, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 4, 2, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 4, 2, 0, 0, 0, }, +{b: 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, 0, 0, }, +{e: 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +{f: 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 4:6, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 2, 0, 0, 0, 8, 4, 6, 6, 0, 0, }, +{2: 16, 0, 8, 0, 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{4: 16, 0, 0, 4, 0, 6, 2, 0, 2, 0, 2, 4, 0, 2, 2, 0, }, +{8: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{3: 16, 6, 0, 8, 0, 4, 4, 0, 2, 0, 0, 6, 0, 0, 0, 2, }, +{5: 16, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{6: 16, 0, 2, 0, 0, 0, 2, 2, 0, 2, 6, 6, 4, 0, 0, 0, }, +{9: 16, 0, 4, 0, 8, 2, 2, 4, 2, 4, 0, 0, 0, 0, 4, 2, }, +{a: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 16, 8, 0, 6, 0, 0, 4, 2, 0, 0, 4, 0, 0, 6, 0, 2, }, +{7: 16, 0, 0, 6, 0, 4, 0, 2, 2, 0, 4, 8, 6, 0, 0, 0, }, +{b: 16, 2, 4, 0, 8, 0, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, }, +{d: 16, 6, 2, 0, 0, 2, 0, 2, 0, 2, 6, 0, 0, 4, 0, 0, }, +{e: 16, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +{f: 16, 4, 0, 4, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:110, 2:58, 4:30, 6:14, 8:12, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 0, 0, -8, 0, 8, 0, -8, 0, 8, -8, 0, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, -8, -8, }, +{3: 16, -16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, 8, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, 8, 0, 0, -16, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, -8, 8, 8, }, +{c: 16, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, -8, -8, -8, 8, 0, }, +{7: 16, 0, 0, -8, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, 0, -8, 8, -8, }, +{d: 16, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, -8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , , x, x, , x, , x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , , x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, , , x, , x, x, x, x, , x, x, x, x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , x, x, x, , x, x, x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x01,}}, +{{0x09,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_038.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_038.txt new file mode 100644 index 0000000..3ce066b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_038.txt @@ -0,0 +1,420 @@ +038 Sbox: +LUT = { +0x0c,0x00,0x01,0x02,0x03,0x05,0x06,0x0d,0x04,0x09,0x0a,0x0b,0x08,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{2: 0, 0, 4, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 4, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, }, +{5: 0, 2, 0, 2, 0, 4, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 2, 0, 4, 2, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 4, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{7: 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +{e: 0, 0, 4, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 4:6, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{2: 16, 0, 8, 0, 4, 0, 2, 2, 4, 4, 0, 0, 4, 2, 2, 0, }, +{4: 16, 8, 0, 4, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 6, 4, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 6, 0, 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, 0, 4, 10, }, +{5: 16, 6, 0, 10, 0, 4, 4, 0, 2, 0, 2, 4, 0, 0, 0, 0, }, +{6: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{9: 16, 0, 0, 4, 2, 6, 2, 0, 2, 2, 0, 4, 0, 2, 0, 0, }, +{a: 16, 0, 8, 0, 4, 0, 2, 2, 4, 4, 0, 0, 4, 2, 2, 0, }, +{c: 16, 0, 0, 6, 0, 8, 0, 2, 0, 0, 4, 4, 0, 2, 0, 6, }, +{7: 16, 4, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 4, 4, }, +{b: 16, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, }, +{d: 16, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +{e: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{f: 16, 0, 0, 0, 2, 6, 0, 2, 2, 2, 4, 0, 0, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:62, 4:36, 6:8, 8:10, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{6: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 8, 0, }, +{2: 16, 8, 0, 0, 0, -8, 8, 0, 0, -8, 0, 8, -8, 0, -8, -8, }, +{4: 16, 0, 0, -16, 0, 8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, }, +{8: 16, 0, 0, 16, -8, 0, 0, 0, 8, -8, -8, 0, -8, 8, -8, -8, }, +{3: 16, -8, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, 8, 0, -8, 0, }, +{5: 16, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, 0, -8, 8, }, +{6: 16, 8, -8, 0, 0, -8, 8, -8, 0, -8, 0, -8, 0, 0, 8, 0, }, +{9: 16, 0, 8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, -8, 0, 8, -8, 8, 0, 0, 8, 0, }, +{c: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 8, -8, }, +{b: 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, }, +{e: 16, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, 8, -16, 0, }, +{f: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{5: , , x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, , x, x, , x, x, , x, , , x, x, x, }, +{9: , x, x, , x, x, , x, x, , x, x, x, , , x, }, +{a: , x, x, , , x, , , , x, x, , x, , x, x, }, +{c: , x, x, , x, x, , x, x, , x, x, , , x, x, }, +{7: , , x, , , x, , x, x, , , , , x, , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , , , x, , , x, x, , x, x, , , , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x08,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x0f,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +038 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x0d,0x0c,0x09,0x0a,0x0b,0x00,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, }, +{2: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{6: 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, }, +{9: 0, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 4, 2, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, 0, }, +{7: 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, }, +{b: 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, }, +{e: 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{f: 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 4:6, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 0, 6, 6, 0, 0, 0, 0, 4, 2, 2, 0, 0, }, +{2: 16, 0, 8, 0, 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{4: 16, 4, 0, 4, 0, 0, 10, 0, 4, 0, 6, 2, 0, 0, 2, 0, }, +{8: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{3: 16, 2, 0, 0, 0, 4, 4, 0, 6, 0, 8, 2, 0, 0, 0, 6, }, +{5: 16, 4, 2, 6, 0, 0, 4, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{6: 16, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, }, +{9: 16, 0, 4, 0, 8, 2, 2, 4, 2, 4, 0, 0, 0, 0, 4, 2, }, +{a: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 16, 2, 0, 2, 0, 4, 2, 2, 0, 0, 4, 0, 2, 2, 0, 4, }, +{7: 16, 0, 0, 2, 0, 2, 4, 2, 4, 0, 4, 2, 2, 2, 0, 0, }, +{b: 16, 2, 4, 0, 8, 0, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, }, +{d: 16, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, }, +{e: 16, 0, 2, 6, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 2, }, +{f: 16, 2, 0, 4, 0, 10, 0, 0, 0, 0, 6, 4, 0, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:62, 4:36, 6:8, 8:10, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 0, 0, -8, 0, 8, 0, -8, 0, 8, -8, 0, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, -8, 8, 8, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, -8, -8, }, +{3: 16, -16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -8, 0, 0, 8, -8, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, 8, 0, 0, -16, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, -8, 8, 8, }, +{c: 16, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -8, 0, 8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, 0, -8, 8, -8, }, +{d: 16, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 8, -8, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, -8, 0, 0, 8, 8, -8, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , , x, x, , x, , x, x, , x, , x, x, , x, }, +{5: , , x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , x, , , x, x, x, }, +{9: , , x, x, x, x, , x, x, , x, x, x, , , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, x, , x, x, , , x, x, }, +{7: , , x, , , x, , x, x, , x, , , x, , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , x, x, x, , x, x, , x, x, , , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x01,}}, +{{0x09,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_039.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_039.txt new file mode 100644 index 0000000..b001c7d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_039.txt @@ -0,0 +1,408 @@ +039 Sbox: +LUT = { +0x08,0x0a,0x01,0x02,0x03,0x05,0x06,0x09,0x04,0x07,0x00,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, }, +{3: 0, 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 2, }, +{6: 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 4, 2, }, +{a: 0, 2, 0, 2, 2, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, }, +{7: 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, }, +{b: 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:7, 2:6, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 6, 0, 0, 8, 4, 6, 0, 0, 0, 0, 2, 0, 0, 2, }, +{2: 16, 4, 8, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, }, +{4: 16, 4, 0, 2, 2, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, 2, }, +{8: 16, 2, 0, 0, 4, 4, 0, 2, 2, 0, 2, 0, 4, 2, 0, 2, }, +{3: 16, 8, 4, 0, 4, 6, 0, 0, 4, 8, 0, 2, 10, 0, 0, 2, }, +{5: 16, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 4, 2, 2, 4, 2, }, +{6: 16, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, }, +{9: 16, 0, 2, 0, 0, 4, 0, 0, 8, 6, 0, 6, 0, 0, 4, 2, }, +{a: 16, 2, 0, 2, 2, 8, 4, 4, 4, 4, 0, 0, 0, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 4, 0, 2, 8, 2, }, +{7: 16, 4, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 6, 2, 0, 0, }, +{b: 16, 0, 0, 0, 4, 10, 6, 4, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:71, 4:34, 6:9, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 8, 8, 0, -8, 0, 0, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, -8, 0, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, -8, 0, 0, }, +{3: 16, -8, -16, 8, 0, 8, 0, -8, -8, 0, 0, 0, 8, -8, 0, 8, }, +{5: 16, -8, 8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 8, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, -8, 0, -8, -8, 0, 8, 0, 0, 0, -8, 8, 8, -8, 0, }, +{a: 16, 0, 8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, -8, 0, 0, 0, -8, }, +{7: 16, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{d: 16, 0, 8, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , , x, x, x, x, x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, x, x, x, , x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , , , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{7: , , , , x, x, x, x, x, x, , , , , , x, }, +{b: , x, , , x, , x, x, x, , , x, x, , , x, }, +{d: , , x, x, , , x, x, x, x, , x, , x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0010,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +039 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x08,0x05,0x06,0x09,0x00,0x07,0x01,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{8: 0, 0, 2, 2, 4, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{3: 0, 4, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, }, +{5: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +{6: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 0, }, +{a: 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 0, 2, }, +{b: 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:7, 2:6, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 2, 8, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 16, 6, 8, 0, 0, 4, 0, 2, 2, 0, 4, 0, 0, 0, 6, 0, }, +{4: 16, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{8: 16, 0, 2, 2, 4, 4, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, }, +{3: 16, 8, 4, 0, 4, 6, 0, 2, 4, 8, 0, 0, 10, 0, 2, 0, }, +{5: 16, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 6, 2, 2, 2, }, +{6: 16, 6, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 4, 2, 2, 0, }, +{9: 16, 0, 2, 0, 2, 4, 4, 0, 8, 4, 4, 2, 0, 2, 0, 0, }, +{a: 16, 0, 0, 6, 0, 8, 0, 2, 6, 4, 0, 4, 2, 0, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{7: 16, 0, 0, 2, 0, 2, 4, 2, 6, 0, 4, 2, 0, 0, 0, 2, }, +{b: 16, 2, 0, 4, 4, 10, 2, 0, 0, 0, 0, 6, 4, 0, 0, 0, }, +{d: 16, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, }, +{e: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:71, 4:34, 6:9, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{3: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{6: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, -8, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 8, 0, -16, 0, -8, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, 0, 8, -8, }, +{9: 16, -8, 8, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, 0, 0, -8, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, -8, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, -8, }, +{7: 16, 0, 0, -8, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{b: 16, -8, 0, 0, 8, 8, -8, -8, 0, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , , , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{a: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{7: , x, , x, x, x, x, x, x, x, , , , , , x, }, +{b: , , x, , , x, x, x, x, , , x, x, , , x, }, +{d: , x, x, , , x, x, x, x, x, , x, , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x0c,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x05,0x09,0x0c,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x0e,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_040.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_040.txt new file mode 100644 index 0000000..4884ae4 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_040.txt @@ -0,0 +1,408 @@ +040 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x0e,0x06,0x07,0x04,0x09,0x0a,0x0b,0x03,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, }, +{2: 0, 0, 4, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{8: 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 2, 4, 2, 4, 0, 0, 0, 0, 2, 0, }, +{6: 0, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 0, 6, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, }, +{7: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +{b: 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 4, 2, 0, }, +{e: 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:4, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 6, 0, 4, 0, 0, 2, 6, 0, 0, 8, 2, 0, }, +{2: 16, 0, 4, 6, 0, 0, 0, 10, 4, 0, 2, 0, 0, 0, 2, 4, }, +{4: 16, 0, 8, 4, 0, 0, 4, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{8: 16, 2, 0, 0, 6, 4, 0, 0, 2, 0, 2, 2, 6, 0, 0, 0, }, +{3: 16, 2, 0, 2, 4, 6, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, }, +{5: 16, 0, 2, 0, 0, 0, 6, 4, 6, 4, 0, 0, 0, 0, 2, 8, }, +{6: 16, 2, 6, 4, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 16, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, }, +{a: 16, 2, 6, 0, 4, 0, 6, 0, 0, 6, 0, 6, 2, 4, 0, 4, }, +{c: 16, 4, 0, 2, 0, 2, 0, 2, 0, 0, 4, 2, 2, 6, 0, 0, }, +{7: 16, 0, 0, 0, 2, 0, 0, 6, 4, 0, 2, 2, 2, 0, 2, 4, }, +{b: 16, 0, 0, 2, 8, 6, 4, 0, 0, 2, 0, 0, 4, 6, 0, 0, }, +{d: 16, 4, 0, 0, 0, 2, 2, 0, 2, 2, 4, 0, 2, 4, 2, 0, }, +{e: 16, 2, 4, 0, 2, 0, 6, 0, 0, 0, 0, 4, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 0, 2, 6, 0, 2, 4, 2, 2, 0, 0, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:107, 2:62, 4:32, 6:19, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 0, -8, -8, 0, 8, -8, 0, -8, 0, 8, -8, 0, }, +{4: 16, 0, -8, -8, 0, 8, 0, 0, 0, 8, -8, -8, 8, 0, 0, -8, }, +{8: 16, -8, 0, 8, 0, 8, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{3: 16, 0, 8, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, -8, 0, }, +{5: 16, 8, -8, 0, 0, -16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 8, -8, -8, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, }, +{a: 16, -8, 0, 0, 8, -8, 8, -8, -8, 8, -8, 0, -8, 8, 0, 0, }, +{c: 16, 0, 0, -8, 0, 8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{b: 16, 0, 0, 8, -8, 8, 0, -8, 0, 0, -8, 8, 0, -8, 0, -8, }, +{d: 16, -8, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 8, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, 0, -8, 0, -8, -8, }, +{f: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, x, x, x, x, x, , x, , , , x, x, x, }, +{7: , , , , x, x, x, x, , x, , x, , , x, x, }, +{b: , x, , , x, x, , , , , x, , x, , , x, }, +{d: , x, x, x, , x, x, x, , x, , , , x, x, x, }, +{e: , x, , x, , x, x, x, , x, , , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0011,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x06,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +040 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0c,0x08,0x0e,0x06,0x07,0x00,0x09,0x0a,0x0b,0x03,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 2, 4, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{8: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, }, +{3: 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 2, 0, 0, 0, 4, 4, 2, 0, 2, 2, 0, 0, 0, 0, }, +{9: 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 4, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{e: 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:9, 2:4, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 2, 0, 2, 2, 2, 4, 0, 0, 4, 2, 0, }, +{2: 16, 0, 4, 8, 0, 0, 2, 6, 2, 6, 0, 0, 0, 0, 4, 0, }, +{4: 16, 0, 6, 4, 0, 2, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, }, +{8: 16, 6, 0, 0, 6, 4, 0, 0, 0, 4, 0, 2, 8, 0, 2, 0, }, +{3: 16, 0, 0, 0, 4, 6, 0, 2, 0, 0, 2, 0, 6, 2, 0, 2, }, +{5: 16, 4, 0, 4, 0, 2, 6, 0, 0, 6, 0, 0, 4, 2, 6, 6, }, +{6: 16, 0, 10, 4, 0, 0, 4, 4, 2, 0, 2, 6, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 6, 2, 2, 0, 0, 4, 0, 2, 0, 2, }, +{a: 16, 2, 0, 2, 0, 0, 4, 0, 2, 6, 0, 0, 2, 2, 0, 4, }, +{c: 16, 6, 2, 0, 2, 2, 0, 0, 0, 0, 4, 2, 0, 4, 0, 2, }, +{7: 16, 0, 0, 4, 2, 0, 0, 2, 0, 6, 2, 2, 0, 0, 4, 2, }, +{b: 16, 0, 0, 2, 6, 4, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 16, 8, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 6, 4, 2, 0, }, +{e: 16, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{f: 16, 0, 4, 2, 0, 2, 8, 0, 2, 4, 0, 4, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:107, 2:62, 4:32, 6:19, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{2: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{6: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 8, 0, 0, -8, 0, 0, -8, 0, }, +{8: 16, -8, -8, 8, 0, 8, -8, 0, -8, 0, 0, 8, 0, 0, 0, -8, }, +{3: 16, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 8, -8, -8, 0, 0, }, +{5: 16, 0, -8, 0, -8, -8, 8, -8, -8, 8, 0, 0, 8, -8, 0, 8, }, +{6: 16, 0, 0, -8, 8, -8, 0, 0, 0, -8, -8, 0, -8, 8, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, 8, 0, 8, -8, 0, 0, -8, 0, -8, 0, }, +{a: 16, -8, 8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, 0, 8, 0, 0, -8, -8, 8, -8, -8, 0, 0, 0, }, +{7: 16, 8, 0, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, -8, 0, 0, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, 8, 0, -8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 8, -8, }, +{e: 16, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, }, +{f: 16, -8, -8, -8, 0, 8, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, x, x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, x, x, x, x, x, , x, , , , x, x, x, }, +{7: , , , x, x, x, x, x, , x, , x, , , x, x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , x, , , x, x, x, , x, , , , x, x, x, }, +{e: , x, x, x, , x, x, x, , x, , , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x05,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_041.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_041.txt new file mode 100644 index 0000000..176605a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_041.txt @@ -0,0 +1,408 @@ +041 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x0d,0x03,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x05,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, }, +{2: 0, 2, 4, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, }, +{8: 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 0, 0, 2, 0, 0, 2, 6, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 4, 0, 0, 2, 0, }, +{9: 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, }, +{a: 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +{c: 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{d: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 2, 2, }, +{f: 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:7, 2:4, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 2, 8, 0, 6, 0, 6, 0, 0, 4, 2, 4, 0, 0, 0, 0, }, +{4: 16, 4, 2, 4, 0, 0, 4, 2, 0, 2, 2, 0, 0, 2, 0, 2, }, +{8: 16, 0, 6, 0, 4, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{3: 16, 2, 0, 0, 0, 4, 6, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 16, 4, 6, 4, 0, 6, 6, 6, 2, 0, 0, 4, 2, 0, 0, 0, }, +{6: 16, 0, 0, 4, 2, 10, 6, 4, 0, 0, 0, 4, 0, 0, 2, 0, }, +{9: 16, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, }, +{a: 16, 2, 4, 0, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, 2, 2, }, +{c: 16, 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 6, }, +{7: 16, 0, 4, 4, 0, 4, 4, 0, 2, 2, 2, 8, 0, 0, 0, 2, }, +{b: 16, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{d: 16, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 2, 4, }, +{e: 16, 0, 0, 4, 2, 0, 2, 2, 4, 2, 0, 0, 0, 4, 2, 2, }, +{f: 16, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 2, 2, 4, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:70, 4:40, 6:11, 8:2, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{a: 0, 4, 4, 0, 4, 0, 4, 4, 8, 8, 4, 0, 4, 0, 0, 4, }, +{c: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{e: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:9, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, -8, 8, 8, 8, 0, -16, 0, -8, -8, 0, }, +{2: 16, 8, 0, 8, 0, -8, 8, -8, -8, 0, 0, -8, -8, 0, 0, 0, }, +{4: 16, 8, 0, -8, 0, 0, 0, -8, 8, 0, 0, -8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 0, -8, -8, -8, 0, 8, 8, 0, 0, 0, 0, }, +{5: 16, -8, 0, 0, 8, -8, 0, -8, 0, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 0, -8, -8, 8, 0, 0, 8, -8, -8, -8, 8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, 8, 0, -8, }, +{c: 16, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, -8, 0, }, +{7: 16, -8, -8, 0, 0, 8, 0, 0, -8, -8, 0, -8, 8, 0, 0, 8, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, 0, 8, -8, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{f: 16, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, -8, 8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, x, , x, x, , x, , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x06,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x06,0x09,0x0f,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x01,0x06,0x07,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x07,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +041 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x0d,0x08,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x05,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + + + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 4, 2, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 6, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, }, +{a: 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{c: 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, }, +{d: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, }, +{e: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:7, 2:4, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 0, 2, }, +{2: 16, 0, 8, 2, 6, 0, 6, 0, 2, 4, 0, 4, 0, 0, 0, 0, }, +{4: 16, 16, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 16, 0, 6, 0, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{3: 16, 4, 0, 0, 2, 4, 6, 10, 0, 0, 0, 4, 2, 0, 0, 0, }, +{5: 16, 4, 6, 4, 0, 6, 6, 6, 0, 0, 2, 4, 0, 0, 2, 0, }, +{6: 16, 0, 0, 2, 0, 4, 6, 4, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 16, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, 6, }, +{a: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{c: 16, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{7: 16, 4, 4, 0, 0, 0, 4, 4, 2, 2, 2, 8, 0, 0, 0, 2, }, +{b: 16, 4, 0, 0, 2, 2, 2, 0, 0, 2, 4, 0, 2, 4, 0, 2, }, +{d: 16, 4, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 4, 4, }, +{e: 16, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 4, 0, 2, 0, 0, 0, 0, 0, 2, 6, 2, 2, 4, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:70, 4:40, 6:11, 8:2, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 8, 0, 0, 0, 4, 4, }, +{c: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:9, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 8, 0, 8, 0, -8, 8, -8, 0, 0, -8, -8, 0, 0, -8, 0, }, +{4: 16, 0, 8, -8, 0, 8, -8, 0, 0, 8, 8, -16, -8, -8, 0, 0, }, +{8: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 8, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 0, 0, 8, -8, 8, -8, 8, }, +{6: 16, 0, 0, -8, 0, -8, -8, 0, 8, 0, -8, 8, 0, 0, 0, 0, }, +{9: 16, -8, 8, 0, 0, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, 8, -8, -8, }, +{c: 16, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, 0, 0, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, -8, -8, 0, 0, 8, 8, }, +{b: 16, -8, 0, 0, -8, 0, 8, -8, 0, 0, 0, 8, 0, -8, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, -8, -8, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{f: 16, 0, 0, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, , , x, , , x, , x, x, , x, , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0111,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x09,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x0c,}, {0x0b,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x09,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x05,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_042.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_042.txt new file mode 100644 index 0000000..a2d7f7f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_042.txt @@ -0,0 +1,408 @@ +042 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x0a,0x03,0x07,0x06,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 2, 6, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 2, 4, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, }, +{8: 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 2, 0, 0, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 4, 0, 2, 0, }, +{6: 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 4, 0, 2, }, +{a: 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 2, }, +{d: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 0, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:7, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 2, 8, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{2: 16, 6, 6, 4, 2, 6, 6, 4, 0, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 0, 6, 4, 0, 0, 0, 10, 0, 4, 4, 0, 2, 0, 0, 2, }, +{8: 16, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{3: 16, 10, 4, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 6, 0, 0, }, +{5: 16, 0, 6, 0, 0, 0, 8, 2, 0, 2, 0, 4, 4, 0, 6, 0, }, +{6: 16, 0, 6, 8, 2, 6, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 16, 4, 0, 0, 0, 0, 0, 4, 2, 6, 10, 0, 0, 4, 0, 2, }, +{a: 16, 4, 0, 0, 0, 0, 2, 0, 0, 2, 6, 2, 2, 4, 0, 2, }, +{c: 16, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 16, 0, 4, 4, 2, 4, 4, 0, 2, 2, 0, 8, 2, 0, 0, 0, }, +{b: 16, 0, 0, 2, 2, 0, 6, 0, 0, 0, 0, 0, 6, 2, 4, 2, }, +{d: 16, 0, 2, 0, 2, 0, 0, 6, 2, 4, 4, 0, 2, 0, 2, 0, }, +{e: 16, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 4, 2, 6, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:63, 4:31, 6:16, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{b: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, -8, 8, 0, 8, 0, -8, 0, -8, -8, -8, }, +{2: 16, 0, 0, 8, 8, -8, 8, -8, 0, -8, 8, 0, -8, 0, -8, -8, }, +{4: 16, 8, -8, 0, 0, 0, 0, -8, 8, 8, -8, -8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, -8, -8, }, +{3: 16, -8, 8, 0, 0, 0, -8, -8, -8, -8, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, -8, 0, 0, -8, 0, -8, 0, 8, -8, 8, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, 0, 8, 0, -16, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, -8, -8, -8, 0, 0, 8, -8, 0, 0, 0, -8, 8, 8, }, +{a: 16, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, -8, -8, 0, 8, 0, }, +{c: 16, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{7: 16, -8, -8, 8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, }, +{b: 16, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, }, +{d: 16, 8, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, }, +{e: 16, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, x, , x, , x, , x, , x, }, +{6: , x, , x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, , , , , x, x, , x, , x, , , , x, }, +{b: , , , x, x, x, x, x, , x, , , x, , , x, }, +{d: , , x, , , , x, x, , x, , , , x, , x, }, +{e: , x, , x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x06,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +042 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x0a,0x08,0x07,0x03,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 6, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{8: 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, }, +{3: 0, 0, 2, 0, 2, 4, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 4, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 2, 0, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +{a: 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 4, 0, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, 0, 2, }, +{d: 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 2, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:155, 2:81, 4:18, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:7, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 6, 0, 0, 10, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, }, +{2: 16, 4, 6, 6, 2, 4, 6, 6, 0, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 4, 4, 4, 2, 0, 0, 8, 0, 0, 2, 4, 2, 0, 0, 2, }, +{8: 16, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, }, +{3: 16, 8, 6, 0, 2, 4, 0, 6, 0, 0, 2, 4, 0, 0, 0, 0, }, +{5: 16, 0, 6, 0, 0, 2, 8, 0, 0, 2, 0, 4, 6, 0, 4, 0, }, +{6: 16, 0, 4, 10, 0, 0, 2, 4, 4, 0, 2, 0, 0, 6, 0, 0, }, +{9: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +{a: 16, 0, 0, 4, 0, 0, 2, 0, 6, 2, 0, 2, 0, 4, 2, 2, }, +{c: 16, 0, 0, 4, 0, 4, 0, 0, 10, 6, 2, 0, 0, 4, 0, 2, }, +{7: 16, 4, 4, 0, 2, 0, 4, 4, 0, 2, 2, 8, 0, 0, 2, 0, }, +{b: 16, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 6, 2, 4, 2, }, +{d: 16, 0, 2, 0, 2, 6, 0, 0, 4, 4, 2, 0, 2, 0, 2, 0, }, +{e: 16, 2, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 4, 2, 6, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:63, 4:31, 6:16, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 8, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{2: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{b: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, -8, 8, 0, -8, 0, 0, -8, 8, 8, -8, 0, -8, 0, 0, }, +{2: 16, 8, 0, 0, 8, -8, 8, -8, 8, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, 8, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, -8, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, }, +{3: 16, 0, -8, 0, 8, 8, 0, 0, -8, -16, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, -8, 0, 0, -8, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, }, +{6: 16, 0, 8, -8, 0, -8, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, }, +{9: 16, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, }, +{a: 16, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, -8, 8, 0, -8, 0, }, +{c: 16, -8, 0, 0, -8, 0, 0, -8, 0, -8, 8, 0, 8, -8, 0, 8, }, +{7: 16, 8, -8, -8, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, -8, 0, -8, 0, 0, 8, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, 0, }, +{e: 16, -8, 0, 0, -8, 0, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, , x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, , x, , , x, x, , x, , , x, , , x, }, +{d: , , x, , , x, x, , , x, , , , x, , x, }, +{e: , x, , , x, x, x, x, , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{1010,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x03,0x09,0x0a,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x05,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_043.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_043.txt new file mode 100644 index 0000000..53f6766 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_043.txt @@ -0,0 +1,420 @@ +043 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x05,0x04,0x0c,0x00,0x09,0x0a,0x0b,0x07,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{8: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, 2, 0, }, +{6: 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, }, +{9: 0, 0, 4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 4, 4, 0, 0, 0, 2, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 4, }, +{e: 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:75, 4:21, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 2, 2, 2, 0, 0, 0, 0, 2, 0, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 4, 8, 6, 0, 4, 8, 4, 0, 0, 0, 10, 0, 2, 2, 0, }, +{8: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 2, 0, 6, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{5: 16, 8, 0, 4, 0, 2, 4, 2, 0, 0, 4, 0, 2, 4, 2, 0, }, +{6: 16, 0, 8, 6, 0, 0, 4, 4, 0, 0, 0, 6, 0, 2, 2, 0, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 4, 0, 0, 0, 4, 0, 0, 0, 2, 10, 0, 2, 6, 0, 4, }, +{c: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 16, 2, 0, 6, 0, 8, 0, 0, 0, 2, 4, 4, 0, 0, 0, 6, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 4, 2, 2, 0, 2, 6, 0, 2, 0, 2, 4, }, +{e: 16, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +{f: 16, 4, 0, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 6, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:61, 4:35, 6:13, 8:7, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{6: 0, 8, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 8, 0, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, -8, 8, 0, -8, 8, 0, 0, -8, -8, -16, 8, 8, 0, 0, }, +{4: 16, 0, 8, -16, 8, 0, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, }, +{8: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, -8, }, +{9: 16, 8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, -8, }, +{a: 16, -8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{c: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, -16, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 8, -8, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, 8, }, +{e: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, , x, , , x, }, +{5: , x, x, , x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, , , x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, , x, , x, x, , , x, x, , x, x, x, }, +{7: , x, x, , , x, x, x, , , x, , , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , x, x, , x, , x, , , , x, x, , x, , x, }, +{e: , x, x, , , , x, x, , , x, x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x07,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x07,0x08,0x0f,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +043 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x05,0x00,0x0c,0x01,0x09,0x0a,0x0b,0x07,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 6, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, }, +{8: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{9: 0, 2, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 0, 4, }, +{7: 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{e: 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 4, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:75, 4:21, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 8, 0, 0, 4, 2, 2, 0, 0, 0, 4, }, +{2: 16, 0, 16, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{4: 16, 4, 4, 6, 2, 6, 4, 6, 0, 0, 0, 6, 0, 0, 2, 0, }, +{8: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{3: 16, 2, 0, 4, 2, 4, 2, 0, 0, 4, 2, 8, 0, 4, 0, 0, }, +{5: 16, 4, 4, 8, 0, 0, 4, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 16, 2, 4, 4, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 4, 0, 2, 0, 0, 0, 6, 2, 0, 2, 4, 2, 0, 0, }, +{c: 16, 0, 0, 0, 0, 0, 4, 0, 0, 10, 2, 4, 2, 6, 0, 4, }, +{7: 16, 0, 4, 10, 0, 4, 0, 6, 0, 0, 2, 4, 0, 0, 2, 0, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 4, 2, 0, 6, 2, 0, 2, 0, 0, 6, }, +{e: 16, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{f: 16, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 6, 0, 4, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:61, 4:35, 6:13, 8:7, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, -8, 0, -8, 8, 0, }, +{2: 16, 0, -8, 8, 0, -8, -8, 0, 16, -8, -8, 0, -8, 8, 0, 0, }, +{4: 16, 8, 0, -8, 8, 8, -8, 0, 0, 0, -8, 0, 8, -8, -8, -8, }, +{8: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -16, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, }, +{9: 16, 0, -8, 8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, -8, }, +{a: 16, 0, 0, 8, 0, -8, 8, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{c: 16, -8, -8, -8, -8, 8, 8, 0, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 0, 8, -8, 0, -8, 0, 0, 8, }, +{e: 16, 0, 8, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, -8, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, 8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, , x, , , x, }, +{5: , x, x, , x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{7: , , x, , , x, x, x, , , x, , , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, x, , x, x, x, , , , x, x, , x, , x, }, +{e: , x, x, x, x, , x, x, , , x, x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x03,0x05,0x06,}}, +{{0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x04,0x09,0x0d,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x04,0x09,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_044.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_044.txt new file mode 100644 index 0000000..29c911c --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_044.txt @@ -0,0 +1,420 @@ +044 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x05,0x04,0x0d,0x00,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{2: 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{8: 0, 2, 4, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, }, +{5: 0, 0, 0, 0, 0, 2, 6, 2, 0, 0, 2, 2, 2, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 4, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 0, 2, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 4, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:75, 4:21, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:1, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 0, 2, 4, 2, 4, 0, 0, 0, 2, 4, 2, 0, }, +{2: 16, 0, 16, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{4: 16, 4, 4, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{8: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 2, 0, 4, 4, 8, 4, 0, 0, 0, 2, 0, 2, 4, }, +{5: 16, 4, 4, 4, 0, 6, 6, 6, 0, 0, 2, 6, 2, 0, 0, 0, }, +{6: 16, 0, 4, 0, 0, 4, 10, 4, 0, 0, 2, 6, 0, 0, 2, 0, }, +{9: 16, 0, 4, 2, 4, 2, 0, 0, 2, 6, 0, 0, 2, 0, 0, 2, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 0, 0, 0, 2, 0, 6, 4, 2, 2, 0, 0, 2, 2, 4, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{d: 16, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 16, 0, 0, 4, 2, 0, 2, 0, 6, 0, 0, 2, 0, 6, 2, 0, }, +{f: 16, 0, 0, 4, 2, 0, 0, 4, 10, 0, 0, 0, 0, 4, 2, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:61, 4:35, 6:13, 8:7, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{7: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 8, -8, 8, 0, 0, 16, 0, -8, -8, -8, -8, 0, 0, 0, -8, }, +{4: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{8: 16, 0, -8, 8, 0, -8, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 0, 0, -16, 0, 0, 0, 0, 0, 8, 0, -8, 0, }, +{5: 16, -8, 0, -8, 8, 0, 0, -8, -8, 0, -8, 8, -8, 8, 0, 8, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, }, +{9: 16, 0, 0, 8, -8, 8, 0, 0, 0, 0, -8, 0, 0, -8, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, 8, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, }, +{e: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, -8, 0, 8, 8, -8, 0, 8, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{5: , , x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, , x, x, , x, x, , x, , , x, x, x, }, +{9: , x, x, x, x, x, , x, x, , x, x, x, , , x, }, +{a: , x, , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, , x, x, , , x, x, }, +{7: , , x, , , x, , x, x, , x, , , x, , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , x, , x, , , , x, , x, x, , , , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x05,0x09,0x0c,}}, +{{0x09,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x03,0x05,0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +044 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x05,0x00,0x0d,0x01,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, }, +{8: 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 4, }, +{9: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 4, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{7: 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 0, }, +{b: 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 4, }, +{e: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:75, 4:21, 6:1, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:1, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 8, 0, 4, 0, 2, 4, 0, 2, 0, 0, 2, 0, 2, 4, 4, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 4, 2, 2, 2, 0, 2, 0, 0, 0, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 0, 0, 0, 4, 0, 2, 2, 0, }, +{6: 16, 2, 0, 0, 2, 8, 6, 4, 0, 0, 6, 0, 0, 0, 0, 4, }, +{9: 16, 4, 0, 0, 2, 4, 0, 0, 2, 0, 4, 0, 0, 0, 6, 10, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{7: 16, 0, 8, 4, 0, 0, 6, 6, 0, 0, 0, 4, 0, 2, 2, 0, }, +{b: 16, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 16, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 6, 4, }, +{e: 16, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 2, 4, 0, 0, 2, 0, 4, 2, 0, 2, 0, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:61, 4:35, 6:13, 8:7, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 8, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 0, 0, 0, 0, 8, -8, -8, 8, -16, 0, 0, -8, }, +{4: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, -8, -8, }, +{8: 16, 0, -8, 8, -8, -8, 0, 0, 8, 0, 0, -8, 0, 8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, 8, -16, 8, -8, 0, -8, 0, 8, -8, 8, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, -16, -8, 0, 8, }, +{9: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, -8, 8, 0, 0, -8, 0, 0, 0, 8, 0, -8, }, +{b: 16, -8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, -8, -8, -8, 8, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{5: , x, x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{9: , , x, x, x, x, , , x, , x, x, x, , , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{7: , x, x, , , x, , x, x, , x, , , x, , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, , x, x, , , x, , x, x, , , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0101,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x0b,}}, +{{0x05,0x06,}, {0x04,0x0b,0x0f,}}, +{{0x09,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_045.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_045.txt new file mode 100644 index 0000000..817bc1a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_045.txt @@ -0,0 +1,420 @@ +045 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x05,0x04,0x09,0x00,0x07,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 4, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 2, 4, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +{a: 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, }, +{b: 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:75, 4:21, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:12, 2:1, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{2: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 16, 4, 4, 4, 0, 0, 8, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 16, 0, 0, 4, 2, 0, 0, 4, 6, 2, 0, 0, 6, 0, 0, 8, }, +{3: 16, 6, 4, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 16, 4, 0, 8, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 4, }, +{6: 16, 6, 4, 0, 2, 0, 4, 4, 0, 0, 0, 10, 0, 0, 2, 0, }, +{9: 16, 2, 4, 0, 4, 0, 0, 0, 2, 6, 0, 2, 2, 0, 2, 0, }, +{a: 16, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 6, 0, 2, 0, 0, 0, 8, 6, 0, 2, 4, 0, 0, 0, 4, }, +{b: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 2, 0, 2, 2, 0, 0, }, +{d: 16, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 6, 0, 2, 6, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 2, 0, 6, 4, 0, 2, 0, 0, 0, 2, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:59, 4:40, 6:16, 8:4, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{3: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{5: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{f: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 0, 0, 8, -8, -8, -8, 0, -16, 0, 8, 8, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 8, 0, -8, 0, -8, -8, 0, 8, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, -8, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, -8, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, }, +{a: 16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, -8, 0, -8, 8, -8, 0, 0, -8, 8, 0, 0, }, +{d: 16, 0, 0, -8, 0, 8, -8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , , x, x, , , x, }, +{5: , , x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , , , , , x, x, }, +{9: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{7: , , x, x, , x, x, x, x, , , , , , , x, }, +{b: , x, x, , x, , x, , x, , , x, x, , , x, }, +{d: , , x, x, x, , x, , x, , , x, , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x03,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +045 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x05,0x00,0x09,0x01,0x07,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{8: 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{9: 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 4, }, +{a: 0, 0, 4, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, }, +{7: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 2, 2, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:75, 4:21, 6:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:12, 2:1, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 6, 4, 6, 2, 2, 0, 6, 0, 0, 0, 0, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 4, 0, 4, 4, 2, 8, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{8: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 2, 2, }, +{3: 16, 6, 4, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 16, 4, 4, 8, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 6, 0, 0, 4, 0, 2, 4, 0, 0, 0, 8, 2, 0, 0, 6, }, +{9: 16, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 6, 2, 0, 2, 4, }, +{a: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 6, 4, 4, 0, 0, 0, 10, 2, 0, 0, 4, 0, 0, 2, 0, }, +{b: 16, 0, 0, 2, 6, 2, 4, 0, 2, 0, 0, 0, 2, 6, 0, 0, }, +{d: 16, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 8, 0, 4, 0, 0, 0, 2, 4, 0, 6, 2, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:59, 4:40, 6:16, 8:4, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{f: 0, 4, 4, 4, 0, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 8, -8, 0, 0, -8, 0, -8, 8, 0, }, +{2: 16, 8, -8, 0, 0, 0, -8, -8, 8, -8, 0, 0, -16, 8, 8, 0, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 16, -8, 0, -8, }, +{8: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -16, -8, 0, 0, }, +{9: 16, -8, -8, 0, -8, 8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 0, }, +{c: 16, 0, -8, 0, 0, 0, 8, -8, 8, 0, 0, -8, 0, 0, 0, -8, }, +{7: 16, 0, -8, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{b: 16, -8, 8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, -8, 0, }, +{d: 16, 0, 0, 0, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, 8, 8, -8, -8, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , , , , , x, x, }, +{9: , , x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{7: , x, x, x, , x, x, x, x, , , , , , , x, }, +{b: , , x, , x, x, x, x, x, , , x, x, , , x, }, +{d: , , x, x, x, x, x, , x, , , x, , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0101,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x03,0x08,0x0b,}}, +{{0x05,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x04,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_046.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_046.txt new file mode 100644 index 0000000..d136d6f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_046.txt @@ -0,0 +1,408 @@ +046 Sbox: +LUT = { +0x0d,0x0a,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x00,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 6, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, }, +{4: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{5: 0, 0, 0, 2, 2, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{9: 0, 0, 2, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 0, 2, }, +{c: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:7, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, 0, }, +{2: 16, 0, 6, 2, 2, 0, 6, 0, 4, 0, 6, 6, 4, 0, 4, 0, }, +{4: 16, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 0, 4, 4, 2, }, +{8: 16, 6, 0, 0, 4, 2, 0, 4, 8, 0, 0, 0, 0, 2, 0, 6, }, +{3: 16, 0, 0, 2, 0, 4, 0, 6, 10, 4, 0, 0, 2, 0, 0, 4, }, +{5: 16, 0, 4, 2, 2, 0, 4, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{6: 16, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, }, +{9: 16, 4, 6, 2, 4, 4, 0, 0, 6, 6, 0, 0, 6, 0, 2, 0, }, +{a: 16, 2, 0, 0, 0, 8, 2, 0, 4, 4, 0, 0, 2, 4, 4, 2, }, +{c: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 2, 4, 2, 2, 0, 4, 0, 0, 2, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 4, 8, 2, 2, 0, 4, 0, 2, 4, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 6, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 6, 8, 0, }, +{f: 16, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:71, 4:35, 6:14, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{6: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:8, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 8, 0, 8, -8, 0, -8, 0, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 0, 0, 8, -8, 8, 0, 0, 0, 0, -8, -8, }, +{8: 16, -8, 8, 8, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, -8, 0, }, +{3: 16, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, }, +{6: 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, -8, 8, 8, -8, 0, }, +{a: 16, -8, 0, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 8, -8, 0, -8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, 0, -8, 0, -8, -8, 0, 8, 8, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, , x, x, x, , x, x, x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , , x, , x, x, x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{7: , x, x, , , , x, , x, x, x, x, , x, , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , , , x, x, , , , x, , , , x, , x, }, +{e: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0f,}}, +{{0x0a,0x04,}, {0x03,0x09,0x0a,}}, +{{0x02,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x04,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +046 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x0d,0x09,0x01,0x0b,0x0c,0x00,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, }, +{4: 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, }, +{9: 0, 0, 0, 0, 4, 2, 2, 0, 6, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 2, 0, 0, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, }, +{b: 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:7, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 6, 0, 0, 0, 4, 2, 2, 2, 0, 2, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 4, 2, 6, 0, 6, 4, 4, 0, 6, 2, }, +{4: 16, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 16, 4, 2, 2, 4, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 16, 2, 0, 4, 2, 4, 0, 2, 4, 8, 0, 0, 0, 0, 4, 2, }, +{5: 16, 0, 6, 2, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 2, }, +{6: 16, 2, 0, 0, 4, 6, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, }, +{9: 16, 4, 4, 0, 8, 10, 2, 0, 6, 4, 0, 0, 8, 0, 0, 2, }, +{a: 16, 0, 0, 0, 0, 4, 0, 2, 6, 4, 0, 2, 2, 2, 2, 0, }, +{c: 16, 0, 6, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 2, 4, 0, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 0, 2, 4, 0, 2, 0, 0, }, +{b: 16, 2, 4, 0, 0, 2, 0, 2, 6, 2, 0, 2, 4, 0, 0, 0, }, +{d: 16, 2, 0, 4, 2, 0, 0, 2, 0, 4, 2, 0, 0, 2, 6, 0, }, +{e: 16, 0, 4, 4, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 8, 2, }, +{f: 16, 0, 0, 2, 6, 4, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:71, 4:35, 6:14, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 12, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:8, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 0, -8, 0, 0, 8, -8, 8, -8, -8, 8, -8, 0, }, +{4: 16, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, 0, -8, 0, -8, -8, }, +{3: 16, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, -8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, -8, 0, 8, 0, }, +{9: 16, -8, 8, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 0, -16, 8, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 8, 0, }, +{7: 16, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, }, +{e: 16, 0, 0, -8, -8, 0, -8, 0, 8, 8, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, , x, x, , x, , x, x, x, , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{7: , x, x, , , , , , , x, , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , x, , x, x, , , , , x, , , , x, , x, }, +{e: , x, , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x08,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_047.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_047.txt new file mode 100644 index 0000000..fa29409 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_047.txt @@ -0,0 +1,408 @@ +047 Sbox: +LUT = { +0x0e,0x00,0x01,0x0a,0x03,0x05,0x06,0x07,0x04,0x09,0x02,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 2, 0, 4, 0, 0, 0, }, +{c: 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, }, +{b: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, }, +{d: 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 6, 2, 2, 0, }, +{2: 16, 0, 6, 6, 4, 0, 2, 6, 0, 6, 4, 0, 0, 0, 4, 2, }, +{4: 16, 0, 4, 8, 2, 0, 2, 4, 4, 2, 0, 2, 0, 4, 0, 0, }, +{8: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 8, 4, 0, 0, 2, 4, 0, 2, }, +{5: 16, 0, 0, 0, 4, 4, 2, 2, 2, 0, 2, 0, 6, 2, 0, 0, }, +{6: 16, 0, 6, 4, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 16, 0, 0, 2, 2, 4, 0, 0, 4, 6, 0, 2, 0, 0, 2, 2, }, +{a: 16, 4, 4, 0, 8, 10, 2, 0, 4, 6, 2, 0, 8, 0, 0, 0, }, +{c: 16, 0, 6, 2, 0, 0, 2, 0, 2, 0, 4, 2, 0, 2, 4, 0, }, +{7: 16, 2, 0, 6, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 0, 2, }, +{b: 16, 4, 2, 0, 2, 0, 2, 0, 0, 4, 2, 0, 4, 2, 2, 0, }, +{d: 16, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 4, 6, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:71, 4:35, 6:14, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{c: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{f: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, 0, 0, -8, -8, 0, -8, 0, }, +{4: 16, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 0, 8, -8, 0, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, 0, 8, 0, 0, 0, -8, -8, 0, }, +{5: 16, -8, 0, 0, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 8, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -16, -8, 8, -8, 0, 0, 0, 8, 8, }, +{c: 16, 0, 8, -8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 8, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, -8, 8, 8, 0, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, 8, 0, -8, }, +{d: 16, 0, 0, 0, 0, -8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, 0, 0, 0, 8, 0, 8, -8, -8, 0, 0, -8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , x, , x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , x, , , , , x, , , x, x, , , x, x, }, +{b: , x, , , , x, , x, , x, x, , x, , x, x, }, +{d: , , , x, , x, , x, , x, x, , , x, x, x, }, +{e: , , , , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0110,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x03,}}, +{{0x03,0x0c,}, {0x03,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0d,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x09,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +047 Inverse Sbox: +LUT = { +0x01,0x02,0x0a,0x04,0x08,0x05,0x06,0x07,0x0e,0x09,0x03,0x0b,0x0c,0x0d,0x00,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{4: 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{3: 0, 0, 0, 0, 2, 4, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 2, 4, 0, 0, 0, 0, }, +{a: 0, 0, 2, 2, 2, 0, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +{b: 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 4, 0, }, +{f: 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 2, 2, }, +{2: 16, 0, 6, 4, 4, 0, 0, 6, 0, 4, 6, 0, 2, 2, 6, 0, }, +{4: 16, 0, 6, 8, 0, 4, 0, 4, 2, 0, 2, 6, 0, 0, 0, 0, }, +{8: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{3: 16, 0, 0, 0, 2, 4, 4, 0, 4, 10, 0, 0, 0, 2, 0, 6, }, +{5: 16, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 2, 6, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 16, 2, 0, 4, 2, 8, 2, 0, 4, 4, 2, 4, 0, 0, 0, 0, }, +{a: 16, 4, 6, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 2, 4, 2, }, +{7: 16, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +{b: 16, 6, 0, 0, 0, 2, 6, 0, 0, 8, 0, 2, 4, 0, 0, 4, }, +{d: 16, 2, 0, 4, 0, 4, 2, 0, 0, 0, 2, 4, 2, 2, 2, 0, }, +{e: 16, 2, 4, 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 2, 4, 0, }, +{f: 16, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:71, 4:35, 6:14, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 0, -8, 0, -8, 8, -8, 8, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 8, 8, -8, -8, 0, -8, 0, -8, 8, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 8, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, 0, 0, 0, 0, 8, -8, -8, 0, 0, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, -8, 8, 0, 0, 0, 0, 8, -8, -8, -8, -8, 0, 8, 0, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, 0, 0, -8, -8, 8, -8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, -8, 8, 0, 0, 0, -8, -8, 8, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, 0, -8, -8, -8, 8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, , x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , , x, x, , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , x, , , , x, , , , x, , x, , , , x, }, +{b: , , x, , , , , x, , x, x, , x, , x, x, }, +{d: , , , , x, , , x, , x, x, , , x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x0e,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_048.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_048.txt new file mode 100644 index 0000000..c3922a0 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_048.txt @@ -0,0 +1,408 @@ +048 Sbox: +LUT = { +0x08,0x0a,0x01,0x02,0x03,0x05,0x09,0x07,0x04,0x06,0x00,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, }, +{2: 0, 0, 6, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 2, 0, 2, }, +{6: 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 6, 0, }, +{a: 0, 2, 0, 2, 2, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, }, +{b: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, }, +{e: 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 0, 0, 6, 0, 2, 0, 0, 4, 0, 2, 0, 6, 0, }, +{2: 16, 4, 6, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 2, 0, 0, }, +{4: 16, 0, 0, 2, 4, 0, 10, 0, 0, 0, 0, 0, 4, 4, 6, 2, }, +{8: 16, 2, 8, 0, 4, 0, 0, 0, 2, 4, 4, 2, 0, 0, 4, 2, }, +{3: 16, 4, 4, 2, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 16, 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 2, 2, 4, 2, }, +{6: 16, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, }, +{9: 16, 0, 10, 0, 0, 0, 4, 2, 8, 2, 4, 4, 8, 0, 6, 0, }, +{a: 16, 2, 4, 2, 10, 0, 4, 0, 0, 4, 0, 0, 0, 6, 0, 0, }, +{c: 16, 0, 0, 2, 0, 2, 0, 0, 6, 0, 2, 4, 0, 2, 4, 2, }, +{7: 16, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, }, +{b: 16, 0, 4, 2, 0, 2, 0, 2, 4, 2, 2, 2, 4, 0, 0, 0, }, +{d: 16, 2, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 4, 0, 6, 0, }, +{e: 16, 2, 0, 0, 4, 2, 6, 2, 0, 0, 0, 0, 0, 4, 2, 2, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:71, 4:33, 6:12, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{4: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{e: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, -8, 8, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, }, +{2: 16, 8, 0, 8, 0, -8, 8, -8, 8, -8, 0, -8, 0, 0, -8, -8, }, +{4: 16, 0, 0, 0, -8, 8, 0, 0, 0, 8, -8, 8, -8, 0, -8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, -8, -8, 0, -8, -8, 0, 0, 0, }, +{3: 16, 0, -8, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, -8, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{9: 16, 8, -8, 0, -8, -16, -8, 8, 0, 0, 0, 0, 8, 8, -8, 0, }, +{a: 16, 0, 8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, -8, 0, -8, 0, 8, 0, 0, 0, -8, 0, -8, 8, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, }, +{b: 16, 0, -8, 0, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, }, +{e: 16, -8, 0, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, -8, 0, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , , x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, , x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, x, x, x, , , x, x, x, }, +{7: , x, , , x, , , x, x, x, , x, , , , x, }, +{b: , , , , x, x, , x, x, , , , x, , , x, }, +{d: , x, x, x, , x, , x, x, x, , , , x, , x, }, +{e: , x, , x, , x, , x, x, x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0011,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0f,}}, +{{0x0a,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x0b,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,}}, +{{0x05,0x02,}, {0x09,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x03,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +048 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x08,0x05,0x09,0x07,0x00,0x06,0x01,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{2: 0, 4, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, }, +{8: 0, 0, 2, 4, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +{5: 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 2, 2, }, +{6: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 4, 2, 4, 0, 2, 0, 0, 0, 0, 0, }, +{a: 0, 0, 2, 0, 0, 2, 2, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 2, }, +{b: 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 4, 0, }, +{e: 0, 2, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{2: 16, 8, 6, 0, 8, 4, 0, 2, 10, 4, 0, 0, 4, 2, 0, 0, }, +{4: 16, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, }, +{8: 16, 0, 6, 4, 4, 0, 0, 0, 0, 10, 0, 2, 0, 0, 4, 2, }, +{3: 16, 6, 4, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +{5: 16, 0, 0, 10, 0, 0, 2, 0, 4, 4, 0, 0, 0, 4, 6, 2, }, +{6: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 4, 2, 8, 0, 6, 0, 4, 0, 0, 0, }, +{a: 16, 0, 6, 0, 4, 2, 2, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 16, 4, 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 2, 2, 0, 2, }, +{7: 16, 0, 0, 0, 2, 0, 4, 2, 4, 0, 4, 2, 2, 2, 0, 2, }, +{b: 16, 2, 4, 4, 0, 2, 2, 0, 8, 0, 0, 2, 4, 4, 0, 0, }, +{d: 16, 0, 2, 4, 0, 0, 2, 2, 0, 6, 2, 2, 0, 0, 4, 0, }, +{e: 16, 6, 0, 6, 4, 0, 4, 0, 6, 0, 4, 0, 0, 6, 2, 2, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:71, 4:33, 6:12, 8:4, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{2: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{3: 0, 4, 0, 0, 4, 12, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{d: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 0, 0, 8, 8, -16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, }, +{4: 16, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 8, 0, 0, 0, 8, 8, 0, 0, 0, -8, -8, 0, -8, -8, -8, }, +{3: 16, -8, -8, 0, 0, 8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, -8, -8, -8, 8, -8, 0, 8, 0, 0, 8, -8, 0, 0, }, +{6: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, 0, -8, 8, -8, 8, }, +{a: 16, 0, -8, 8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 8, -8, -8, 0, 0, }, +{7: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, }, +{b: 16, -8, 0, 0, 8, 8, -8, -8, 0, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, 8, -8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 16, -8, 8, 0, -8, -8, -8, 8, 8, 0, 0, -8, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , x, x, , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , , x, x, x, }, +{7: , , , x, x, , , x, x, x, , x, , , , x, }, +{b: , x, x, , , , , x, x, , , , x, , , x, }, +{d: , , x, , , , , x, x, x, , , , x, , x, }, +{e: , x, x, , x, x, , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x0c,}}, +{{0x03,0x08,}, {0x0f,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x0e,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_049.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_049.txt new file mode 100644 index 0000000..e8882d0 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_049.txt @@ -0,0 +1,408 @@ +049 Sbox: +LUT = { +0x08,0x00,0x01,0x0d,0x02,0x05,0x06,0x07,0x04,0x09,0x03,0x0b,0x0c,0x0a,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 2, 2, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{6: 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 4, 2, 0, 0, }, +{c: 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, }, +{b: 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 8, 4, 0, 2, 4, 0, 2, 2, 4, 2, 0, 0, }, +{2: 16, 0, 6, 2, 0, 0, 6, 0, 6, 0, 4, 6, 4, 2, 4, 0, }, +{4: 16, 0, 0, 2, 2, 2, 6, 0, 0, 4, 0, 2, 0, 2, 0, 4, }, +{8: 16, 4, 2, 0, 4, 0, 0, 2, 6, 0, 2, 0, 0, 0, 2, 2, }, +{3: 16, 2, 0, 2, 0, 4, 4, 0, 4, 10, 0, 0, 0, 0, 0, 6, }, +{5: 16, 0, 6, 0, 0, 0, 4, 2, 0, 0, 2, 4, 2, 2, 2, 0, }, +{6: 16, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, }, +{9: 16, 6, 4, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 0, 2, 4, 8, 2, 0, 4, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 6, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 4, 2, }, +{7: 16, 0, 4, 2, 0, 0, 8, 2, 2, 4, 0, 4, 2, 0, 0, 4, }, +{b: 16, 0, 4, 0, 6, 4, 0, 0, 6, 0, 2, 0, 8, 2, 0, 0, }, +{d: 16, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:69, 4:33, 6:16, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{c: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:4, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, -8, 8, -8, }, +{2: 16, 0, 0, 0, 8, -8, 8, -8, 8, -8, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 8, -8, 0, 0, }, +{8: 16, 8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, -8, 0, }, +{3: 16, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 8, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, -8, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, -16, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 8, }, +{7: 16, -8, -8, -8, 0, 8, 0, 8, 8, 0, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -8, 8, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, -8, -8, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, x, x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, , x, , , x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , , x, x, x, x, x, , x, x, x, , , , x, x, }, +{7: , , x, , , x, x, , x, , x, x, , x, , x, }, +{b: , x, , , , , x, , x, x, x, , x, x, , x, }, +{d: , , , x, , , x, , x, x, x, , , , , x, }, +{e: , , , , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0110,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x01,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x05,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x0b,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x02,0x08,0x0a,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +049 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0a,0x08,0x05,0x06,0x07,0x00,0x09,0x0d,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 0, 4, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, }, +{5: 0, 0, 2, 2, 0, 4, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 2, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 2, }, +{a: 0, 0, 0, 4, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, }, +{c: 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 2, 0, 2, }, +{d: 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 4, 2, 0, 2, 6, 0, 0, 0, 0, 2, 2, 2, }, +{2: 16, 0, 6, 0, 2, 0, 6, 0, 4, 0, 6, 4, 4, 2, 6, 0, }, +{4: 16, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 16, 8, 0, 2, 4, 0, 0, 2, 6, 4, 0, 0, 6, 0, 0, 0, }, +{3: 16, 4, 0, 2, 0, 4, 0, 2, 4, 8, 0, 0, 4, 2, 0, 2, }, +{5: 16, 0, 6, 6, 0, 4, 4, 0, 0, 2, 2, 8, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 16, 4, 6, 0, 6, 4, 0, 0, 6, 4, 0, 2, 6, 0, 0, 2, }, +{a: 16, 0, 0, 4, 0, 10, 0, 2, 6, 4, 2, 4, 0, 0, 0, 0, }, +{c: 16, 2, 4, 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 4, 0, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 4, 4, 0, 0, 0, 2, 0, 4, 4, 0, 2, 8, 2, 0, 2, }, +{d: 16, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 4, 2, 6, 0, 2, 0, 0, 2, 4, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:69, 4:33, 6:16, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:4, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, 8, -8, 0, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, 0, 0, 0, }, +{8: 16, 0, 8, 8, 0, 0, -8, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, -8, -8, 0, 0, 8, -8, -8, 8, 0, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, -8, -8, -8, 0, 8, -8, 0, }, +{a: 16, 8, 0, 0, 0, 0, -8, -8, 0, 0, -8, -8, 8, -8, 0, 8, }, +{c: 16, 0, 8, 0, -8, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, -8, 0, 8, -8, 0, 8, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 8, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, x, x, x, , , , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, , x, x, x, x, , x, x, x, , , x, x, x, }, +{7: , x, , , , x, , , , x, , x, , , , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , , , x, x, x, , x, , x, , , , , x, }, +{e: , , , x, , , x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x09,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x03,}}, +{{0x03,0x0c,}, {0x03,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_050.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_050.txt new file mode 100644 index 0000000..2277154 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_050.txt @@ -0,0 +1,408 @@ +050 Sbox: +LUT = { +0x08,0x00,0x01,0x06,0x02,0x05,0x0d,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, }, +{4: 0, 2, 0, 4, 2, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{5: 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 4, 2, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, }, +{a: 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 2, }, +{b: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 4, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 16, 0, 6, 0, 0, 0, 4, 2, 6, 0, 6, 4, 4, 0, 6, 2, }, +{4: 16, 10, 0, 4, 2, 0, 6, 0, 0, 4, 2, 0, 4, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 16, 2, 0, 0, 2, 4, 6, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{5: 16, 4, 6, 4, 0, 4, 6, 6, 0, 0, 0, 6, 2, 2, 0, 0, }, +{6: 16, 0, 0, 4, 2, 8, 6, 4, 0, 2, 0, 6, 0, 0, 0, 0, }, +{9: 16, 4, 6, 2, 0, 0, 0, 0, 4, 6, 2, 0, 8, 0, 0, 0, }, +{a: 16, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 16, 0, 4, 2, 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 4, 2, }, +{7: 16, 0, 4, 4, 0, 4, 4, 0, 2, 0, 0, 8, 2, 2, 0, 2, }, +{b: 16, 0, 6, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 2, 2, 0, }, +{d: 16, 6, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 4, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:69, 4:33, 6:16, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 0, -8, 0, 0, 8, -8, 8, -8, -8, 8, -8, 0, }, +{4: 16, 8, 8, 0, 0, 0, 0, -8, -8, 8, -8, -8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 8, 0, -8, -8, 0, }, +{5: 16, -8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, 0, 0, -8, -8, -8, 8, 0, -8, 0, 8, }, +{9: 16, 0, 8, 8, 0, -8, -8, 0, 0, 0, 0, -16, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 8, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, 0, 8, -8, }, +{e: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , x, , , x, x, , x, , x, x, , x, , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, x, x, , x, , x, , , , , x, }, +{e: , , x, , x, , x, x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0111,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +050 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0d,0x08,0x05,0x03,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{8: 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 6, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 2, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, }, +{a: 0, 2, 0, 4, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{c: 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, 0, }, +{7: 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 4, 4, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:154, 2:84, 4:15, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 10, 0, 2, 4, 0, 4, 2, 0, 0, 0, 6, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 6, 0, 6, 2, 4, 4, 6, 0, 4, 2, }, +{4: 16, 8, 0, 4, 0, 0, 4, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{8: 16, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 16, 4, 0, 0, 2, 4, 4, 8, 0, 0, 2, 4, 2, 0, 0, 2, }, +{5: 16, 4, 4, 6, 0, 6, 6, 6, 0, 2, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 2, 0, 2, 4, 6, 4, 0, 0, 2, 0, 0, 2, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 0, 2, 2, }, +{a: 16, 2, 0, 4, 0, 0, 0, 2, 6, 2, 0, 0, 2, 4, 0, 2, }, +{c: 16, 0, 6, 2, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 4, 0, }, +{7: 16, 4, 4, 0, 0, 0, 6, 6, 0, 0, 2, 8, 0, 0, 0, 2, }, +{b: 16, 0, 4, 4, 2, 0, 2, 0, 8, 2, 0, 2, 4, 4, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, }, +{e: 16, 0, 6, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 4, 2, }, +{f: 16, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:69, 4:33, 6:16, 8:4, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 12, 0, 0, 4, 0, }, +{b: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:107, 4:119, 8:28, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 0, 0, 0, 0, -8, 8, -8, 0, 0, }, +{2: 16, 0, -8, 8, 0, -8, 8, -8, 8, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, -16, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, -8, }, +{3: 16, 0, -8, 0, 0, 8, -8, 0, 0, -8, 0, 8, -8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, 0, -8, 0, -8, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, 0, -8, 0, -8, 0, 8, -8, 0, }, +{a: 16, 0, 0, 0, 0, 0, -8, 0, 8, 8, -8, -8, 0, -8, 0, 0, }, +{c: 16, 8, 8, 0, -8, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, -8, 0, 0, -8, -8, 0, 8, 0, }, +{b: 16, -8, 0, 0, -8, 0, 8, -8, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , x, x, , , , x, x, x, , x, x, , x, , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , x, , x, x, , x, x, x, , x, , , , , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 1 */ +{0111,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 7, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x09,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x04,0x0b,0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_051.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_051.txt new file mode 100644 index 0000000..d095eaf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_051.txt @@ -0,0 +1,420 @@ +051 Sbox: +LUT = { +0x08,0x0c,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 2, 2, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 4, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 0, 4, 8, 6, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 16, 0, 10, 4, 4, 0, 0, 4, 2, 4, 10, 2, 0, 0, 8, 0, }, +{4: 16, 4, 4, 6, 0, 8, 8, 10, 2, 0, 0, 4, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 2, 2, 0, 2, 6, 0, 0, 2, 0, 2, 0, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 0, 6, 0, 8, 0, 4, 0, 2, }, +{5: 16, 4, 0, 4, 0, 4, 8, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{6: 16, 0, 6, 4, 2, 0, 0, 4, 0, 2, 2, 2, 2, 0, 0, 0, }, +{9: 16, 2, 0, 0, 2, 0, 2, 0, 2, 4, 0, 4, 2, 4, 2, 0, }, +{a: 16, 0, 6, 2, 4, 0, 0, 0, 0, 8, 0, 4, 2, 6, 0, 0, }, +{c: 16, 2, 4, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 2, }, +{7: 16, 2, 0, 6, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 6, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:63, 4:34, 6:14, 8:7, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:5, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 8, 0, 0, -16, 0, 0, }, +{2: 16, 8, -8, 0, 0, -8, 0, 0, 0, -8, 8, -8, 0, 16, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, -8, -8, 8, 8, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, -8, 0, -8, 8, 0, 0, -8, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, 0, 0, 8, -8, 0, 0, -8, -8, 8, 0, 8, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, , , x, x, x, , , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, , x, x, , x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , , , , x, , , x, x, , , , x, }, +{b: , x, , , x, x, , x, , , x, , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x05,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +051 Inverse Sbox: +LUT = { +0x0c,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x01,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 4, }, +{4: 0, 2, 0, 6, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 4, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 2, 0, 0, 4, 4, 0, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 2, 2, 0, 2, 4, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{e: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, }, +{f: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 0, 6, 4, 0, 0, 4, 6, 4, }, +{4: 16, 6, 4, 6, 0, 6, 4, 4, 0, 2, 0, 6, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 0, 2, 2, 4, 2, 2, 2, 0, 0, 2, }, +{3: 16, 4, 0, 8, 2, 4, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{5: 16, 8, 0, 8, 2, 0, 8, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 16, 6, 4, 10, 0, 0, 4, 4, 0, 0, 0, 0, 2, 0, 2, 0, }, +{9: 16, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 16, 0, 4, 0, 6, 6, 0, 2, 4, 8, 0, 0, 0, 2, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 4, 6, }, +{7: 16, 0, 2, 4, 0, 8, 0, 2, 4, 4, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 4, 2, 0, 4, 6, 2, 0, 0, 2, 0, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:63, 4:34, 6:14, 8:7, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 0, }, +{9: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:5, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +{2: 16, 8, -16, 0, 0, -8, 8, 0, 8, 0, 8, -8, -8, 0, -8, 0, }, +{4: 16, 0, 0, 0, 8, 8, -8, -8, 0, 8, -8, -8, 8, -8, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 8, 8, 0, -8, 0, -8, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, -8, 0, 0, 8, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, -8, }, +{a: 16, 0, 0, 8, -8, -8, 0, 0, 0, -8, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -16, 0, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{e: 16, 8, 0, 0, -8, -8, 0, 0, 0, -8, 8, 0, 0, 8, -8, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , , , x, x, x, , , x, }, +{5: , x, , x, x, , x, x, , , x, x, , x, , x, }, +{6: , x, , x, , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , x, , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , , , , , , x, x, , , , x, }, +{b: , x, , , , , , , , , x, , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,}}, +{{0x03,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x04,}}, +{{0x0d,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_052.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_052.txt new file mode 100644 index 0000000..09b887a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_052.txt @@ -0,0 +1,420 @@ +052 Sbox: +LUT = { +0x06,0x08,0x0d,0x02,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 4, 2, }, +{9: 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{a: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 2, 2, 0, }, +{7: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{e: 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 16, 0, 10, 0, 4, 0, 4, 0, 4, 4, 4, 6, 6, 0, 6, 0, }, +{4: 16, 8, 0, 8, 2, 0, 8, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{8: 16, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 16, 6, 0, 4, 0, 4, 10, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 16, 6, 4, 4, 0, 6, 6, 6, 0, 2, 0, 4, 2, 0, 0, 0, }, +{6: 16, 0, 2, 0, 0, 8, 4, 4, 0, 2, 0, 2, 0, 4, 4, 2, }, +{9: 16, 0, 10, 0, 4, 0, 0, 2, 4, 4, 0, 0, 6, 0, 0, 2, }, +{a: 16, 0, 0, 0, 2, 6, 0, 2, 0, 2, 2, 0, 2, 4, 4, 0, }, +{c: 16, 0, 4, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 6, 10, 0, }, +{7: 16, 4, 4, 4, 2, 0, 8, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{e: 16, 2, 4, 2, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, 4, 0, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:65, 4:37, 6:11, 8:6, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, 8, 0, -8, }, +{4: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, -8, 0, 0, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, 0, 8, 0, 0, 0, -8, -8, 0, }, +{5: 16, -8, 0, 0, 8, -8, 0, -8, -8, 8, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, -16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, 8, -8, -8, 0, -8, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 0, 8, 0, -8, 8, 0, }, +{c: 16, 0, 0, 0, -8, 0, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, }, +{b: 16, 0, 0, 0, 0, 0, 0, -16, 8, 0, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , , x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , , , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , , x, , , x, , x, , x, x, , x, , x, }, +{b: , x, , , x, x, x, x, x, , x, , x, x, , x, }, +{d: , , , x, x, x, x, x, x, , x, , , , , x, }, +{e: , , , x, , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0110,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +052 Inverse Sbox: +LUT = { +0x08,0x0d,0x03,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x02,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, }, +{a: 0, 0, 4, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, }, +{e: 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 6, 6, 0, 0, 0, 0, 4, 0, 0, 2, 0, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 10, 0, 4, 4, 8, 2, 4, 0, }, +{4: 16, 4, 0, 8, 2, 4, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{8: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 2, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 8, 0, 6, 4, 0, 0, 0, 2, 0, }, +{5: 16, 4, 4, 8, 0, 10, 6, 4, 0, 0, 0, 8, 2, 2, 0, 0, }, +{6: 16, 2, 0, 0, 2, 4, 6, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 16, 2, 4, 2, 2, 0, 0, 0, 4, 0, 2, 0, 4, 0, 2, 2, }, +{a: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 0, 6, 0, 2, 0, 4, 2, 0, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 0, 6, 0, 0, 2, 2, 0, 6, 2, 0, 2, 4, 0, 0, 0, }, +{d: 16, 2, 0, 2, 0, 0, 0, 4, 0, 4, 6, 0, 2, 2, 0, 2, }, +{e: 16, 2, 6, 0, 0, 0, 0, 4, 0, 4, 10, 0, 0, 0, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:65, 4:37, 6:11, 8:6, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{b: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 8, -16, 0, 0, 0, 0, 0, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 16, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, 0, 8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -16, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, -8, 8, -8, 8, 0, 0, -16, 0, 8, -8, 8, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, -8, 0, 8, }, +{9: 16, 0, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, }, +{a: 16, 8, 0, 0, 0, -8, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 8, 8, 0, -8, 0, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, -8, 0, -8, 8, 0, }, +{e: 16, 8, -8, -8, 0, -8, -8, 8, 0, 0, 8, 0, -8, 0, 0, 0, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, , , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , x, , x, , x, x, , x, , x, }, +{b: , x, x, , x, , x, , x, , x, , x, x, , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x01,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x05,0x08,0x0d,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x06,0x09,0x0f,}}, +{{0x09,0x02,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_053.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_053.txt new file mode 100644 index 0000000..4884f4f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_053.txt @@ -0,0 +1,420 @@ +053 Sbox: +LUT = { +0x06,0x08,0x0e,0x02,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x01,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, }, +{2: 0, 0, 6, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 2, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, }, +{e: 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 6, 6, 0, 2, 8, 0, 0, 4, 0, }, +{2: 16, 0, 10, 4, 10, 0, 0, 4, 0, 8, 4, 2, 0, 2, 4, 0, }, +{4: 16, 4, 4, 8, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 16, 2, 4, 2, 4, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 2, }, +{3: 16, 6, 0, 4, 0, 4, 8, 6, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 6, 6, 4, 0, 4, 4, 6, 0, 0, 0, 6, 0, 2, 0, 2, }, +{9: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, }, +{a: 16, 0, 6, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 8, 0, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 2, 2, 2, 2, 0, 0, }, +{d: 16, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, }, +{e: 16, 0, 6, 2, 0, 0, 0, 0, 6, 0, 4, 4, 0, 0, 8, 2, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 6, 0, 2, 6, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:35, 6:17, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, -16, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 16, 8, -8, 8, 0, -8, 16, -8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, 0, 0, 0, 8, 8, -16, -8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 0, -8, -8, 8, -8, 0, 8, 8, -8, 0, 0, -8, -8, 8, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, }, +{a: 16, 8, -8, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, }, +{b: 16, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, -8, 0, 8, 0, -8, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 8, -8, -8, }, +{f: 16, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , , x, , x, x, , , , x, x, , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , , , x, , x, x, x, , , x, x, }, +{b: , , x, , x, x, , , , x, x, , x, , x, x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +053 Inverse Sbox: +LUT = { +0x08,0x0e,0x03,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x02,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 2, 6, 2, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 4, }, +{a: 0, 0, 4, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 4, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{e: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 6, 0, 6, 0, 0, 0, 8, 0, 2, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 0, 4, 8, 2, 4, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 0, 4, 6, 0, 2, 4, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 4, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 16, 0, 0, 4, 2, 8, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 6, 4, 4, 2, 6, 6, 6, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 16, 6, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 6, 4, }, +{a: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 2, 4, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 4, 0, }, +{7: 16, 8, 2, 0, 0, 0, 0, 6, 0, 0, 0, 4, 2, 0, 4, 6, }, +{b: 16, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, }, +{d: 16, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{e: 16, 4, 4, 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 0, 8, 6, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:35, 6:17, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{d: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 8, -8, -8, 0, 0, 0, -8, 8, -8, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, 0, 8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 8, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 8, -8, -8, 8, 0, -8, -8, 8, -8, -8, 0, 8, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, 0, }, +{a: 16, 8, 0, 0, 0, -8, 8, -16, 0, 0, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, 0, 8, -8, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, -8, }, +{b: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, -8, 8, -8, 8, 8, -8, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, , x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, x, x, , x, , x, x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , , , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , x, , x, , , , x, , x, x, x, , , x, x, }, +{b: , , , , x, , , x, , x, x, , x, , x, x, }, +{d: , , , x, x, , , , , x, x, , , x, x, x, }, +{e: , , , , x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0110,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_054.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_054.txt new file mode 100644 index 0000000..a9c18bf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_054.txt @@ -0,0 +1,420 @@ +054 Sbox: +LUT = { +0x04,0x00,0x01,0x0f,0x02,0x05,0x03,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{2: 0, 2, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{4: 0, 0, 2, 4, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{5: 0, 2, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 2, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:6, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 0, 6, 0, 0, 0, 10, 0, 0, 2, 2, }, +{2: 16, 2, 6, 0, 0, 0, 8, 0, 8, 0, 10, 4, 4, 0, 4, 2, }, +{4: 16, 0, 2, 4, 2, 6, 2, 2, 0, 2, 0, 4, 0, 0, 0, 0, }, +{8: 16, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{3: 16, 2, 0, 6, 0, 4, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, }, +{5: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{6: 16, 6, 0, 4, 2, 6, 0, 4, 0, 2, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 0, 0, 2, 2, 4, 2, 0, 0, 6, 2, 0, 2, }, +{a: 16, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{c: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 4, 4, 10, 0, 8, 4, 4, 0, 0, 0, 10, 0, 2, 2, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 0, 0, 4, 0, 2, 2, }, +{d: 16, 2, 0, 0, 2, 2, 4, 0, 4, 0, 6, 0, 2, 2, 0, 0, }, +{e: 16, 0, 10, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 2, 4, 0, }, +{f: 16, 2, 0, 0, 0, 2, 4, 0, 6, 2, 4, 0, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:63, 4:34, 6:12, 8:6, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{a: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, -8, 8, 0, -8, 8, 0, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 0, 0, 0, 8, -8, 8, -8, 0, 0, 8, -8, -16, 8, -8, 0, }, +{4: 16, 8, 0, 0, 8, 0, 0, -8, 0, 0, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -16, 8, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, 0, 8, -8, -8, -8, 0, 0, -8, 8, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 8, }, +{a: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 0, -8, -8, 0, 0, 16, 0, 0, -8, }, +{b: 16, 0, -8, 8, -16, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, -8, 8, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 8, 0, 0, -8, -8, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, -8, 0, 8, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, , , x, x, x, , x, x, x, , x, x, x, x, }, +{b: , , , x, , , x, , x, x, x, x, , x, x, x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1000,1011,1,}, +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x01,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x0b,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x06,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x0b,}}, +{{0x09,0x06,}, {0x0f,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +054 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x05,0x08,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 4, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 4, 0, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 2, 0, 2, 0, 2, 2, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 4, 0, 2, 2, }, +{c: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 4, }, +{7: 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, }, +{f: 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:6, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 0, 0, 2, 2, 6, 0, 0, 0, 4, 0, 2, 0, 2, }, +{2: 16, 0, 6, 2, 2, 0, 8, 0, 4, 0, 4, 4, 8, 0, 10, 0, }, +{4: 16, 4, 0, 4, 2, 6, 0, 4, 0, 0, 2, 10, 0, 0, 0, 0, }, +{8: 16, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, 0, 6, 2, 4, 0, }, +{3: 16, 4, 0, 6, 0, 4, 0, 6, 0, 0, 0, 8, 0, 2, 0, 2, }, +{5: 16, 0, 8, 2, 0, 2, 4, 0, 2, 0, 0, 4, 0, 4, 2, 4, }, +{6: 16, 6, 0, 2, 0, 2, 2, 4, 2, 2, 0, 4, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, 2, 0, 0, 0, 4, 0, 2, 0, 6, 4, 0, 6, }, +{a: 16, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, 4, 0, 6, 2, }, +{c: 16, 0, 10, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 6, 4, 4, }, +{7: 16, 10, 4, 4, 0, 4, 4, 8, 0, 2, 2, 10, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 2, 4, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 2, }, +{f: 16, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:63, 4:34, 6:12, 8:6, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 8, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 8, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, -8, 8, -16, -8, }, +{4: 16, 0, 8, 0, 8, 8, -8, 0, -8, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, }, +{3: 16, -8, -8, -8, 8, 8, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{6: 16, 0, 0, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -16, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 8, -8, 0, 0, 8, -8, -8, 0, 0, 8, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, -8, -8, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 8, -8, 8, 0, 0, 0, 0, 0, -8, }, +{f: 16, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, x, , , x, , x, x, x, x, , x, x, x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , x, , x, x, x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1000,1001,1,}, +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x07,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x09,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_055.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_055.txt new file mode 100644 index 0000000..1ef65b2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_055.txt @@ -0,0 +1,420 @@ +055 Sbox: +LUT = { +0x04,0x00,0x01,0x0a,0x02,0x08,0x06,0x07,0x03,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{8: 0, 2, 0, 2, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{6: 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, 4, }, +{a: 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, }, +{c: 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 2, 4, 4, 0, 0, 4, 8, 0, 0, 10, 0, 2, 0, }, +{2: 16, 4, 6, 6, 0, 4, 6, 6, 0, 2, 0, 4, 0, 0, 0, 2, }, +{4: 16, 0, 4, 4, 2, 0, 0, 6, 0, 0, 0, 2, 2, 2, 0, 2, }, +{8: 16, 6, 0, 2, 4, 0, 2, 0, 6, 0, 0, 2, 0, 0, 2, 0, }, +{3: 16, 6, 8, 0, 2, 4, 2, 0, 0, 0, 6, 0, 0, 0, 4, 0, }, +{5: 16, 0, 10, 0, 0, 0, 4, 2, 0, 2, 4, 4, 0, 0, 6, 0, }, +{6: 16, 0, 8, 4, 0, 2, 0, 4, 2, 0, 4, 2, 0, 2, 4, 0, }, +{9: 16, 4, 0, 2, 8, 2, 0, 0, 4, 2, 0, 4, 0, 2, 0, 4, }, +{a: 16, 6, 2, 0, 0, 2, 0, 0, 0, 4, 2, 2, 6, 0, 0, 0, }, +{c: 16, 4, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 4, 2, 0, 2, }, +{7: 16, 0, 4, 0, 4, 2, 4, 2, 2, 0, 2, 8, 0, 0, 0, 4, }, +{b: 16, 4, 0, 0, 2, 0, 2, 2, 2, 4, 0, 0, 4, 2, 0, 2, }, +{d: 16, 4, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 4, 2, 2, 0, }, +{e: 16, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 4, 0, 2, 2, 6, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:64, 4:39, 6:13, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{e: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, -8, 0, -8, 16, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, 0, 0, -8, -8, 0, -8, 0, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 8, 0, -8, 0, 0, -8, 0, -8, }, +{8: 16, 0, 8, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 0, -8, 0, -16, 0, 8, 8, 0, 0, -8, 0, }, +{5: 16, 8, 0, -8, 0, -8, 0, -8, -8, 0, 0, 0, -8, 8, 0, 8, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 8, -16, 0, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 8, -8, -8, 8, }, +{a: 16, 0, -8, 8, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{c: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, }, +{7: 16, 0, 0, 0, 0, 8, 0, 8, -8, -16, -8, 0, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, -8, 0, 0, 0, 8, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, }, +{e: 16, -8, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, , x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, , x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, x, , x, , x, , , , , , x, , , x, }, +{d: , x, , x, , x, x, , , , , , , x, , x, }, +{e: , x, , x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1001,0011,1,}, +{1010,0001,0,}, +{1010,0110,1,}, +{1010,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x06,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x0a,}}, +{{0x03,0x04,}, {0x03,0x09,0x0a,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x08,}, {0x07,0x09,0x0e,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +055 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x0a,0x06,0x07,0x05,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 2, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, }, +{8: 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, }, +{5: 0, 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, }, +{6: 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, 2, }, +{a: 0, 4, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 4, 0, }, +{b: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 6, 6, 0, 0, 4, 6, 4, 0, 4, 4, 0, 0, }, +{2: 16, 4, 6, 4, 0, 8, 10, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{4: 16, 2, 6, 4, 2, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, }, +{8: 16, 4, 0, 2, 4, 2, 0, 0, 8, 0, 2, 4, 2, 0, 4, 0, }, +{3: 16, 4, 4, 0, 0, 4, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, }, +{5: 16, 0, 6, 0, 2, 2, 4, 0, 0, 0, 2, 4, 2, 0, 2, 0, }, +{6: 16, 0, 6, 6, 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, }, +{9: 16, 4, 0, 0, 6, 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, 2, }, +{a: 16, 8, 2, 0, 0, 0, 2, 0, 2, 4, 4, 0, 4, 4, 2, 0, }, +{c: 16, 0, 0, 0, 0, 6, 4, 4, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 4, 2, 0, 8, 0, 0, 4, 0, }, +{b: 16, 10, 0, 2, 0, 0, 0, 0, 0, 6, 4, 0, 4, 4, 0, 2, }, +{d: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 16, 2, 0, 0, 2, 4, 6, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 6, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:64, 4:39, 6:13, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, -8, 0, -16, 0, 8, -8, -8, -8, 8, 0, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, -8, }, +{8: 16, 0, 0, 0, 0, 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, -8, }, +{3: 16, 0, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 8, }, +{5: 16, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 8, -8, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, 0, -16, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, }, +{c: 16, -8, 0, -8, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 8, }, +{7: 16, 8, -8, -8, 0, 0, 0, 8, -8, 0, -8, 0, 8, 0, 0, -8, }, +{b: 16, -8, 0, 0, -8, 0, 0, -8, 8, 8, 0, 0, 0, -8, 8, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 8, 0, -8, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, -8, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, , x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, x, , x, , x, , , x, , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , x, x, x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x03,}}, +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x02,0x09,0x0b,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x03,0x09,0x0a,}}, +{{0x03,0x08,}, {0x03,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x0a,}, {0x03,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_056.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_056.txt new file mode 100644 index 0000000..81be78e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_056.txt @@ -0,0 +1,420 @@ +056 Sbox: +LUT = { +0x04,0x00,0x01,0x0a,0x02,0x05,0x06,0x08,0x03,0x09,0x07,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, }, +{2: 0, 0, 6, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, }, +{5: 0, 2, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, }, +{9: 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 2, }, +{a: 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 4, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 2, 0, 4, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, }, +{2: 16, 8, 6, 8, 0, 4, 10, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{4: 16, 0, 6, 4, 0, 0, 2, 6, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 16, 2, 0, 0, 4, 4, 0, 2, 2, 0, 4, 4, 8, 0, 2, 0, }, +{3: 16, 6, 4, 0, 6, 10, 0, 0, 4, 6, 0, 0, 4, 4, 4, 0, }, +{5: 16, 2, 6, 0, 2, 0, 4, 0, 2, 0, 2, 4, 0, 0, 2, 0, }, +{6: 16, 0, 6, 4, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, }, +{9: 16, 0, 0, 0, 0, 10, 0, 2, 4, 6, 0, 0, 0, 4, 4, 2, }, +{a: 16, 0, 2, 0, 0, 8, 2, 0, 4, 4, 2, 0, 2, 4, 4, 0, }, +{c: 16, 4, 0, 4, 2, 2, 6, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 0, 0, 2, 6, 4, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, }, +{d: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 16, 6, 0, 4, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 2, 0, 0, 0, 0, 2, 2, 0, 6, 4, 4, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:64, 4:39, 6:13, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{8: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 8, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 8, -8, }, +{2: 16, 8, 0, 0, 8, -8, 8, -16, 8, 0, 0, -8, 0, 0, -8, -8, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 8, 0, -8, -8, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 16, -8, -8, -8, 0, 0, 0, 0, -8, }, +{3: 16, 0, -8, 8, 0, 0, -8, 0, -16, 0, 8, 8, 8, -8, -8, 0, }, +{5: 16, 0, 8, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, -8, -8, 0, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 8, -8, 0, 8, }, +{a: 16, 0, -8, 8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{c: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, }, +{7: 16, 8, 0, -8, 0, 8, 0, 0, -8, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, -8, 0, 0, -8, 8, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, 0, -8, 0, -8, 0, 8, 0, 0, 0, -8, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , , , x, , x, }, +{6: , x, x, x, , , x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{7: , , x, x, , , x, x, , x, , , , , , x, }, +{b: , x, , , x, x, x, x, , , , x, x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , x, x, x, , , x, x, , x, , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x06,0x09,0x0f,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x02,}, {0x06,0x09,0x0f,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x0e,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +056 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x0a,0x07,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, 2, 0, }, +{c: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 4, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 0, 2, 6, 2, 0, 0, 0, 4, 0, 0, 0, 6, 0, }, +{2: 16, 4, 6, 6, 0, 4, 6, 6, 0, 2, 0, 4, 0, 0, 0, 2, }, +{4: 16, 2, 8, 4, 0, 0, 0, 4, 0, 0, 4, 2, 2, 2, 4, 0, }, +{8: 16, 0, 0, 0, 4, 6, 2, 2, 0, 0, 2, 2, 6, 0, 0, 0, }, +{3: 16, 4, 4, 0, 4, 10, 0, 2, 10, 8, 2, 0, 4, 0, 0, 0, }, +{5: 16, 0, 10, 2, 0, 0, 4, 0, 0, 2, 6, 4, 0, 0, 4, 0, }, +{6: 16, 0, 4, 6, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, 2, }, +{9: 16, 0, 0, 2, 2, 4, 2, 0, 4, 4, 0, 0, 2, 2, 0, 2, }, +{a: 16, 2, 2, 0, 0, 6, 0, 0, 6, 4, 0, 2, 0, 0, 2, 0, }, +{c: 16, 2, 0, 0, 4, 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 6, }, +{7: 16, 2, 4, 2, 4, 0, 4, 0, 0, 0, 0, 8, 2, 0, 2, 4, }, +{b: 16, 2, 0, 0, 8, 4, 0, 2, 0, 2, 0, 4, 4, 2, 0, 4, }, +{d: 16, 0, 2, 0, 0, 4, 0, 2, 4, 4, 2, 0, 2, 2, 2, 0, }, +{e: 16, 2, 0, 0, 2, 4, 2, 0, 4, 4, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:64, 4:39, 6:13, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{d: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, -8, 0, -16, 0, 8, 0, -8, 0, 0, 0, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, 0, 0, -8, -8, 0, -8, 0, }, +{4: 16, 0, 0, 0, 8, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, -16, }, +{8: 16, 0, 0, 0, 0, 8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 0, }, +{3: 16, 0, -8, 8, 0, 0, -8, -8, -8, -8, 0, 0, 8, -8, 0, 16, }, +{5: 16, 8, 0, -8, 0, -8, 0, -8, -8, 8, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, 8, -8, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, }, +{c: 16, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, 0, 0, 0, 8, 0, 8, -8, 0, -8, 0, 0, 0, 0, -16, }, +{b: 16, -8, -8, 0, -8, 0, 0, 0, 8, 8, 0, 0, -8, -8, 8, 0, }, +{d: 16, 0, 0, 0, -8, -8, -8, 0, 8, -8, 0, 0, 0, 8, 0, 0, }, +{e: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 8, 0, -8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, , , x, x, , x, , x, , , x, x, }, +{9: , x, , x, x, x, x, x, x, x, , x, x, x, , x, }, +{a: , x, , x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{7: , , x, x, , , x, x, , x, , , , , , x, }, +{b: , x, , , x, x, x, x, , x, , x, x, , , x, }, +{d: , x, , , x, x, x, x, , , , x, , x, , x, }, +{e: , x, , x, , , x, x, , x, , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1001,0001,1,}, +{1111,0011,0,}, +{1111,0100,1,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0f,}}, +{{0x01,0x02,0x04,}, {0x0f,}}, +{{0x09,0x0a,0x04,}, {0x0f,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x0f,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x08,}, {0x02,0x09,0x0b,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x06,0x09,0x0f,}}, +{{0x05,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x06,0x09,0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0a,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_057.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_057.txt new file mode 100644 index 0000000..0eb248c --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_057.txt @@ -0,0 +1,420 @@ +057 Sbox: +LUT = { +0x06,0x00,0x08,0x0f,0x03,0x05,0x04,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x02, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 0, 2, 4, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 0, 2, }, +{9: 0, 2, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 0, }, +{7: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 6, 0, 2, 0, 0, }, +{b: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, }, +{e: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{f: 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:5, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 6, 4, 8, 0, 0, 2, 6, 0, 0, 0, 0, }, +{2: 16, 0, 10, 0, 0, 0, 4, 0, 4, 0, 4, 6, 6, 4, 6, 4, }, +{4: 16, 0, 0, 4, 2, 8, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 16, 2, 0, 6, 2, 4, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, }, +{5: 16, 0, 4, 0, 2, 4, 8, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{6: 16, 8, 2, 0, 0, 0, 0, 4, 0, 6, 0, 6, 4, 0, 0, 2, }, +{9: 16, 2, 4, 0, 0, 2, 2, 2, 4, 0, 0, 0, 4, 0, 2, 2, }, +{a: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 6, 4, }, +{7: 16, 6, 4, 6, 0, 6, 4, 4, 0, 0, 2, 6, 0, 2, 0, 0, }, +{b: 16, 4, 4, 0, 0, 0, 0, 0, 6, 6, 0, 0, 8, 2, 2, 0, }, +{d: 16, 6, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 6, 2, 0, 2, }, +{e: 16, 0, 8, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 4, 4, 4, }, +{f: 16, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:35, 6:17, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{5: 0, 0, 0, 0, 4, 8, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{c: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{7: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, 0, -8, 8, -8, -8, 0, 0, -8, -8, 8, 0, }, +{2: 16, 0, -16, 0, 0, 0, 8, 0, 8, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, -8, 0, }, +{3: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, -8, 8, }, +{6: 16, 0, -16, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, }, +{9: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, -8, 8, }, +{a: 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 8, 0, -8, -8, -8, 0, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 8, 8, 0, 0, -8, -8, 0, -8, 8, 0, 8, -8, }, +{b: 16, -8, 0, 8, -8, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, -8, 0, -8, 8, 0, }, +{e: 16, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -16, -8, }, +{f: 16, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , , x, , x, x, x, x, x, x, , x, x, x, x, }, +{b: , , , , x, , x, , x, x, x, x, , x, x, x, }, +{d: , x, , , x, x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x02,0x09,0x0b,}}, +{{0x03,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +057 Inverse Sbox: +LUT = { +0x01,0x08,0x0f,0x04,0x06,0x05,0x00,0x07,0x02,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, }, +{2: 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{8: 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{6: 0, 4, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 4, 0, 0, }, +{c: 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 0, }, +{7: 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 4, 2, }, +{f: 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:5, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 8, 2, 0, 0, 6, 4, 6, 0, 0, }, +{2: 16, 0, 10, 0, 2, 0, 4, 2, 4, 0, 10, 4, 4, 0, 8, 0, }, +{4: 16, 0, 0, 4, 2, 6, 0, 0, 0, 0, 0, 6, 0, 2, 2, 2, }, +{8: 16, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, }, +{3: 16, 6, 0, 8, 0, 4, 4, 0, 2, 0, 0, 6, 0, 0, 0, 2, }, +{5: 16, 4, 4, 4, 2, 0, 8, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{6: 16, 8, 0, 4, 0, 0, 4, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{9: 16, 0, 4, 2, 2, 2, 0, 0, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 0, 0, 0, 2, 2, 0, 6, 0, 2, 2, 0, 6, 4, 0, 0, }, +{c: 16, 2, 4, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 0, }, +{7: 16, 6, 6, 4, 2, 4, 4, 6, 0, 2, 0, 6, 0, 0, 0, 0, }, +{b: 16, 0, 6, 0, 0, 0, 2, 4, 4, 2, 0, 0, 8, 6, 0, 0, }, +{d: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{e: 16, 0, 6, 0, 0, 2, 0, 0, 2, 0, 6, 0, 2, 0, 4, 2, }, +{f: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:35, 6:17, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 0, 0, -8, 0, 0, 0, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, -8, 0, }, +{3: 16, -16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, -8, -8, -8, 8, 8, }, +{9: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 0, 8, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -8, 0, 8, 0, 8, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, -8, 0, -8, 8, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, -8, 0, -8, 0, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, 0, 0, -8, 8, 0, 8, -8, 0, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, , x, , x, x, x, x, x, x, , x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , , x, x, , , x, x, x, x, x, , x, x, x, x, }, +{b: , , , , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , x, , , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x04,0x09,0x0d,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x09,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x05,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x06,0x07,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_058.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_058.txt new file mode 100644 index 0000000..91384b1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_058.txt @@ -0,0 +1,420 @@ +058 Sbox: +LUT = { +0x06,0x00,0x08,0x0c,0x03,0x05,0x04,0x07,0x01,0x09,0x0a,0x0b,0x02,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + x1 + + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 0, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 2, 4, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 4, 0, 0, }, +{d: 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, }, +{e: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 2, 6, 8, 4, 0, 0, 0, 0, 0, 0, 0, 2, }, +{2: 16, 0, 10, 4, 4, 0, 0, 4, 0, 4, 8, 2, 2, 0, 10, 0, }, +{4: 16, 4, 4, 6, 0, 10, 8, 8, 0, 0, 2, 4, 2, 0, 0, 0, }, +{8: 16, 2, 6, 0, 4, 0, 0, 0, 2, 10, 0, 4, 0, 4, 0, 0, }, +{3: 16, 2, 0, 6, 2, 4, 0, 0, 0, 4, 0, 8, 0, 6, 0, 0, }, +{5: 16, 4, 0, 4, 2, 4, 8, 4, 0, 0, 2, 0, 2, 0, 0, 2, }, +{6: 16, 0, 6, 4, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, }, +{9: 16, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 6, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 6, 0, }, +{7: 16, 2, 0, 6, 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 2, 0, 0, 0, 0, 2, 0, 2, 6, 2, 4, 2, 4, 0, 0, }, +{d: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{e: 16, 2, 4, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 2, }, +{f: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:65, 4:37, 6:11, 8:6, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 0, 4, 4, 0, 4, 12, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{7: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {4:12, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, -16, 0, 0, }, +{2: 16, 8, -8, 0, 0, 0, 0, -8, 0, -8, 8, -8, -8, 16, 0, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 8, 8, -8, -8, -8, -8, 0, 0, 0, -8, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, 0, 0, 0, 0, 8, 8, -8, -8, 0, -8, 0, 0, 0, }, +{9: 16, -8, -8, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 8, 8, }, +{c: 16, 8, 0, -8, 0, 0, -8, -8, 0, -8, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, -8, 8, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, }, +{d: 16, 0, -8, 0, 0, 0, 8, -8, 8, 0, 0, -8, 0, 0, 0, -8, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, x, x, , x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , , , , , , x, x, , , , x, }, +{b: , x, x, , x, x, , x, , , x, , x, , , x, }, +{d: , x, x, x, , x, , x, , , x, , , x, , x, }, +{e: , , x, x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x05,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0e,}, {0x01,0x08,0x09,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +058 Inverse Sbox: +LUT = { +0x01,0x08,0x0c,0x04,0x06,0x05,0x00,0x07,0x02,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{2: 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, }, +{4: 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{6: 0, 4, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 4, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, 0, }, +{7: 0, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 0, }, +{b: 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 4, }, +{f: 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{2: 16, 0, 10, 4, 6, 0, 0, 6, 0, 4, 6, 0, 0, 4, 4, 4, }, +{4: 16, 6, 4, 6, 0, 6, 4, 4, 0, 0, 2, 6, 0, 2, 0, 0, }, +{8: 16, 2, 4, 0, 4, 2, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, }, +{3: 16, 6, 0, 10, 0, 4, 4, 0, 2, 0, 2, 4, 0, 0, 0, 0, }, +{5: 16, 8, 0, 8, 0, 0, 8, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{6: 16, 4, 4, 8, 0, 0, 4, 4, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{a: 16, 0, 4, 0, 10, 4, 0, 0, 0, 4, 0, 0, 6, 2, 2, 0, }, +{c: 16, 0, 8, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 4, 4, 4, }, +{7: 16, 0, 2, 4, 4, 8, 0, 2, 2, 0, 0, 4, 4, 2, 0, 0, }, +{b: 16, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{d: 16, 0, 0, 0, 4, 6, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 4, 4, 4, }, +{f: 16, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:65, 4:37, 6:11, 8:6, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{8: 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 8, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {4:12, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, 8, -8, 8, -16, 8, 0, -8, 0, 0, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 0, 0, -8, 8, -8, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 8, -8, -8, -8, 0, }, +{3: 16, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, 0, -8, 0, 0, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, -8, -8, -8, 8, 8, }, +{9: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -8, -8, 0, 0, 8, 8, -8, 0, 0, }, +{c: 16, 8, 0, 0, 0, 0, 0, -16, 0, 0, 0, -8, -8, 8, 0, 0, }, +{7: 16, 0, 0, 0, 0, 0, 8, 8, 0, -16, -8, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, -8, -8, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 8, -8, 0, 8, -8, 0, }, +{f: 16, -8, 0, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , x, , , , , x, x, , , , x, }, +{b: , x, x, , x, x, , , , , x, , x, , , x, }, +{d: , x, x, x, x, x, , x, , , x, , , x, , x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,1100,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x06,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x0a,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x02,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x04,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_059.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_059.txt new file mode 100644 index 0000000..68fd07b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_059.txt @@ -0,0 +1,420 @@ +059 Sbox: +LUT = { +0x06,0x08,0x01,0x0c,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x02,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{8: 0, 4, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{a: 0, 2, 0, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, }, +{b: 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 2, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +{e: 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 16, 0, 10, 6, 4, 0, 4, 4, 0, 6, 6, 4, 0, 0, 4, 0, }, +{4: 16, 4, 10, 6, 0, 4, 8, 4, 0, 0, 0, 8, 2, 2, 0, 0, }, +{8: 16, 4, 4, 0, 4, 0, 0, 2, 0, 10, 0, 2, 6, 0, 0, 0, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 2, 2, 0, 4, 2, 2, 0, 0, }, +{5: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{6: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{a: 16, 2, 4, 0, 4, 2, 2, 2, 0, 4, 2, 0, 0, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 4, 2, 0, 0, 0, 8, 0, 0, 0, 6, 6, }, +{7: 16, 2, 0, 6, 0, 8, 0, 0, 2, 0, 6, 4, 0, 0, 0, 4, }, +{b: 16, 0, 2, 0, 2, 4, 2, 0, 2, 0, 4, 0, 2, 2, 0, 4, }, +{d: 16, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 6, 2, 2, 2, }, +{e: 16, 2, 4, 2, 2, 2, 0, 0, 2, 0, 4, 2, 0, 0, 4, 0, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:66, 4:39, 6:11, 8:6, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 8, 0, 8, -8, 0, -8, 0, -16, 0, 8, 0, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 8, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, 0, -8, -8, 8, -8, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{9: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 8, 8, }, +{c: 16, 0, 0, -8, 0, 8, -8, -8, -8, 0, 8, 0, 0, 0, -8, 8, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, -8, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, }, +{d: 16, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , , x, x, , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , , , , x, x, , , , x, }, +{b: , x, x, , x, x, , x, , , x, , x, , , x, }, +{d: , , x, x, x, x, , x, , , x, , , x, , x, }, +{e: , , x, x, , x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x07,0x09,0x0e,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x03,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +059 Inverse Sbox: +LUT = { +0x08,0x02,0x0c,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 0, 2, 6, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 4, 0, 0, 2, }, +{7: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 2, 2, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 4, 2, 8, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{2: 16, 0, 10, 10, 4, 0, 0, 8, 0, 4, 4, 0, 2, 2, 4, 0, }, +{4: 16, 4, 6, 6, 0, 6, 4, 4, 0, 0, 2, 6, 0, 0, 2, 0, }, +{8: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 4, 8, 4, 0, 2, 0, }, +{5: 16, 4, 4, 8, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 2, 4, 4, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 16, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 16, 0, 6, 0, 10, 2, 4, 0, 2, 4, 0, 0, 0, 4, 0, 0, }, +{c: 16, 0, 6, 0, 0, 0, 0, 0, 0, 2, 8, 6, 4, 0, 4, 2, }, +{7: 16, 0, 4, 8, 2, 4, 0, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 0, 0, 2, 6, 2, 4, 0, 2, 0, 0, 0, 2, 6, 0, 0, }, +{d: 16, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 2, 2, 0, 6, 4, 4, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:66, 4:39, 6:11, 8:6, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{8: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 8, -16, 0, 0, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 8, -8, 0, -8, 16, -8, 0, 0, -8, 0, 0, -8, }, +{4: 16, 8, 0, -8, 8, 8, -8, -8, 0, 0, 0, -8, 8, 0, -8, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -16, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, -8, 0, 8, }, +{9: 16, -8, -8, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, -8, -8, 8, -8, 0, -8, 0, 0, 8, -8, 0, 0, }, +{c: 16, 0, -8, 0, -8, 8, 0, -8, 0, 0, 0, -8, -8, 8, 8, 0, }, +{7: 16, 0, -8, 0, 0, 0, 8, 8, 0, -8, 0, -8, 0, 8, -8, -8, }, +{b: 16, -8, 8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, -8, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , , x, x, , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , x, , , , , x, x, , , , x, }, +{b: , x, x, , x, x, , , , , x, , x, , , x, }, +{d: , x, x, x, x, x, , x, , , x, , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x07,0x09,0x0e,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0d,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x07,0x09,0x0e,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x06,0x09,0x0f,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_060.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_060.txt new file mode 100644 index 0000000..0e5f358 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_060.txt @@ -0,0 +1,420 @@ +060 Sbox: +LUT = { +0x06,0x08,0x01,0x0d,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x02,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 6, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, 2, }, +{a: 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, 0, 0, 0, 2, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 4, 0, 0, }, +{d: 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:2, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 0, 2, 4, 2, 2, 4, 2, 0, 0, 0, 4, 0, }, +{2: 16, 0, 10, 0, 0, 0, 10, 0, 4, 2, 4, 8, 4, 2, 4, 0, }, +{4: 16, 4, 4, 4, 0, 0, 8, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 16, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 6, 4, 0, 2, }, +{3: 16, 2, 0, 2, 0, 4, 4, 8, 2, 0, 2, 0, 4, 4, 0, 0, }, +{5: 16, 4, 6, 4, 0, 6, 6, 6, 2, 0, 0, 4, 2, 0, 0, 0, }, +{6: 16, 0, 4, 0, 2, 4, 8, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 2, 4, 0, 2, 0, 0, 0, 4, 2, 0, 2, 6, 0, 0, 2, }, +{a: 16, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, }, +{c: 16, 0, 6, 4, 0, 2, 0, 0, 0, 4, 4, 0, 0, 0, 10, 2, }, +{7: 16, 2, 4, 2, 2, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 16, 0, 6, 0, 2, 0, 0, 6, 4, 0, 2, 0, 8, 4, 0, 0, }, +{d: 16, 0, 0, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 2, 6, 2, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:66, 4:39, 6:11, 8:6, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{f: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:10, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, -16, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 16, 0, -8, 0, 8, -8, 16, -8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{3: 16, -8, 0, 8, 0, 8, -16, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, -8, 0, 0, 8, -8, 0, -8, 0, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, }, +{a: 16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{c: 16, 8, -8, 0, -8, 0, 0, -8, -8, 0, 8, -8, 0, 0, 0, 8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 0, 0, -8, 8, -8, 0, 8, -8, 0, 8, -8, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, 8, -8, -8, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , x, x, x, , , x, , x, , x, x, , x, , x, }, +{b: , , x, , x, x, x, x, x, , x, , x, x, , x, }, +{d: , x, x, x, x, x, x, x, x, , x, , , , , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x01,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +060 Inverse Sbox: +LUT = { +0x08,0x02,0x0d,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, }, +{7: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 2, }, +{e: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:2, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 16, 0, 10, 4, 0, 0, 6, 4, 4, 0, 6, 4, 6, 0, 4, 0, }, +{4: 16, 8, 0, 4, 0, 2, 4, 0, 0, 2, 4, 2, 0, 4, 2, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 4, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 4, 8, 6, 4, 0, 0, 0, 0, 6, 0, 0, 2, }, +{9: 16, 2, 4, 0, 0, 2, 2, 2, 4, 0, 0, 0, 4, 0, 2, 2, }, +{a: 16, 4, 2, 2, 2, 0, 0, 0, 2, 2, 4, 0, 0, 6, 0, 0, }, +{c: 16, 2, 4, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 4, 0, }, +{7: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 0, 4, 2, 6, 4, 2, 0, 6, 0, 0, 0, 8, 0, 0, 0, }, +{d: 16, 0, 2, 2, 4, 4, 0, 0, 0, 2, 0, 0, 4, 2, 2, 2, }, +{e: 16, 4, 4, 0, 0, 0, 0, 2, 0, 0, 10, 2, 0, 6, 4, 0, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:66, 4:39, 6:11, 8:6, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{d: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:10, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 8, -8, 0, -8, 8, -8, 0, 0, -16, 8, 0, 0, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 16, -8, 0, -8, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -16, -8, 0, 0, }, +{9: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, -8, 8, }, +{a: 16, 8, 8, 0, -8, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, 0, 8, -8, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -8, 0, 0, 0, 8, 8, 0, -8, 0, -8, 0, 8, -8, -8, }, +{b: 16, -8, 0, 8, 0, 8, -8, -8, 0, 0, -8, 8, 0, 0, -8, 0, }, +{d: 16, 0, -8, 0, -8, 0, 0, -8, 8, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 8, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , x, x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{d: , , x, x, x, x, x, x, x, , x, , , , , x, }, +{e: , , x, , x, , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0101,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x0b,}}, +{{0x05,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x04,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_061.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_061.txt new file mode 100644 index 0000000..0605e22 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_061.txt @@ -0,0 +1,420 @@ +061 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x05,0x06,0x07,0x04,0x03,0x0a,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, }, +{8: 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 2, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 4, }, +{c: 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{b: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 0, 4, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, }, +{e: 0, 2, 2, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 6, 6, 0, 4, 4, 4, 0, 4, 4, 0, 6, 0, 0, }, +{2: 16, 0, 4, 2, 6, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, }, +{4: 16, 4, 0, 4, 0, 0, 6, 0, 0, 2, 0, 2, 2, 2, 2, 0, }, +{8: 16, 4, 4, 0, 10, 10, 0, 0, 4, 4, 2, 2, 8, 0, 0, 0, }, +{3: 16, 2, 0, 2, 4, 4, 2, 2, 2, 0, 0, 0, 4, 0, 0, 2, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 4, 0, 0, 0, 2, 0, 4, }, +{6: 16, 0, 0, 0, 4, 4, 0, 2, 2, 2, 2, 2, 4, 0, 2, 0, }, +{9: 16, 4, 0, 2, 4, 0, 0, 2, 4, 2, 2, 0, 2, 0, 0, 2, }, +{a: 16, 0, 6, 0, 4, 0, 6, 0, 0, 8, 2, 0, 2, 0, 0, 4, }, +{c: 16, 10, 0, 0, 0, 2, 0, 4, 0, 0, 4, 4, 0, 6, 0, 2, }, +{7: 16, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{b: 16, 0, 2, 0, 6, 6, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 16, 8, 2, 0, 0, 0, 2, 4, 2, 0, 4, 4, 0, 4, 2, 0, }, +{e: 16, 2, 2, 2, 4, 4, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:65, 4:41, 6:11, 8:4, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 8, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 0, -8, 8, -16, }, +{2: 16, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 8, -8, 0, 8, 0, 0, -8, }, +{8: 16, 0, 0, 8, -8, 16, 0, 0, -8, -8, -8, 8, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 8, }, +{9: 16, 0, 0, 0, -8, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, 0, 8, }, +{c: 16, 0, 0, -8, 0, 0, -8, 0, 0, -8, 8, 0, -8, -8, 8, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, -8, 8, 0, 0, -16, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, -8, -8, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , x, , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, , , , , x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , x, , x, , , x, x, x, }, +{7: , x, x, , , x, , , , , x, x, , , , x, }, +{b: , x, x, , , , , , x, , x, , x, , , x, }, +{d: , , , x, x, x, , , , , x, , , x, , x, }, +{e: , , , x, , , , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0101,1,}, +{0011,1000,0,}, +{0011,1101,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x03,}}, +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x05,0x06,0x08,}, {0x03,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x09,}}, +{{0x0d,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +061 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x09,0x08,0x05,0x06,0x07,0x00,0x0c,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, }, +{4: 0, 2, 2, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{8: 0, 2, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 4, }, +{6: 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 2, }, +{7: 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 4, 4, 2, 4, 0, 4, 0, 10, 0, 0, 8, 2, 0, }, +{2: 16, 0, 4, 0, 4, 0, 2, 0, 0, 6, 0, 2, 2, 2, 2, 0, }, +{4: 16, 6, 2, 4, 0, 2, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{8: 16, 6, 6, 0, 10, 4, 0, 4, 4, 4, 0, 0, 6, 0, 4, 0, }, +{3: 16, 0, 0, 0, 10, 4, 0, 4, 0, 0, 2, 0, 6, 0, 4, 2, }, +{5: 16, 4, 0, 6, 0, 2, 8, 0, 0, 6, 0, 0, 0, 2, 0, 4, }, +{6: 16, 4, 0, 0, 0, 2, 2, 2, 2, 0, 4, 2, 0, 4, 2, 0, }, +{9: 16, 4, 2, 0, 4, 2, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, }, +{a: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{c: 16, 4, 2, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 4, 0, 2, }, +{7: 16, 4, 2, 2, 2, 0, 0, 2, 0, 0, 4, 2, 0, 4, 0, 2, }, +{b: 16, 0, 0, 2, 8, 4, 0, 4, 2, 2, 0, 2, 4, 0, 4, 0, }, +{d: 16, 6, 0, 2, 0, 0, 2, 0, 0, 0, 6, 2, 2, 4, 0, 0, }, +{e: 16, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:65, 4:41, 6:11, 8:4, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, -8, 0, -8, 0, 16, 0, 0, -8, 8, -8, }, +{2: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 8, 0, -8, }, +{4: 16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 8, 0, -8, -8, }, +{8: 16, 8, 0, 8, -8, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, -16, }, +{3: 16, 0, -8, 0, 0, 8, -8, 0, 0, -8, 0, 8, -8, -8, 0, 8, }, +{5: 16, -8, 0, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, -8, -8, 8, }, +{6: 16, 0, 0, -8, 0, 0, -8, 0, -8, -8, 0, 0, 0, 8, 0, 8, }, +{9: 16, -8, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, 8, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{c: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 8, }, +{7: 16, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, -8, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, 0, 0, 0, 0, -16, 0, 0, 0, 0, -8, }, +{d: 16, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{e: 16, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, , , x, }, +{5: , , x, x, x, x, x, , x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , , x, x, x, x, , , x, , x, , , x, x, x, }, +{7: , , x, , , x, , , x, , , x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , , x, x, x, , , x, , , , , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1100,0001,0,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0d,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x02,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x09,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_062.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_062.txt new file mode 100644 index 0000000..cd542fc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_062.txt @@ -0,0 +1,420 @@ +062 Sbox: +LUT = { +0x08,0x00,0x01,0x0a,0x02,0x05,0x06,0x03,0x04,0x09,0x07,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, }, +{3: 0, 4, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 0, 4, 0, 2, }, +{a: 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 2, 0, 2, 2, }, +{c: 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, }, +{d: 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 4, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{2: 16, 4, 6, 6, 0, 6, 4, 6, 2, 2, 0, 4, 0, 0, 0, 0, }, +{4: 16, 0, 4, 8, 2, 0, 2, 4, 4, 2, 0, 2, 0, 4, 0, 0, }, +{8: 16, 2, 0, 0, 4, 4, 0, 2, 2, 0, 4, 4, 8, 0, 2, 0, }, +{3: 16, 8, 10, 0, 4, 10, 0, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{5: 16, 4, 8, 0, 2, 4, 4, 0, 2, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{9: 16, 2, 0, 6, 0, 4, 0, 0, 8, 6, 0, 0, 0, 4, 0, 2, }, +{a: 16, 0, 0, 0, 0, 6, 2, 0, 4, 4, 2, 0, 2, 0, 2, 2, }, +{c: 16, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, }, +{d: 16, 2, 0, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, 6, 2, 0, }, +{e: 16, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 2, 0, 0, 0, 0, 2, 2, 0, 6, 4, 4, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:67, 4:39, 6:11, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{c: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, -8, }, +{2: 16, 8, -8, 8, 8, -8, 0, -8, 8, -8, 0, -8, 0, 0, -8, 0, }, +{4: 16, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, -8, 8, 0, -8, 0, }, +{8: 16, 8, 8, 0, -8, 0, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, -8, -8, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -8, -8, 0, }, +{5: 16, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -16, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 8, }, +{c: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, }, +{7: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{b: 16, -8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, , , x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , , , x, , x, }, +{6: , x, , x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, , , x, x, x, , , x, x, x, , x, }, +{a: , , x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{7: , x, , , , x, x, x, , x, , , , , , x, }, +{b: , , x, , , , x, x, , , , x, x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , x, x, x, x, x, , x, , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0110,1,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x05,0x09,0x0c,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x02,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x05,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +062 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x07,0x08,0x05,0x06,0x0a,0x00,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 0, 2, 0, 0, 6, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 2, 0, 0, 0, 2, 2, 4, 0, 2, 0, 0, 2, 0, }, +{c: 0, 2, 0, 0, 4, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 4, }, +{b: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 8, 4, 4, 2, 0, 2, 0, 0, 2, 0, 0, }, +{2: 16, 4, 6, 4, 0, 10, 8, 8, 0, 0, 0, 4, 0, 0, 2, 2, }, +{4: 16, 0, 6, 8, 0, 0, 0, 4, 6, 0, 2, 2, 0, 4, 0, 0, }, +{8: 16, 2, 0, 2, 4, 4, 2, 0, 0, 0, 2, 2, 6, 0, 0, 0, }, +{3: 16, 4, 6, 0, 4, 10, 4, 4, 4, 6, 0, 0, 6, 0, 0, 0, }, +{5: 16, 2, 4, 2, 0, 0, 4, 0, 0, 2, 2, 4, 0, 2, 2, 0, }, +{6: 16, 0, 6, 4, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 16, 0, 2, 4, 2, 4, 2, 0, 8, 4, 0, 0, 0, 4, 0, 2, }, +{a: 16, 0, 2, 2, 0, 4, 0, 2, 6, 4, 0, 2, 0, 0, 2, 0, }, +{c: 16, 2, 0, 0, 4, 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 6, }, +{7: 16, 2, 4, 2, 4, 0, 4, 0, 0, 0, 0, 8, 2, 0, 2, 4, }, +{b: 16, 2, 0, 0, 8, 4, 0, 2, 0, 2, 0, 4, 4, 2, 0, 4, }, +{d: 16, 2, 0, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, 6, 2, 0, }, +{e: 16, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:67, 4:39, 6:11, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{c: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, -8, 0, -8, -8, 8, 0, 0, -8, 0, 0, }, +{2: 16, 0, -8, 0, 8, -8, 8, -8, 0, 0, 8, 0, -8, 8, -16, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -8, 8, -8, 0, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 8, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, }, +{3: 16, 0, -16, 8, 8, 0, -8, -8, 0, -8, 0, 8, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 0, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, -16, 0, }, +{a: 16, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, }, +{c: 16, 0, 8, 0, -8, 0, 8, 0, -8, 0, 0, 0, -8, -8, 0, 0, }, +{7: 16, -8, -8, -8, 0, 8, 0, 8, 0, 8, 0, -8, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 16, -8, }, +{d: 16, -8, 8, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{f: 16, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , , , x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, , x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, , , , x, , , , x, , x, , , , x, }, +{b: , x, , , , x, x, x, , x, , x, x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0011,1,}, +{1110,0010,1,}, +{1110,1001,1,}, +{1110,1011,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x06,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x05,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_063.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_063.txt new file mode 100644 index 0000000..3ef4fff --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_063.txt @@ -0,0 +1,420 @@ +063 Sbox: +LUT = { +0x08,0x00,0x01,0x0d,0x02,0x05,0x03,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, }, +{2: 0, 2, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 4, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{6: 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, 0, }, +{9: 0, 2, 0, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, }, +{a: 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 4, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 2, 0, 4, 0, 0, 2, 2, 2, 0, 2, 0, 0, }, +{2: 16, 2, 6, 0, 0, 0, 4, 0, 8, 0, 4, 8, 4, 2, 10, 0, }, +{4: 16, 4, 2, 4, 2, 0, 10, 0, 0, 4, 0, 0, 0, 0, 0, 6, }, +{8: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 16, 2, 0, 0, 2, 4, 8, 6, 0, 4, 0, 0, 0, 0, 0, 6, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 0, 0, 0, 4, 0, 2, 2, 0, }, +{6: 16, 0, 0, 0, 2, 6, 4, 4, 0, 2, 0, 2, 2, 2, 0, 0, }, +{9: 16, 2, 8, 4, 0, 0, 0, 4, 4, 2, 2, 2, 4, 0, 0, 0, }, +{a: 16, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 16, 0, 10, 6, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 4, 2, }, +{7: 16, 0, 4, 2, 0, 2, 8, 0, 0, 4, 2, 4, 2, 0, 0, 4, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 4, 2, 2, 4, 0, }, +{e: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 2, 0, 0, 6, 2, 0, 4, 0, 0, 6, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:65, 4:35, 6:11, 8:7, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 8, 8, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{5: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:6, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 0, 0, 8, 0, -16, 0, 0, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 8, 0, 0, 0, 0, 8, -8, 0, 8, -8, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 8, 0, 0, 0, -8, 0, 0, 8, -8, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, -16, 8, -8, 0, 0, 0, 8, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, -8, 8, 0, }, +{9: 16, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, -16, 8, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 8, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, -8, 0, 0, 8, }, +{7: 16, -8, -8, -8, 0, 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, -8, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, -8, 8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, , x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , , x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , x, x, x, , , x, x, x, , x, x, , x, , x, }, +{b: , , , , x, x, x, , x, , x, , x, x, , x, }, +{d: , , , , x, , x, x, x, , x, , , , , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0011,0101,1,}, +{0011,0111,0,}, +{0111,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x01,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x01,0x02,0x03,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x03,0x08,0x0b,}}, +{{0x09,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +063 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x08,0x05,0x0d,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{5: 0, 0, 0, 2, 0, 4, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 4, 0, 0, 0, 2, 0, }, +{9: 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{a: 0, 2, 0, 4, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 2, 2, 0, }, +{d: 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, 4, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 0, 2, }, +{2: 16, 0, 6, 2, 0, 0, 8, 0, 8, 2, 10, 4, 4, 0, 4, 0, }, +{4: 16, 6, 0, 4, 0, 0, 8, 0, 4, 2, 6, 2, 0, 0, 0, 0, }, +{8: 16, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 16, 0, 0, 0, 2, 4, 4, 6, 0, 0, 0, 2, 2, 2, 0, 2, }, +{5: 16, 4, 4, 10, 0, 8, 6, 4, 0, 2, 0, 8, 2, 0, 0, 0, }, +{6: 16, 0, 0, 0, 2, 6, 10, 4, 4, 0, 4, 0, 0, 0, 2, 0, }, +{9: 16, 0, 8, 0, 2, 0, 0, 0, 4, 0, 2, 0, 6, 4, 0, 6, }, +{a: 16, 2, 0, 4, 0, 4, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, }, +{c: 16, 2, 4, 0, 2, 0, 0, 0, 2, 2, 4, 2, 0, 2, 4, 0, }, +{7: 16, 2, 8, 0, 0, 0, 4, 2, 2, 0, 0, 4, 0, 4, 2, 4, }, +{b: 16, 0, 4, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 2, 2, 0, }, +{d: 16, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{e: 16, 0, 10, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 4, 4, 6, }, +{f: 16, 0, 0, 6, 0, 6, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:65, 4:35, 6:11, 8:7, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{5: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 12, 0, 0, 4, 0, }, +{b: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:6, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 8, 0, 0, 8, -8, 8, -16, 0, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, -16, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, -8, }, +{3: 16, -8, -8, 0, 0, 8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, }, +{5: 16, -8, 0, 0, 8, 0, 0, -16, -8, 8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, 0, -8, 0, 0, -8, 0, -8, -8, 0, 8, -8, 0, 0, 8, }, +{9: 16, 0, 0, 8, -8, 0, 0, 0, 8, -8, 0, -8, -8, 8, -8, 0, }, +{a: 16, 0, 0, 0, 0, 0, -8, 0, 8, 8, -8, -8, 0, -8, 0, 0, }, +{c: 16, 0, 8, 0, -8, 0, 0, 0, -8, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 0, 0, 0, 16, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, 0, -8, -8, 0, 8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, , x, x, x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , x, , , x, x, , x, , , , , x, , , x, }, +{d: , , , , x, x, x, , x, , x, , , , , x, }, +{e: , , , , x, , x, x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0010,1,}, +{0110,0101,1,}, +{0110,0111,0,}, +{0111,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x02,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x02,0x05,0x07,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x03,}}, +{{0x03,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,}}, +{{0x01,0x02,}, {0x06,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x06,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_064.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_064.txt new file mode 100644 index 0000000..26879e6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_064.txt @@ -0,0 +1,420 @@ +064 Sbox: +LUT = { +0x08,0x00,0x01,0x0a,0x02,0x05,0x06,0x07,0x04,0x09,0x0d,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{2: 0, 0, 6, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 2, 2, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, }, +{3: 0, 2, 2, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, }, +{9: 0, 4, 0, 2, 0, 0, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 0, 2, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 4, 2, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:5, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 6, 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, 2, }, +{2: 16, 0, 6, 2, 0, 0, 8, 0, 8, 2, 10, 4, 4, 0, 4, 0, }, +{4: 16, 4, 0, 2, 2, 2, 2, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{8: 16, 6, 0, 0, 4, 0, 4, 2, 10, 0, 4, 0, 0, 0, 2, 0, }, +{3: 16, 2, 2, 2, 0, 4, 2, 0, 4, 4, 0, 0, 0, 2, 0, 2, }, +{5: 16, 0, 8, 0, 0, 0, 4, 2, 0, 0, 2, 6, 0, 6, 0, 4, }, +{6: 16, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, }, +{9: 16, 8, 4, 2, 4, 4, 0, 0, 6, 10, 0, 2, 8, 0, 0, 0, }, +{a: 16, 0, 0, 2, 0, 6, 4, 0, 8, 4, 6, 0, 2, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 2, 2, 2, 0, 0, 4, 0, 2, 0, 4, 2, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 8, 0, 2, 2, 2, 0, 4, 0, 0, 0, 4, 4, 2, 4, }, +{d: 16, 6, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 4, 2, 2, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:65, 4:35, 6:11, 8:7, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{f: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, -8, 8, -8, }, +{2: 16, 8, 0, 8, 0, -8, 0, -8, 8, -8, 0, -16, 0, 8, -8, 0, }, +{4: 16, 0, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 8, -8, 0, 0, }, +{8: 16, 8, 8, 0, -8, 0, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 0, 8, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, 0, -8, 0, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, 0, -8, -8, 8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -16, -8, 8, -8, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 16, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, -8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, x, x, x, , , , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, , x, x, x, x, , x, , x, , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{7: , x, , x, , x, , , , x, , x, , , , x, }, +{b: , , , , x, x, x, , x, , x, , x, x, , x, }, +{d: , x, , x, x, x, x, , x, , x, , , , , x, }, +{e: , , x, x, , , x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,1010,1,}, +{0111,0010,1,}, +{0111,1001,1,}, +{0111,1011,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x07,}}, +{{0x09,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x01,0x04,}, {0x05,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x08,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +064 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0d,0x08,0x05,0x06,0x07,0x00,0x09,0x03,0x0b,0x0c,0x0a,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 4, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{7: 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:5, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 6, 2, 0, 2, 8, 0, 0, 0, 0, 6, 0, 0, }, +{2: 16, 0, 6, 0, 0, 2, 8, 0, 4, 0, 4, 4, 8, 0, 10, 2, }, +{4: 16, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 16, 6, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 16, 0, 0, 2, 0, 4, 0, 2, 4, 6, 2, 0, 2, 0, 0, 2, }, +{5: 16, 0, 8, 2, 4, 2, 4, 0, 0, 4, 2, 4, 2, 0, 0, 0, }, +{6: 16, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 16, 4, 8, 0, 10, 4, 0, 0, 6, 8, 0, 0, 4, 0, 2, 2, }, +{a: 16, 0, 2, 4, 0, 4, 0, 2, 10, 4, 0, 0, 0, 6, 0, 0, }, +{c: 16, 0, 10, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 2, 4, 0, }, +{7: 16, 2, 4, 2, 0, 0, 6, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 2, 4, 4, 0, 0, 0, 0, 8, 2, 2, 2, 4, 4, 0, 0, }, +{d: 16, 2, 0, 2, 0, 2, 6, 0, 0, 0, 0, 0, 4, 2, 6, 0, }, +{e: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 4, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:65, 4:35, 6:11, 8:7, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{7: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, -8, 0, 8, -8, 8, -8, 0, 0, 8, 0, -8, 8, -16, 0, }, +{4: 16, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, 0, -8, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, 0, 0, -16, -8, 8, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, 0, 8, 8, -8, 0, -8, 0, 8, -16, 0, }, +{a: 16, 8, 0, 0, 0, -8, 0, -8, 8, 0, -8, -8, 8, -8, 0, 0, }, +{c: 16, 8, 8, 0, -8, 0, 8, -8, -8, -8, 0, 0, -8, 0, 0, 0, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 16, -8, }, +{d: 16, -8, 0, 0, 0, 0, -8, -8, 0, 8, 0, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, x, x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, x, , x, , x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , , , x, x, }, +{7: , , x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , x, x, , x, , x, , x, x, x, , x, x, , x, }, +{d: , x, , , , , x, , x, x, x, , , , , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0101,1,}, +{1110,0010,1,}, +{1110,1001,1,}, +{1110,1011,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x07,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x03,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x05,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_065.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_065.txt new file mode 100644 index 0000000..732f4a4 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_065.txt @@ -0,0 +1,420 @@ +065 Sbox: +LUT = { +0x08,0x00,0x01,0x0e,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x02,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, 0, 0, }, +{9: 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 0, 4, 2, 0, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 2, }, +{b: 0, 0, 0, 0, 4, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 6, 2, 0, 6, 0, 0, 0, 8, 0, 2, 0, 4, }, +{2: 16, 0, 10, 4, 4, 0, 0, 4, 2, 4, 10, 2, 0, 0, 8, 0, }, +{4: 16, 4, 4, 8, 2, 0, 4, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, }, +{3: 16, 4, 0, 6, 0, 4, 8, 6, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 4, 6, 6, 0, 4, 4, 6, 0, 0, 2, 6, 2, 0, 0, 0, }, +{9: 16, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{a: 16, 2, 6, 0, 10, 0, 0, 0, 0, 4, 0, 4, 2, 0, 0, 4, }, +{c: 16, 2, 4, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{7: 16, 8, 0, 4, 0, 0, 4, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{b: 16, 0, 0, 0, 4, 2, 0, 0, 2, 2, 2, 6, 2, 0, 0, 4, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:36, 6:16, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 8, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:5, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, -8, -16, 0, 0, }, +{2: 16, 8, -8, 0, 0, -8, 0, 0, 0, -8, 8, -8, 0, 16, -8, -8, }, +{4: 16, 0, 8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, }, +{3: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 8, 0, 0, -16, 0, 0, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 8, -8, -8, 8, 0, -8, 0, 8, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, 0, 0, 8, 0, -8, 0, -8, -8, 0, 0, 8, -8, }, +{c: 16, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 8, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , x, x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , x, x, , , x, , x, }, +{7: , , x, , , , , , , x, x, x, , , x, x, }, +{b: , x, , , x, x, , , , x, x, , x, , x, x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , x, x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +065 Inverse Sbox: +LUT = { +0x01,0x02,0x0e,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x03,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 4, }, +{4: 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 2, 6, 2, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, }, +{f: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 0, 4, 2, 2, 2, 8, 0, 0, 0, 2, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 0, 6, 4, 0, 0, 4, 6, 4, }, +{4: 16, 0, 4, 8, 0, 6, 0, 6, 2, 0, 2, 4, 0, 0, 0, 0, }, +{8: 16, 6, 4, 2, 4, 0, 0, 0, 0, 10, 0, 0, 4, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 16, 0, 0, 4, 2, 8, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 6, 4, 4, 2, 6, 6, 6, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 16, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 16, 0, 4, 2, 4, 0, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 4, 6, }, +{7: 16, 8, 2, 0, 0, 0, 0, 6, 0, 4, 0, 4, 6, 0, 0, 2, }, +{b: 16, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:36, 6:16, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{6: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 8, 4, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:7, 4:5, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, 8, }, +{2: 16, 8, -16, 0, 0, -8, 8, 0, 8, 0, 8, -8, -8, 0, -8, 0, }, +{4: 16, 0, 0, -8, 8, 8, -8, 0, 0, -8, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 8, -8, 8, 0, 0, 0, 8, -8, 0, -8, -8, 0, -8, }, +{3: 16, -8, 0, 0, 0, 0, -8, -8, -8, 0, 8, 8, 0, 0, 0, 0, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 8, -8, -8, 8, 0, -8, -8, 8, -8, -8, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, -8, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 8, -8, 0, 8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -16, 0, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, 0, -8, -8, 0, 0, 0, -8, 8, 0, 0, 8, -8, -8, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, , x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, , x, , x, , x, x, x, , , x, x, }, +{9: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , x, , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , x, , x, , x, x, x, , , x, x, }, +{b: , x, , , , x, , x, , x, x, , x, , x, x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_066.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_066.txt new file mode 100644 index 0000000..e9b520e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_066.txt @@ -0,0 +1,420 @@ +066 Sbox: +LUT = { +0x06,0x00,0x01,0x08,0x0d,0x05,0x04,0x07,0x02,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 13, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 13, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{2: 0, 0, 6, 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{5: 0, 2, 0, 0, 0, 2, 6, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 4, 2, 0, 2, 0, 0, }, +{9: 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 4, }, +{7: 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, 0, }, +{b: 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, }, +{f: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{2: 16, 0, 10, 0, 4, 0, 4, 0, 6, 4, 6, 6, 4, 0, 4, 0, }, +{4: 16, 8, 0, 8, 0, 0, 8, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 4, 0, 4, 0, 4, 8, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{5: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 0, 2, 0, 2, 8, 4, 4, 0, 0, 4, 2, 0, 2, 0, 4, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 0, 2, 2, 4, 0, 0, 0, 2, 6, 0, 2, 0, 0, 4, }, +{c: 16, 0, 4, 0, 0, 6, 0, 0, 0, 2, 8, 2, 0, 0, 6, 4, }, +{7: 16, 6, 4, 4, 0, 0, 10, 0, 2, 0, 0, 4, 0, 2, 0, 0, }, +{b: 16, 0, 10, 0, 6, 0, 0, 0, 4, 4, 0, 2, 4, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{f: 16, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:63, 4:34, 6:14, 8:7, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{5: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{2: 16, 8, 0, 8, 0, 0, 8, 0, 0, -16, 0, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, 8, -8, 0, 0, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, -8, 0, 0, 8, -8, 0, 0, 8, }, +{6: 16, 8, 0, -8, 0, 0, 0, 0, 0, -16, 0, 0, -8, 0, 8, 0, }, +{9: 16, 0, -8, 8, -8, -8, 0, 0, 8, 0, 0, -8, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, -8, -8, -8, 8, 0, 0, -8, 0, 8, -8, 0, 0, 0, 8, }, +{7: 16, -8, 8, -8, 8, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , , x, , x, x, , x, , x, x, , x, , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , x, , x, x, , x, , , , , , x, , x, }, +{e: , , , x, , , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,1101,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x0a,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x01,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x02,0x08,0x0a,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +066 Inverse Sbox: +LUT = { +0x01,0x02,0x08,0x0d,0x06,0x05,0x00,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x04,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{8: 0, 2, 4, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 2, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{9: 0, 2, 2, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 4, 0, 0, 2, 0, 0, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 2, 0, }, +{b: 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 4, 6, 0, 0, 2, 0, 6, 0, 0, 0, 0, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 8, 0, 4, 4, 10, 0, 4, 2, }, +{4: 16, 4, 0, 8, 2, 4, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{8: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{3: 16, 2, 0, 0, 2, 4, 6, 8, 0, 4, 6, 0, 0, 0, 0, 0, }, +{5: 16, 4, 4, 8, 0, 8, 6, 4, 0, 0, 0, 10, 0, 2, 0, 2, }, +{6: 16, 2, 0, 0, 2, 4, 6, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{9: 16, 2, 6, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, 0, 0, 2, }, +{a: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{c: 16, 0, 6, 0, 0, 0, 2, 4, 0, 6, 8, 0, 0, 2, 4, 0, }, +{7: 16, 0, 6, 0, 0, 0, 4, 2, 0, 0, 2, 4, 2, 2, 2, 0, }, +{b: 16, 2, 4, 2, 2, 0, 0, 0, 6, 2, 0, 0, 4, 0, 2, 0, }, +{d: 16, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 16, 0, 4, 2, 0, 2, 0, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 4, 2, 4, 4, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:63, 4:34, 6:14, 8:7, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, 0, 0, -16, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, -8, 8, 0, -8, 0, 0, 16, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 0, 8, 8, 0, 0, 0, -8, -8, 8, -8, 0, -8, }, +{8: 16, 8, -8, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -16, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, -8, 8, -16, 8, 0, 8, -8, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, }, +{9: 16, -8, 0, 8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, -8, 0, -8, 0, -8, 0, -8, 0, 0, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 8, -8, }, +{b: 16, 0, 0, 8, -8, 0, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, 8, -8, -8, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, , , x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , , x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , , x, , , x, x, , x, , x, x, , x, , x, }, +{b: , x, , x, x, , x, , x, , x, , x, x, , x, }, +{d: , , x, , , x, x, x, x, , x, , , , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x01,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x04,0x09,0x0d,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_067.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_067.txt new file mode 100644 index 0000000..892e832 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_067.txt @@ -0,0 +1,420 @@ +067 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x0f,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 14, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 14, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 4, 2, }, +{9: 0, 0, 2, 0, 4, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, }, +{a: 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, 4, }, +{7: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 6, 0, 2, 0, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 4, 4, 8, 2, 2, 0, 4, 0, 2, 2, 0, }, +{2: 16, 0, 10, 0, 4, 0, 4, 0, 4, 4, 4, 6, 6, 0, 6, 0, }, +{4: 16, 0, 0, 4, 2, 8, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 2, 0, 6, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{5: 16, 0, 4, 0, 0, 6, 8, 4, 2, 0, 0, 6, 0, 2, 0, 0, }, +{6: 16, 8, 2, 0, 0, 0, 0, 4, 0, 2, 0, 6, 0, 0, 4, 6, }, +{9: 16, 0, 10, 0, 4, 0, 0, 0, 4, 6, 0, 2, 4, 0, 0, 2, }, +{a: 16, 4, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 4, 4, }, +{c: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 10, 4, }, +{7: 16, 6, 4, 6, 0, 6, 4, 4, 0, 0, 2, 6, 0, 2, 0, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{e: 16, 0, 4, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 2, }, +{f: 16, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:36, 6:16, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, 8, -8, 0, 0, }, +{2: 16, 8, -16, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, 8, 0, -8, }, +{4: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, -8, 0, -8, 8, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 8, }, +{6: 16, 8, -16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 8, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, -8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, 0, -8, 8, 8, -8, -8, 0, 0, 8, }, +{7: 16, -8, 0, -8, 8, 8, 0, 0, -8, -8, 0, -8, 8, 0, 8, -8, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 8, -8, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, }, +{f: 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , , , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , x, , , x, x, x, x, x, , x, x, x, x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , x, x, x, x, , x, x, x, x, x, , x, x, }, +{e: , , , x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0100,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x08,0x0a,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,}}, +{{0x01,0x06,}, {0x02,0x09,0x0b,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +067 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x0f,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{8: 0, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 0, 0, 0, 0, 2, 0, 4, 4, 0, 2, 0, 0, 0, 2, 0, 2, }, +{9: 0, 2, 0, 2, 2, 2, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 2, 4, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 2, 0, 8, 0, 4, 6, 6, 0, 0, 0, 0, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 10, 0, 4, 4, 8, 2, 4, 0, }, +{4: 16, 0, 0, 4, 2, 6, 0, 0, 0, 0, 0, 6, 0, 2, 2, 2, }, +{8: 16, 0, 4, 2, 2, 2, 0, 0, 4, 2, 0, 0, 6, 0, 2, 0, }, +{3: 16, 4, 0, 8, 2, 4, 6, 0, 0, 2, 0, 6, 0, 0, 0, 0, }, +{5: 16, 4, 4, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{6: 16, 8, 0, 4, 2, 0, 4, 4, 0, 2, 0, 4, 0, 2, 0, 2, }, +{9: 16, 2, 4, 2, 2, 2, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, }, +{a: 16, 2, 4, 0, 2, 0, 0, 2, 6, 2, 2, 0, 4, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 4, 6, 4, 0, 4, 6, 6, 2, 0, 0, 6, 0, 0, 0, 2, }, +{b: 16, 0, 6, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 2, 2, 0, }, +{d: 16, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 16, 2, 6, 0, 0, 0, 0, 4, 0, 4, 10, 0, 0, 0, 4, 2, }, +{f: 16, 0, 0, 0, 0, 2, 0, 6, 2, 4, 4, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:61, 4:36, 6:16, 8:5, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 4, 4, 12, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, -8, 0, -8, 8, 0, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 16, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{3: 16, -8, 0, 8, 8, 0, 0, 0, -16, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, -8, -8, 0, 8, }, +{9: 16, -8, 8, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, 0, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 8, 8, 0, -8, -8, -8, 0, 8, 0, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 8, -8, -8, 0, -8, -8, 8, 0, 0, 8, 0, -8, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, , x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , x, , , x, x, x, x, x, x, , x, x, x, x, }, +{b: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x01,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x04,0x09,0x0d,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x05,0x09,0x0c,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x04,0x09,0x0d,}}, +{{0x09,0x06,}, {0x0f,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_068.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_068.txt new file mode 100644 index 0000000..7c109a1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_068.txt @@ -0,0 +1,420 @@ +068 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x0a,0x04,0x07,0x00,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, 0, 0, }, +{4: 0, 0, 2, 4, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{8: 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{a: 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 2, }, +{e: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 16, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 16, 4, 10, 4, 0, 4, 10, 4, 0, 2, 0, 8, 0, 2, 0, 0, }, +{4: 16, 4, 10, 8, 0, 4, 6, 8, 0, 0, 2, 4, 2, 0, 0, 0, }, +{8: 16, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 16, 8, 4, 4, 0, 4, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{5: 16, 0, 4, 0, 0, 4, 8, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{6: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{a: 16, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 6, 4, 0, }, +{c: 16, 2, 0, 0, 0, 4, 2, 0, 4, 6, 2, 0, 0, 2, 0, 2, }, +{7: 16, 4, 4, 4, 2, 0, 8, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 0, 2, 4, 4, 0, }, +{d: 16, 0, 2, 2, 0, 4, 0, 0, 4, 4, 2, 0, 2, 0, 2, 2, }, +{e: 16, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:74, 4:41, 6:3, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{d: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{e: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:12, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 0, 8, 0, -8, 0, }, +{2: 16, 0, -8, 0, 8, -8, 16, -8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 0, 8, -8, 0, -8, 8, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, -8, 0, 0, }, +{3: 16, 0, 0, 0, 0, 8, -16, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{9: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, }, +{c: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, }, +{b: 16, 0, 8, 0, -8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, -8, }, +{d: 16, 8, -8, 0, -8, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, x, x, , , x, , , x, , x, , , , x, }, +{b: , , x, , x, x, x, x, , x, , , x, , , x, }, +{d: , x, x, x, x, x, x, x, , x, , , , x, , x, }, +{e: , x, x, x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +068 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x0a,0x00,0x07,0x01,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 6, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{a: 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 4, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 2, }, +{e: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 2, 8, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, }, +{2: 16, 4, 10, 10, 0, 4, 4, 8, 0, 0, 0, 4, 2, 2, 0, 0, }, +{4: 16, 0, 4, 8, 2, 4, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 16, 16, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{5: 16, 4, 10, 6, 0, 4, 8, 4, 0, 2, 2, 8, 0, 0, 0, 0, }, +{6: 16, 4, 4, 8, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 16, 4, 0, 0, 2, 2, 0, 2, 2, 0, 4, 0, 2, 4, 0, 2, }, +{a: 16, 4, 2, 0, 2, 0, 2, 0, 2, 2, 6, 0, 0, 4, 0, 0, }, +{c: 16, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, }, +{7: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, }, +{d: 16, 4, 2, 0, 0, 0, 2, 0, 0, 6, 2, 0, 4, 0, 2, 2, }, +{e: 16, 4, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 4, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:74, 4:41, 6:3, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{2: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{d: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:12, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, 0, 8, -16, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 0, -8, 16, -8, 0, 0, -8, 0, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, 0, 8, 8, -8, -8, -8, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 8, 0, 0, -8, -8, -16, 0, 8, -8, 0, -8, 8, 8, }, +{5: 16, 8, 8, -8, 8, 0, 0, -16, 0, 8, -8, -8, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, -8, 8, -8, 0, -8, 8, }, +{9: 16, -8, 0, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{a: 16, 0, 8, 0, -8, -8, 8, -8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{c: 16, -8, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, 0, -8, 0, 0, 0, 8, 8, 0, -8, 0, -8, 0, 8, -8, -8, }, +{b: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, }, +{d: 16, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, 0, 0, }, +{e: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , x, x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , , x, x, , , x, , , x, , x, , , , x, }, +{b: , x, x, , x, , x, , , x, , , x, , , x, }, +{d: , x, x, x, x, , x, x, , x, , , , x, , x, }, +{e: , x, x, , x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_069.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_069.txt new file mode 100644 index 0000000..5e9dd96 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_069.txt @@ -0,0 +1,420 @@ +069 Sbox: +LUT = { +0x08,0x00,0x01,0x03,0x02,0x0a,0x06,0x07,0x04,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{2: 0, 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, }, +{3: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 4, 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 2, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, }, +{d: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, }, +{e: 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 4, 0, }, +{f: 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:7, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 6, 2, 4, 0, 0, 0, 0, 8, 0, 0, 6, 2, 0, 0, }, +{2: 16, 0, 4, 2, 2, 2, 4, 0, 2, 0, 0, 4, 2, 2, 0, 0, }, +{4: 16, 2, 4, 4, 6, 0, 0, 0, 0, 8, 0, 2, 0, 0, 6, 0, }, +{8: 16, 0, 2, 0, 4, 4, 4, 0, 2, 0, 2, 2, 0, 8, 4, 0, }, +{3: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, }, +{5: 16, 0, 8, 0, 8, 0, 6, 2, 2, 10, 0, 4, 0, 4, 0, 4, }, +{6: 16, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, 2, 0, 4, 6, 0, }, +{9: 16, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 16, 4, 0, 4, 0, 0, 6, 0, 0, 6, 2, 2, 6, 0, 4, 6, }, +{c: 16, 4, 0, 2, 0, 2, 0, 4, 2, 0, 2, 4, 0, 2, 0, 2, }, +{7: 16, 4, 6, 0, 0, 0, 4, 6, 0, 0, 0, 8, 2, 0, 0, 2, }, +{b: 16, 8, 0, 2, 2, 2, 0, 4, 0, 4, 0, 4, 4, 0, 0, 2, }, +{d: 16, 0, 0, 2, 6, 0, 6, 0, 0, 0, 2, 0, 2, 4, 2, 0, }, +{e: 16, 2, 2, 4, 0, 4, 2, 2, 0, 4, 0, 0, 0, 4, 8, 0, }, +{f: 16, 0, 0, 0, 0, 2, 6, 0, 2, 4, 2, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:64, 4:35, 6:15, 8:8, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{2: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{d: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:7, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, -16, }, +{2: 16, 0, 0, 8, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, -8, -8, }, +{4: 16, 8, 0, 0, 0, 0, 0, 0, -8, 8, -8, -8, 8, -8, 0, -8, }, +{8: 16, 8, 0, 0, -8, 0, 0, 8, -8, -8, 0, 0, 0, 8, -8, -8, }, +{3: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 8, }, +{5: 16, 0, 0, 0, 8, -16, 8, -8, 0, 0, -8, 0, -8, 8, -8, 8, }, +{6: 16, 0, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, }, +{a: 16, 0, -8, 0, -8, 0, 8, -8, -8, 8, -8, -8, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, 0, 0, -8, 0, 8, }, +{7: 16, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, 0, 8, -8, }, +{b: 16, -8, -8, 0, 0, 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{e: 16, 0, 0, -8, 0, -16, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, }, +{f: 16, -8, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, , x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , , x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , x, x, , , x, x, x, x, , x, x, , x, x, x, }, +{d: , , , x, x, , x, , , x, , , , x, , x, }, +{e: , , , x, , x, x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0101,1,}, +{0011,1011,0,}, +{0011,1110,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x03,}}, +{{0x01,0x0a,0x04,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x01,}}, +{{0x02,0x08,}, {0x08,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x03,0x09,0x0a,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x07,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x01,0x02,0x03,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x03,}}, +{{0x05,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x03,0x04,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +069 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x08,0x0f,0x06,0x07,0x00,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, }, +{2: 0, 2, 4, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, }, +{4: 0, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, }, +{8: 0, 4, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{3: 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 4, 0, 0, 2, 2, 2, 6, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{b: 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, }, +{e: 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 4, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:4, 2:7, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 2, 0, 0, 2, 4, 4, 4, 8, 0, 2, 0, }, +{2: 16, 6, 4, 4, 2, 0, 8, 0, 0, 0, 0, 6, 0, 0, 2, 0, }, +{4: 16, 2, 2, 4, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 4, 0, }, +{8: 16, 4, 2, 6, 4, 0, 8, 0, 0, 0, 0, 0, 2, 6, 0, 0, }, +{3: 16, 0, 2, 0, 4, 2, 0, 4, 2, 0, 2, 0, 2, 0, 4, 2, }, +{5: 16, 0, 4, 0, 4, 2, 6, 0, 0, 6, 0, 4, 0, 6, 2, 6, }, +{6: 16, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 6, 4, 0, 2, 0, }, +{9: 16, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 16, 8, 0, 8, 0, 0, 10, 2, 2, 6, 0, 0, 4, 0, 4, 4, }, +{c: 16, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 6, 2, 0, 0, 2, 0, 0, 0, 6, 0, 2, 4, 2, 0, 0, }, +{d: 16, 2, 2, 0, 8, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, }, +{e: 16, 0, 0, 6, 4, 0, 0, 6, 0, 4, 0, 0, 0, 2, 8, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 6, 2, 2, 2, 0, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:64, 4:35, 6:15, 8:8, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{b: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:7, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, -8, 8, 0, 0, -8, }, +{2: 16, 0, 0, 0, 8, -8, 8, 0, -8, 0, 0, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, 0, -8, }, +{8: 16, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, -16, }, +{3: 16, 0, -8, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, 0, 0, 8, }, +{5: 16, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 8, 0, 0, -8, 8, }, +{6: 16, 0, 0, -8, 0, 0, -8, 0, -8, -8, 0, 0, 0, 8, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, }, +{a: 16, 8, 0, 0, 0, -8, 0, -8, 0, 8, -16, -8, 8, -8, 0, 8, }, +{c: 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, }, +{7: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, }, +{e: 16, 8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, -8, -8, -8, }, +{f: 16, -8, -8, 0, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , x, , x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , , x, , , x, , x, x, x, x, , x, x, x, x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , , , x, x, x, , x, x, x, x, x, x, , x, x, }, +{e: , , , x, x, , x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1100,0111,1,}, +{1100,1010,1,}, +{1100,1101,0,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0d,}}, +{{0x0a,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x01,0x06,0x07,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x05,0x09,0x0c,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_070.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_070.txt new file mode 100644 index 0000000..0d2982c --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_070.txt @@ -0,0 +1,420 @@ +070 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x0b,0x07,0x06,0x09,0x0a,0x03,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, }, +{5: 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 2, 2, 2, }, +{9: 0, 0, 4, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, }, +{c: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 2, 2, 0, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 2, 2, }, +{f: 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 2, 0, 4, 0, 0, 4, 0, 2, 2, 4, 0, 0, 2, }, +{2: 16, 4, 6, 0, 6, 4, 2, 0, 6, 6, 2, 0, 4, 0, 0, 0, }, +{4: 16, 0, 0, 4, 0, 4, 2, 2, 0, 4, 2, 8, 0, 4, 0, 2, }, +{8: 16, 0, 10, 0, 4, 0, 2, 0, 6, 4, 0, 0, 4, 0, 2, 0, }, +{3: 16, 10, 4, 8, 0, 6, 8, 4, 0, 0, 2, 4, 0, 0, 2, 0, }, +{5: 16, 2, 2, 0, 0, 6, 4, 6, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 16, 0, 0, 0, 2, 6, 4, 4, 0, 0, 0, 2, 0, 2, 2, 2, }, +{9: 16, 0, 8, 2, 0, 0, 0, 2, 8, 0, 0, 0, 8, 2, 0, 2, }, +{a: 16, 2, 4, 0, 4, 2, 0, 0, 0, 8, 2, 4, 0, 4, 2, 0, }, +{c: 16, 6, 0, 4, 2, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 16, 0, 0, 6, 0, 6, 0, 0, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 2, 2, 0, }, +{d: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 0, 0, 2, 0, 2, 2, 0, 6, 0, 4, 0, 4, 2, 2, }, +{f: 16, 4, 2, 6, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:64, 4:34, 6:14, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:9, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, -8, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{2: 16, 8, 0, 8, 0, -8, 8, -8, 0, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 8, 0, -8, 0, 0, 0, -8, 0, 8, -8, -8, 0, -8, 0, 8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 0, 0, -8, 8, -8, 8, -8, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, -16, 0, 8, 8, 0, 0, -8, 8, }, +{5: 16, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, }, +{6: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, 8, 0, -8, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 16, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, -16, 0, 0, -8, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{7: 16, -8, -8, 0, 0, 8, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{f: 16, 0, 0, 0, 0, 0, -8, 0, 0, 8, 8, -8, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, x, , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , x, x, , , , x, x, x, , x, x, , , x, }, +{b: , x, x, , x, x, , x, x, x, , , , , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, , , x, , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0111,0001,1,}, +{1001,0011,1,}, +{1001,1001,0,}, +{1001,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x09,0x0a,0x04,}, {0x09,}}, +{{0x09,0x0a,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x04,0x09,0x0d,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x04,0x09,0x0d,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x06,0x09,0x0f,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x09,}}, +{{0x0b,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x01,0x06,0x07,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x09,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +070 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0b,0x00,0x05,0x08,0x07,0x03,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 4, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{4: 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{5: 0, 0, 2, 2, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 0, 4, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 0, }, +{a: 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{c: 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 4, 0, }, +{e: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 10, 2, 0, 0, 2, 6, 0, 0, 0, 0, 4, }, +{2: 16, 8, 6, 0, 10, 4, 2, 0, 8, 4, 0, 0, 4, 0, 0, 2, }, +{4: 16, 2, 0, 4, 0, 8, 0, 0, 2, 0, 4, 6, 0, 0, 0, 6, }, +{8: 16, 0, 6, 0, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{3: 16, 4, 4, 4, 0, 6, 6, 6, 0, 2, 0, 6, 0, 2, 0, 0, }, +{5: 16, 0, 2, 2, 2, 8, 4, 4, 0, 0, 4, 0, 0, 0, 2, 4, }, +{6: 16, 0, 0, 2, 0, 4, 6, 4, 2, 0, 0, 0, 2, 2, 2, 0, }, +{9: 16, 4, 6, 0, 6, 0, 0, 0, 8, 0, 0, 2, 4, 2, 0, 0, }, +{a: 16, 0, 6, 4, 4, 0, 0, 0, 0, 8, 0, 2, 2, 0, 6, 0, }, +{c: 16, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{7: 16, 2, 0, 8, 0, 4, 0, 2, 0, 4, 2, 4, 2, 0, 4, 0, }, +{b: 16, 4, 4, 0, 4, 0, 2, 0, 8, 0, 0, 2, 4, 2, 0, 2, }, +{d: 16, 0, 0, 4, 0, 0, 2, 2, 2, 4, 2, 0, 2, 2, 4, 0, }, +{e: 16, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:64, 4:34, 6:14, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{c: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{d: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:9, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 0, -8, 8, 8, -8, -8, -8, 0, 8, }, +{2: 16, 0, 0, 8, 0, -8, 8, 0, 8, -8, 0, -8, -8, 8, -16, 0, }, +{4: 16, 0, 8, -8, 0, 8, -8, 0, 0, 0, 0, -16, 0, 0, 0, 0, }, +{8: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 8, -8, 0, 8, }, +{5: 16, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 8, 0, 0, -16, 0, }, +{6: 16, 0, 0, -8, 0, -8, -8, 0, 8, 0, -8, 8, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, 0, -8, 0, 8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{a: 16, 8, -8, 0, 0, 0, 0, -8, 0, 8, -8, -8, 8, 0, 0, -8, }, +{c: 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, 0, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, 0, 0, -8, 8, 8, 0, 0, 0, -8, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{f: 16, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, x, x, , x, x, , , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0111,0100,1,}, +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x07,0x09,0x0e,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x0e,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x03,0x05,0x06,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x0a,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_071.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_071.txt new file mode 100644 index 0000000..16328e6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_071.txt @@ -0,0 +1,420 @@ +071 Sbox: +LUT = { +0x08,0x00,0x01,0x06,0x02,0x05,0x0c,0x07,0x04,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, }, +{4: 0, 2, 0, 6, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 2, 0, 4, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 4, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{2: 16, 0, 6, 4, 8, 0, 0, 10, 2, 4, 4, 0, 0, 2, 8, 0, }, +{4: 16, 6, 4, 6, 0, 4, 6, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{8: 16, 2, 6, 0, 4, 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 2, 0, 2, 4, 0, 0, 2, 2, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 4, 0, 0, 0, 2, 0, 4, }, +{6: 16, 0, 4, 10, 0, 4, 0, 4, 2, 2, 0, 6, 0, 0, 0, 0, }, +{9: 16, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 16, 0, 6, 0, 4, 0, 6, 0, 0, 8, 2, 0, 2, 0, 0, 4, }, +{c: 16, 0, 4, 0, 4, 0, 0, 4, 2, 0, 4, 0, 2, 2, 8, 2, }, +{7: 16, 0, 0, 8, 2, 8, 0, 0, 0, 0, 2, 8, 2, 0, 0, 2, }, +{b: 16, 2, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, }, +{e: 16, 0, 6, 0, 4, 0, 0, 6, 0, 0, 4, 0, 2, 0, 8, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:66, 4:32, 6:12, 8:10, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 8, 0, 0, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 8, -16, }, +{2: 16, 8, -8, 0, 0, -16, 0, 0, 8, -8, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -8, 0, 8, -8, -8, 8, -8, 0, -8, }, +{8: 16, 0, 8, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, -8, 8, }, +{5: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 8, 0, -8, 0, 0, -8, -8, 0, 8, -8, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, }, +{a: 16, 0, -8, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, 0, 8, }, +{c: 16, 0, 0, -8, -8, 0, -8, 0, 8, -8, 0, 0, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, 0, 16, 0, 0, 0, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, }, +{d: 16, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, }, +{e: 16, 8, -8, 0, -8, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, , , x, , , , , x, x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , , , x, x, x, , , , , x, , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0011,0101,1,}, +{0011,0111,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0d,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +071 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0c,0x08,0x05,0x03,0x07,0x00,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 4, }, +{6: 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 4, 2, 0, 0, 0, 2, }, +{7: 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, }, +{b: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +{d: 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 2, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{2: 16, 0, 6, 4, 6, 0, 2, 4, 0, 6, 4, 0, 2, 0, 6, 0, }, +{4: 16, 8, 4, 6, 0, 4, 4, 10, 2, 0, 0, 8, 2, 0, 0, 0, }, +{8: 16, 2, 8, 0, 4, 0, 0, 0, 0, 4, 4, 2, 2, 2, 4, 0, }, +{3: 16, 4, 0, 4, 0, 4, 0, 4, 2, 0, 0, 8, 2, 2, 0, 2, }, +{5: 16, 4, 0, 6, 0, 2, 8, 0, 0, 6, 0, 0, 0, 2, 0, 4, }, +{6: 16, 0, 10, 4, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 6, 0, }, +{9: 16, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{c: 16, 0, 4, 0, 2, 2, 0, 0, 2, 2, 4, 2, 0, 0, 4, 2, }, +{7: 16, 4, 0, 6, 0, 4, 0, 6, 0, 0, 0, 8, 0, 2, 0, 2, }, +{b: 16, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +{d: 16, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, }, +{e: 16, 2, 8, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 8, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:66, 4:32, 6:12, 8:10, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 0, -8, 8, -8, 0, 0, 0, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, 0, 8, 0, -16, -8, 8, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, 8, 0, 0, 0, -16, }, +{3: 16, -8, -8, 0, 0, 0, -8, 0, 8, -8, 0, 8, 0, -8, 0, 8, }, +{5: 16, -8, 0, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, -8, -8, 8, }, +{6: 16, 8, 0, -8, 0, -8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, 0, -8, 8, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, -8, 8, -8, }, +{b: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, }, +{e: 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, 16, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , , , , x, , , x, x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , , x, x, , , x, , , x, , , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1100,0100,1,}, +{1100,1010,1,}, +{1100,1110,0,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x04,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x04,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_072.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_072.txt new file mode 100644 index 0000000..3e91fd6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_072.txt @@ -0,0 +1,420 @@ +072 Sbox: +LUT = { +0x08,0x00,0x01,0x07,0x02,0x05,0x06,0x0c,0x04,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 4, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, }, +{4: 0, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, }, +{5: 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 4, 2, 2, 2, 0, 0, 0, 2, 0, }, +{9: 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{e: 0, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 0, 4, 2, 0, 2, 0, 2, 0, 2, 2, 0, }, +{2: 16, 0, 4, 10, 0, 0, 0, 4, 4, 0, 0, 2, 0, 6, 2, 0, }, +{4: 16, 4, 8, 6, 0, 4, 10, 4, 0, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 2, 0, 0, 4, 10, 0, 0, 2, 0, 4, 0, 6, 0, 0, 4, }, +{3: 16, 2, 0, 4, 4, 10, 0, 0, 0, 0, 10, 4, 4, 0, 2, 8, }, +{5: 16, 6, 2, 8, 0, 0, 4, 0, 6, 2, 0, 0, 0, 4, 0, 0, }, +{6: 16, 0, 6, 4, 0, 2, 0, 4, 2, 2, 2, 0, 0, 0, 2, 0, }, +{9: 16, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, }, +{a: 16, 2, 6, 0, 0, 0, 4, 0, 0, 2, 2, 4, 2, 0, 2, 0, }, +{c: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 4, 2, 2, 2, 0, 6, }, +{7: 16, 0, 0, 8, 2, 4, 2, 2, 4, 0, 0, 4, 2, 4, 0, 0, }, +{b: 16, 0, 0, 0, 6, 8, 0, 0, 0, 2, 4, 0, 4, 2, 0, 6, }, +{d: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 6, 2, 0, 2, 0, 4, 0, 0, 2, 2, }, +{f: 16, 0, 0, 2, 2, 4, 0, 0, 2, 0, 6, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:63, 4:34, 6:12, 8:6, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 8, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, 8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 0, 8, -16, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 8, -8, 8, -8, 0, -8, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, -8, -8, 0, 0, 8, -8, 0, -8, 0, 16, 0, 0, -8, -8, 8, }, +{5: 16, -8, 8, 0, 0, -16, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 8, -8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, -8, 8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 0, 0, 0, -16, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, }, +{d: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 8, 0, 0, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, , , x, , , , , x, x, , , , x, }, +{b: , , x, , , , x, x, , , , x, x, , , x, }, +{d: , , , x, x, x, , , , , x, , , x, , x, }, +{e: , , x, x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0101,1,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x0d,}}, +{{0x06,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x02,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x01,0x02,0x03,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +072 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0c,0x08,0x05,0x06,0x03,0x00,0x09,0x0a,0x0b,0x07,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +{3: 0, 0, 0, 0, 2, 6, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 4, 0, 0, 4, 0, 2, 0, 2, 2, 0, }, +{6: 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 2, 0, }, +{9: 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 4, 0, 0, 0, 0, 2, }, +{7: 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 6, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{2: 16, 0, 4, 8, 0, 0, 2, 6, 2, 6, 0, 0, 0, 0, 4, 0, }, +{4: 16, 4, 10, 6, 0, 4, 8, 4, 2, 0, 0, 8, 0, 0, 0, 2, }, +{8: 16, 2, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, 6, 0, 2, 2, }, +{3: 16, 0, 0, 4, 10, 10, 0, 2, 0, 0, 4, 4, 8, 2, 0, 4, }, +{5: 16, 4, 0, 10, 0, 0, 4, 0, 0, 4, 0, 2, 0, 2, 6, 0, }, +{6: 16, 2, 4, 4, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 2, 0, }, +{9: 16, 0, 4, 0, 2, 0, 6, 2, 2, 0, 0, 4, 0, 2, 0, 2, }, +{a: 16, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 16, 0, 0, 0, 4, 10, 0, 2, 0, 2, 4, 0, 4, 0, 0, 6, }, +{7: 16, 2, 2, 8, 0, 4, 0, 0, 0, 4, 2, 4, 0, 0, 4, 2, }, +{b: 16, 0, 0, 2, 6, 4, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 16, 2, 6, 0, 0, 0, 4, 0, 2, 0, 2, 4, 2, 2, 0, 0, }, +{e: 16, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 6, 0, 6, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:63, 4:34, 6:12, 8:6, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 8, 0, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, 0, 8, 0, -8, -16, 8, 0, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, -8, 0, 0, 0, -8, 0, 0, -8, }, +{3: 16, -8, -8, 8, 0, 8, -8, -8, 0, -8, 0, 16, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, -8, 8, -8, 0, 8, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -8, -8, 8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 0, 0, -8, 8, 0, 8, -8, 0, 0, -8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, }, +{7: 16, 0, 0, -8, 8, 8, 0, 0, 0, 0, 0, -16, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 8, 0, 0, }, +{e: 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, -8, -8, 0, -8, 8, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, , x, x, x, x, , , x, , x, , , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, , x, x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{7: , x, x, , , x, x, x, , , x, , , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , x, , x, x, x, x, x, , , x, x, , x, , x, }, +{e: , , , , x, x, x, x, , , x, x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0111,0011,0,}, +{0111,0100,1,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x0a,0x04,}, {0x07,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x07,0x08,0x0f,}}, +{{0x09,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x05,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x01,0x06,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_073.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_073.txt new file mode 100644 index 0000000..5f0d781 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_073.txt @@ -0,0 +1,420 @@ +073 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x09,0x07,0x06,0x03,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, }, +{8: 0, 0, 2, 0, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 2, 0, 0, }, +{5: 0, 4, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 2, }, +{6: 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 4, 0, 0, }, +{9: 0, 0, 2, 0, 0, 0, 0, 4, 4, 2, 0, 2, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 2, 0, }, +{c: 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 4, 0, 2, 0, 0, }, +{b: 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 2, }, +{d: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 4, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 6, 0, 4, 6, 4, 2, 0, 0, 6, 0, 0, 2, 0, }, +{2: 16, 4, 6, 0, 8, 8, 2, 0, 4, 4, 2, 0, 10, 0, 0, 0, }, +{4: 16, 4, 0, 4, 2, 0, 6, 2, 0, 2, 0, 0, 0, 0, 2, 2, }, +{8: 16, 0, 6, 0, 8, 4, 0, 0, 0, 4, 0, 2, 6, 0, 2, 0, }, +{3: 16, 10, 4, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 6, 0, 0, }, +{5: 16, 8, 2, 4, 0, 0, 4, 2, 0, 0, 4, 0, 2, 4, 0, 2, }, +{6: 16, 8, 0, 0, 2, 2, 0, 4, 0, 0, 6, 6, 0, 4, 0, 0, }, +{9: 16, 0, 6, 0, 0, 0, 0, 4, 8, 2, 0, 2, 4, 0, 0, 6, }, +{a: 16, 0, 4, 0, 8, 4, 2, 0, 0, 4, 2, 2, 4, 0, 2, 0, }, +{c: 16, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 16, 4, 0, 2, 0, 2, 0, 8, 4, 2, 0, 4, 0, 2, 0, 4, }, +{b: 16, 0, 6, 2, 0, 0, 0, 0, 4, 2, 0, 0, 4, 2, 2, 2, }, +{d: 16, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 0, 2, 2, 0, 2, 4, 4, 2, 0, 0, 0, 2, 2, 4, }, +{f: 16, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:64, 4:34, 6:14, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{8: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 8, -8, 8, 0, -8, 0, 0, 0, -8, }, +{2: 16, 8, 0, 8, 0, 0, 8, -8, 0, -8, 0, 0, -16, 8, -8, -8, }, +{4: 16, 8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, -8, 8, 0, 8, 0, 0, -8, -8, 0, 8, 0, 0, -8, -8, }, +{3: 16, -8, 8, 0, 0, 0, -8, -8, -8, -8, 8, 0, 0, 0, 0, 8, }, +{5: 16, -8, 0, 0, 8, -8, 0, 0, 0, 8, 0, 0, -16, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 0, 0, -16, 0, 8, 0, -8, 8, 0, }, +{9: 16, 0, -8, 0, 0, -8, 0, 8, 8, -8, -8, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, -8, 8, -8, 0, 0, 8, 8, 0, }, +{c: 16, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 16, 0, 0, 0, }, +{b: 16, 0, -8, 0, -8, 0, 0, -8, 8, 8, 0, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, x, , , x, x, , , x, }, +{5: , x, x, x, , x, x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, , , x, , , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , , x, , x, , x, x, , , x, , , , x, }, +{b: , x, , , x, , , x, x, , , , x, , , x, }, +{d: , x, x, x, , x, , x, x, , , , , x, , x, }, +{e: , , , , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1010,0110,1,}, +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x03,0x08,0x0b,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x0b,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x0b,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +073 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x09,0x00,0x05,0x08,0x07,0x03,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +{8: 0, 0, 4, 2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{3: 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{5: 0, 2, 2, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 2, 0, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 4, 0, 2, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{c: 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 10, 8, 8, 0, 0, 0, 4, 0, 2, 0, 2, }, +{2: 16, 4, 6, 0, 6, 4, 2, 0, 6, 4, 0, 0, 6, 2, 0, 0, }, +{4: 16, 6, 0, 4, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +{8: 16, 0, 8, 2, 8, 0, 0, 2, 0, 8, 2, 0, 0, 0, 2, 0, }, +{3: 16, 4, 8, 0, 4, 4, 0, 2, 0, 4, 2, 2, 0, 2, 0, 0, }, +{5: 16, 6, 2, 6, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 16, 4, 0, 2, 0, 0, 2, 4, 4, 0, 2, 8, 0, 2, 4, 0, }, +{9: 16, 2, 4, 0, 0, 2, 0, 0, 8, 0, 0, 4, 4, 2, 4, 2, }, +{a: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{c: 16, 0, 2, 0, 0, 4, 4, 6, 0, 2, 2, 0, 0, 2, 0, 2, }, +{7: 16, 6, 0, 0, 2, 0, 0, 6, 2, 2, 2, 4, 0, 0, 0, 0, }, +{b: 16, 0, 10, 0, 6, 0, 2, 0, 4, 4, 0, 0, 4, 0, 0, 2, }, +{d: 16, 0, 0, 0, 0, 6, 4, 4, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 16, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 0, 0, 2, 0, 0, 2, 0, 6, 0, 2, 4, 2, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:64, 4:34, 6:14, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 8, 0, 0, 4, 4, }, +{7: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 8, -8, 0, 0, -8, 8, 8, 0, -8, -8, 0, 0, }, +{2: 16, 0, 0, 8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, }, +{8: 16, 16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 8, 0, 0, -8, -16, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 8, -8, 0, -8, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, }, +{9: 16, -16, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 8, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, }, +{c: 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 8, 0, 0, -8, 0, 8, }, +{7: 16, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 8, -8, 0, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, -8, -8, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, 8, 0, }, +{e: 16, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 0, 8, 0, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, x, , , x, x, , , x, }, +{5: , , x, x, , x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , , x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , , x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , , x, , x, , x, x, , , x, , , , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , , x, , , x, , x, x, , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0001,0001,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{1010,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x01,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x06,0x08,}, {0x01,}}, +{{0x04,0x08,}, {0x01,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x01,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x07,0x08,0x0f,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x03,0x09,0x0a,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x01,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x01,0x04,0x05,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x01,0x04,0x05,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_074.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_074.txt new file mode 100644 index 0000000..4cf60a1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_074.txt @@ -0,0 +1,420 @@ +074 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x09,0x04,0x07,0x00,0x05,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, }, +{4: 0, 2, 0, 4, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{6: 0, 0, 4, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{9: 0, 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 8, 10, 8, 0, 2, 0, 4, 0, 0, 2, 0, }, +{2: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 16, 10, 4, 8, 2, 4, 10, 4, 0, 0, 2, 4, 0, 0, 0, 0, }, +{8: 16, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, }, +{3: 16, 8, 4, 4, 0, 4, 4, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 16, 4, 0, 4, 0, 4, 8, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{6: 16, 4, 4, 0, 0, 0, 4, 4, 0, 2, 0, 8, 2, 0, 2, 2, }, +{9: 16, 0, 4, 0, 4, 2, 2, 0, 2, 6, 0, 0, 2, 0, 2, 0, }, +{a: 16, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 8, 0, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 2, 2, 2, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:74, 4:41, 6:3, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, -16, 8, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 0, 0, -8, 8, 0, -8, 0, 0, -8, 8, 8, 0, -8, }, +{4: 16, 0, 16, -8, 8, 0, 0, -8, -8, 8, -8, 0, -8, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, -8, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 0, -8, 0, -8, 8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, }, +{b: 16, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, -8, 0, 8, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, 0, 8, 0, 8, -8, 0, -8, 0, 0, -8, -8, }, +{f: 16, 0, 0, 0, 0, 0, -8, 8, -8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, , , x, x, , , x, }, +{5: , , , x, , x, x, x, x, , , x, , x, , x, }, +{6: , , , x, x, x, x, x, x, , , x, , , x, x, }, +{9: , x, x, , x, x, x, x, x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, x, x, x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , , x, , , x, , x, , , x, , , , x, }, +{b: , x, , , x, x, x, x, x, , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x09,0x0b,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +074 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x09,0x00,0x07,0x01,0x05,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{5: 0, 2, 0, 6, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 4, 4, 0, 2, 0, 0, 0, 2, 0, 2, }, +{9: 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{a: 0, 2, 4, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, }, +{d: 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, }, +{f: 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 10, 0, 8, 4, 4, 0, 2, 0, 8, 0, 0, 0, 2, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 4, 0, 8, 2, 4, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{8: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 2, 2, }, +{3: 16, 8, 4, 4, 0, 4, 4, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{5: 16, 10, 4, 10, 0, 4, 8, 4, 2, 0, 2, 4, 0, 0, 0, 0, }, +{6: 16, 8, 0, 4, 2, 0, 4, 4, 0, 2, 0, 4, 0, 2, 0, 2, }, +{9: 16, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{a: 16, 2, 4, 0, 2, 0, 0, 2, 6, 2, 2, 0, 4, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 4, 4, 4, 0, 0, 0, 8, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, }, +{d: 16, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:74, 4:41, 6:3, 8:7, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 8, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{a: 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:8, 4:4, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 8, -8, 8, 0, -16, 0, -8, 8, -8, }, +{2: 16, 8, -16, 0, 0, -8, -8, 0, 8, 0, 0, 8, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, 0, 8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, 8, }, +{5: 16, 0, 16, -8, 8, 0, -8, -8, 0, 8, -8, -8, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, -8, -8, 0, 8, }, +{9: 16, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, 0, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -16, 0, 0, 0, 8, 0, 0, 0, 0, -8, 0, 8, 0, -8, }, +{b: 16, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, 0, 0, 8, -8, 8, -8, -8, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, , , x, x, , , x, }, +{5: , x, , x, , , x, x, x, , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , , x, , , x, x, }, +{9: , , x, x, x, , x, x, x, , , , x, x, , x, }, +{a: , , , x, x, x, x, , x, x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , , x, , x, , , x, , , , x, }, +{b: , , , , x, , x, , x, , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x04,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_075.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_075.txt new file mode 100644 index 0000000..5af0479 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_075.txt @@ -0,0 +1,420 @@ +075 Sbox: +LUT = { +0x06,0x08,0x01,0x09,0x03,0x05,0x04,0x07,0x00,0x02,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, }, +{2: 0, 2, 6, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, 2, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{9: 0, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 4, 4, 0, 0, 0, 2, }, +{b: 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{f: 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 4, 2, 6, 4, 6, 0, 0, 0, 4, 0, 0, 2, 0, }, +{2: 16, 6, 10, 0, 4, 4, 4, 0, 6, 6, 0, 4, 4, 0, 0, 0, }, +{4: 16, 4, 4, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{8: 16, 0, 6, 0, 4, 0, 0, 6, 0, 8, 4, 0, 2, 0, 0, 2, }, +{3: 16, 6, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{5: 16, 4, 0, 8, 0, 2, 4, 2, 4, 0, 0, 0, 2, 4, 2, 0, }, +{6: 16, 4, 4, 0, 0, 0, 4, 4, 0, 0, 2, 8, 0, 2, 2, 2, }, +{9: 16, 0, 4, 2, 2, 2, 0, 0, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{7: 16, 6, 0, 2, 0, 0, 0, 8, 0, 6, 4, 4, 0, 0, 0, 2, }, +{b: 16, 0, 6, 4, 0, 2, 0, 0, 8, 0, 2, 0, 4, 6, 0, 0, }, +{d: 16, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, }, +{e: 16, 0, 0, 4, 2, 0, 2, 0, 6, 0, 0, 2, 0, 6, 2, 0, }, +{f: 16, 0, 0, 0, 2, 0, 2, 4, 2, 4, 6, 2, 0, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:60, 4:35, 6:19, 8:6, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 8, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 4, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 8, 4, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -8, -8, 8, -8, 0, 8, 0, -8, -8, 0, -8, }, +{2: 16, 0, -8, 8, 8, -8, 8, 0, 0, -8, 0, -16, 0, 8, 0, -8, }, +{4: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{8: 16, 8, -8, 8, -8, 0, 8, 0, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, 8, -8, 8, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, -16, 0, 0, 8, 0, }, +{b: 16, -8, 0, 8, -8, 0, -8, -8, 8, -8, 0, 0, 0, 8, 0, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, x, , , x, x, , , x, }, +{5: , x, x, , x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, , x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, , x, , , x, x, x, }, +{7: , x, x, , , , , , x, , , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , x, x, , x, x, , x, x, , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x01,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x02,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +075 Inverse Sbox: +LUT = { +0x08,0x02,0x09,0x04,0x06,0x05,0x00,0x07,0x01,0x03,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, }, +{2: 0, 2, 6, 0, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 4, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 0, 2, 2, }, +{a: 0, 0, 2, 0, 4, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{f: 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 4, 0, 6, 4, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{2: 16, 6, 10, 4, 6, 4, 0, 4, 4, 4, 0, 0, 6, 0, 0, 0, }, +{4: 16, 4, 0, 4, 0, 2, 8, 0, 2, 0, 0, 2, 4, 2, 4, 0, }, +{8: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{3: 16, 6, 4, 0, 0, 4, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, }, +{5: 16, 4, 4, 8, 0, 0, 4, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 16, 6, 0, 0, 6, 0, 2, 4, 0, 0, 2, 8, 0, 0, 0, 4, }, +{9: 16, 0, 6, 0, 0, 2, 4, 0, 4, 0, 0, 0, 8, 0, 6, 2, }, +{a: 16, 0, 6, 0, 8, 0, 0, 0, 2, 4, 2, 6, 0, 0, 0, 4, }, +{c: 16, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 6, }, +{7: 16, 4, 4, 4, 0, 0, 0, 8, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 6, 2, 6, 0, }, +{e: 16, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, }, +{f: 16, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:60, 4:35, 6:19, 8:6, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 4, 4, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, 0, 0, -8, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -8, 0, 0, 8, -8, 0, 0, -16, 0, 0, -8, }, +{4: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 16, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, -16, -8, 0, 8, }, +{9: 16, -8, -8, 8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 8, -8, 0, }, +{a: 16, 8, 0, 8, -8, 0, 8, 0, -8, -8, -8, -8, 0, 0, 0, 0, }, +{c: 16, 0, -8, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, -8, 0, 8, -8, 8, 0, 0, 0, 0, }, +{e: 16, 0, 8, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , x, , , x, x, , , x, }, +{5: , x, x, , x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , , x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , , x, x, x, , , , x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , x, x, , , x, , , x, , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, , x, x, , x, x, , , , , x, , x, }, +{e: , , x, x, x, , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0101,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x03,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x04,0x0b,0x0f,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x06,}, {0x04,0x0b,0x0f,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x0d,}}, +{{0x0d,0x0e,}, {0x03,0x05,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_076.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_076.txt new file mode 100644 index 0000000..20a9257 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_076.txt @@ -0,0 +1,420 @@ +076 Sbox: +LUT = { +0x08,0x00,0x01,0x09,0x02,0x05,0x03,0x07,0x04,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 4, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 4, }, +{c: 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, }, +{d: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:6, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 6, 6, 4, 4, 4, 4, 4, 0, 0, 6, 0, 0, 0, 0, }, +{2: 16, 10, 6, 0, 8, 4, 0, 0, 8, 4, 0, 0, 4, 2, 2, 0, }, +{4: 16, 4, 2, 4, 2, 0, 6, 0, 0, 2, 0, 0, 2, 0, 2, 0, }, +{8: 16, 0, 6, 0, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{3: 16, 8, 4, 0, 4, 4, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 4, 0, 0, 0, 2, 0, 4, }, +{6: 16, 4, 0, 0, 0, 2, 0, 4, 2, 2, 2, 6, 2, 0, 0, 0, }, +{9: 16, 0, 4, 2, 0, 2, 0, 0, 4, 2, 2, 0, 4, 0, 2, 2, }, +{a: 16, 0, 6, 0, 4, 0, 6, 0, 0, 8, 2, 0, 2, 0, 0, 4, }, +{c: 16, 0, 0, 2, 0, 2, 0, 4, 2, 0, 2, 0, 4, 6, 0, 2, }, +{7: 16, 4, 0, 2, 2, 2, 0, 8, 0, 0, 0, 4, 4, 4, 0, 2, }, +{b: 16, 0, 4, 0, 0, 2, 0, 4, 4, 2, 0, 2, 8, 4, 2, 0, }, +{d: 16, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 16, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:67, 4:39, 6:11, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:7, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 8, 0, 0, 8, -8, 0, 0, -8, -8, -8, 0, -16, }, +{2: 16, 0, 0, 8, 0, -16, 0, 0, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 8, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, -8, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, 0, 8, 8, }, +{9: 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, 0, 8, }, +{c: 16, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, 0, 0, -8, 0, 8, }, +{7: 16, -8, -8, 0, 0, 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 8, 8, 0, 8, -8, }, +{d: 16, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, x, , , x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , , x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , x, x, , , , , x, x, , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , , , x, x, , , x, x, , , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0011,0101,1,}, +{0011,0111,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x01,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x01,0x02,0x03,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x04,0x09,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +076 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x08,0x05,0x09,0x07,0x00,0x03,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 6, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, }, +{8: 0, 4, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 4, }, +{6: 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 4, 0, 0, 0, 2, 0, }, +{9: 0, 0, 4, 0, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, }, +{e: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:157, 2:78, 4:18, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:6, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 4, 0, 8, 4, 4, 0, 0, 0, 4, 0, 2, 2, 0, }, +{2: 16, 6, 6, 2, 6, 4, 2, 0, 4, 6, 0, 0, 4, 0, 0, 0, }, +{4: 16, 6, 0, 4, 0, 0, 4, 0, 2, 0, 2, 2, 0, 2, 2, 0, }, +{8: 16, 4, 8, 2, 4, 4, 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, }, +{3: 16, 4, 4, 0, 0, 4, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{5: 16, 4, 0, 6, 0, 2, 8, 0, 0, 6, 0, 0, 0, 2, 0, 4, }, +{6: 16, 4, 0, 0, 2, 2, 2, 4, 0, 0, 4, 8, 4, 0, 2, 0, }, +{9: 16, 4, 8, 0, 0, 4, 2, 2, 4, 0, 2, 0, 4, 0, 0, 2, }, +{a: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{c: 16, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, }, +{7: 16, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 16, 0, 4, 2, 2, 0, 0, 2, 4, 2, 4, 4, 8, 0, 0, 0, }, +{d: 16, 0, 2, 0, 2, 0, 2, 0, 0, 0, 6, 4, 4, 2, 2, 0, }, +{e: 16, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:67, 4:39, 6:11, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:7, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -8, 0, -8, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 0, 0, 0, -8, -8, 0, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, -16, }, +{3: 16, -8, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, }, +{5: 16, -8, 0, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, -8, -8, 8, }, +{6: 16, 8, 0, -8, 0, 0, -8, 0, -8, -8, 0, 8, -8, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, -8, 8, -8, 8, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, }, +{7: 16, -8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, 8, 0, -8, }, +{e: 16, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, x, , , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, , , x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, , , x, x, x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , x, , , x, , , x, , , x, , , , x, }, +{b: , x, x, , , , , x, x, , , , x, , , x, }, +{d: , , , x, x, x, , , x, , , , , x, , x, }, +{e: , , , x, x, , , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1100,0001,0,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x09,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_077.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_077.txt new file mode 100644 index 0000000..7123e37 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_077.txt @@ -0,0 +1,420 @@ +077 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x05,0x03,0x07,0x04,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, }, +{2: 0, 2, 6, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 4, 6, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 0, 4, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, 2, 2, 0, 0, 0, }, +{9: 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, }, +{d: 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:156, 2:81, 4:15, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:5, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 6, 0, 8, 0, 0, 0, 0, 2, 2, 4, 0, 0, }, +{2: 16, 2, 6, 4, 6, 0, 0, 4, 2, 4, 6, 0, 0, 0, 6, 0, }, +{4: 16, 4, 8, 6, 0, 4, 10, 4, 0, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 2, 2, 2, 2, 0, 0, }, +{3: 16, 2, 0, 6, 0, 4, 2, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 4, 0, 0, 0, 2, 0, 4, }, +{6: 16, 0, 4, 4, 0, 2, 0, 4, 2, 2, 2, 2, 2, 0, 0, 0, }, +{9: 16, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 16, 0, 10, 0, 8, 0, 6, 0, 0, 8, 2, 4, 2, 4, 0, 4, }, +{c: 16, 0, 4, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 2, 6, 2, }, +{7: 16, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 16, 2, 0, 0, 4, 2, 4, 0, 0, 2, 0, 0, 2, 6, 2, 0, }, +{d: 16, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, }, +{e: 16, 2, 8, 0, 2, 0, 4, 2, 0, 0, 4, 4, 0, 0, 4, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:68, 4:34, 6:14, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{9: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:9, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -16, }, +{2: 16, 8, 0, 8, 0, -8, 0, 0, 0, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 8, 0, 0, 8, 0, 0, -16, 8, 8, -8, -8, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, -8, 8, }, +{5: 16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 0, 0, -8, 0, -8, 8, }, +{6: 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, 0, 8, 8, }, +{9: 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, -8, 8, -8, 0, -8, 8, 0, 8, }, +{c: 16, 0, 0, -8, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 8, 0, -8, 0, -8, }, +{d: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, , x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, , , x, x, , , , x, }, +{b: , x, , , x, x, , , , , x, , x, , , x, }, +{d: , x, , , x, , , x, , , x, , , x, , x, }, +{e: , , x, x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0100,1,}, +{0110,1010,1,}, +{0110,1110,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x0f,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x04,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +077 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x08,0x05,0x0c,0x07,0x00,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, }, +{2: 0, 0, 6, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 2, 0, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 6, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 2, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, 0, 4, }, +{c: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 2, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, }, +{b: 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, }, +{d: 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:156, 2:81, 4:15, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:5, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 0, 2, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, }, +{2: 16, 0, 6, 8, 4, 0, 2, 4, 0, 10, 4, 0, 0, 2, 8, 0, }, +{4: 16, 6, 4, 6, 2, 6, 4, 4, 2, 0, 0, 6, 0, 0, 0, 0, }, +{8: 16, 6, 6, 0, 4, 0, 0, 0, 0, 8, 0, 0, 4, 2, 2, 0, }, +{3: 16, 0, 0, 4, 0, 4, 0, 2, 2, 0, 2, 6, 2, 0, 0, 2, }, +{5: 16, 8, 0, 10, 0, 2, 8, 0, 0, 6, 0, 0, 4, 2, 4, 4, }, +{6: 16, 0, 4, 4, 0, 2, 2, 4, 2, 0, 2, 0, 0, 2, 2, 0, }, +{9: 16, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{c: 16, 0, 6, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 0, 4, 2, }, +{7: 16, 2, 0, 8, 2, 4, 0, 2, 0, 4, 0, 4, 0, 0, 4, 2, }, +{b: 16, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, }, +{d: 16, 4, 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 6, 2, 0, 0, }, +{e: 16, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:68, 4:34, 6:14, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 8, 0, 0, }, +{9: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:9, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, -8, }, +{2: 16, 8, 0, 0, 8, -8, 8, -16, 8, 0, 0, -8, 0, 0, -8, -8, }, +{4: 16, 0, 8, 0, 8, 8, -8, 0, 0, 0, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, -16, }, +{3: 16, -8, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, -8, 8, -8, 0, 8, -8, 0, 8, }, +{6: 16, 0, 0, -8, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, }, +{a: 16, 0, -8, 0, -8, 0, 0, 0, 8, 8, -8, -8, 0, -8, 0, 8, }, +{c: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, -8, }, +{d: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, , x, , x, , , x, x, , , x, x, }, +{9: , x, x, , x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , x, , , , , x, x, , , , x, }, +{b: , x, , , x, x, , x, , , , , x, , , x, }, +{d: , x, , , x, x, , , , , x, , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0010,1,}, +{0110,0101,1,}, +{0110,0111,0,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x02,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x06,0x09,0x0f,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0b,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x03,0x05,0x06,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x02,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_078.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_078.txt new file mode 100644 index 0000000..dd24e59 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_078.txt @@ -0,0 +1,420 @@ +078 Sbox: +LUT = { +0x08,0x00,0x01,0x03,0x02,0x0f,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, }, +{2: 0, 2, 4, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, }, +{8: 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 4, 0, 0, 6, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, }, +{b: 0, 2, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 6, 4, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, 0, }, +{f: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:156, 2:81, 4:15, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:2, 2:10, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 2, 2, 0, 0, 4, 0, 4, 0, 0, 8, 4, 2, 0, }, +{2: 16, 2, 4, 2, 2, 2, 4, 0, 2, 0, 0, 6, 0, 0, 0, 0, }, +{4: 16, 2, 0, 4, 2, 0, 0, 0, 0, 6, 0, 2, 2, 0, 4, 2, }, +{8: 16, 0, 2, 2, 4, 0, 4, 0, 2, 0, 2, 0, 0, 6, 2, 0, }, +{3: 16, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 2, }, +{5: 16, 0, 6, 0, 4, 0, 6, 2, 2, 4, 0, 6, 0, 4, 0, 6, }, +{6: 16, 0, 0, 0, 4, 4, 0, 2, 2, 2, 2, 2, 4, 0, 2, 0, }, +{9: 16, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, }, +{a: 16, 4, 0, 4, 0, 0, 8, 0, 0, 6, 2, 0, 10, 2, 8, 4, }, +{c: 16, 0, 0, 2, 0, 2, 0, 4, 2, 0, 2, 0, 4, 6, 0, 2, }, +{7: 16, 2, 4, 0, 2, 0, 8, 2, 0, 0, 0, 4, 4, 0, 4, 2, }, +{b: 16, 6, 0, 0, 4, 6, 2, 0, 0, 4, 0, 2, 8, 0, 0, 0, }, +{d: 16, 0, 2, 0, 8, 4, 10, 4, 0, 0, 2, 0, 6, 8, 4, 0, }, +{e: 16, 0, 2, 6, 0, 0, 0, 2, 0, 6, 0, 2, 0, 2, 4, 0, }, +{f: 16, 0, 2, 0, 0, 2, 4, 0, 2, 6, 2, 0, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:67, 4:33, 6:15, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 0, 4, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{9: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:9, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -16, }, +{2: 16, 0, 0, 8, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, -8, 0, -8, }, +{8: 16, 8, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, 8, }, +{5: 16, -8, 0, -8, 8, -8, 8, 0, 0, 0, -8, 0, -8, 8, -8, 8, }, +{6: 16, 0, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, }, +{a: 16, 0, 0, 0, -8, -8, 8, -16, -8, 8, -8, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, 0, 0, -8, 0, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, 0, -8, }, +{b: 16, -8, 0, 8, 0, 8, 0, 0, -8, 0, -8, 8, -8, 0, 0, -8, }, +{d: 16, -8, 0, 0, -8, 0, 0, -16, 8, 0, 0, 8, -8, 8, 8, -8, }, +{e: 16, 8, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, , x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , , x, x, , x, , x, x, x, x, , x, x, x, x, }, +{b: , x, , , x, , x, , , x, , , x, , , x, }, +{d: , x, , , x, x, , x, x, x, x, x, x, , x, x, }, +{e: , , x, x, x, , x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0111,0,}, +{0110,1010,1,}, +{0110,1101,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x01,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x06,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x0b,}}, +{{0x05,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x0f,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x04,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x06,0x09,0x0f,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x01,0x06,0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +078 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x08,0x0a,0x06,0x07,0x00,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{2: 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{4: 0, 2, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, }, +{8: 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, }, +{3: 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 6, 0, 0, 0, 0, 2, 2, }, +{c: 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, }, +{7: 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 6, 0, 0, }, +{d: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, }, +{f: 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, }, +}; +Diff: 6, DDT_spectrum: {0:156, 2:81, 4:15, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:2, 2:10, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 2, 0, 2, 0, 0, 2, 4, 0, 2, 6, 0, 0, 0, }, +{2: 16, 2, 4, 0, 2, 0, 6, 0, 0, 0, 0, 4, 0, 2, 2, 2, }, +{4: 16, 2, 2, 4, 2, 0, 0, 0, 2, 4, 2, 0, 0, 0, 6, 0, }, +{8: 16, 2, 2, 2, 4, 0, 4, 4, 0, 0, 0, 2, 4, 8, 0, 0, }, +{3: 16, 0, 2, 0, 0, 2, 0, 4, 2, 0, 2, 0, 6, 4, 0, 2, }, +{5: 16, 0, 4, 0, 4, 2, 6, 0, 0, 8, 0, 8, 2, 10, 0, 4, }, +{6: 16, 4, 0, 0, 0, 2, 2, 2, 2, 0, 4, 2, 0, 4, 2, 0, }, +{9: 16, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{a: 16, 4, 0, 6, 0, 0, 4, 2, 2, 6, 0, 0, 4, 0, 6, 6, }, +{c: 16, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, }, +{7: 16, 0, 6, 2, 0, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 16, 8, 0, 2, 0, 2, 0, 4, 0, 10, 4, 4, 8, 6, 0, 0, }, +{d: 16, 4, 0, 0, 6, 0, 4, 0, 0, 2, 6, 0, 0, 8, 2, 0, }, +{e: 16, 2, 0, 4, 2, 0, 0, 2, 0, 8, 0, 4, 0, 4, 4, 2, }, +{f: 16, 0, 0, 2, 0, 2, 6, 0, 2, 4, 2, 2, 0, 0, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:67, 4:33, 6:15, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, }, +{9: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:9, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, -8, }, +{2: 16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, 0, -8, 0, -8, -8, }, +{4: 16, 8, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, -16, }, +{3: 16, 0, -8, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, 0, 0, 8, }, +{5: 16, -8, 0, 0, 0, -8, 8, -16, -8, 8, -8, 8, 0, 0, 0, 8, }, +{6: 16, 0, 0, -8, 0, 0, -8, 0, -8, -8, 0, 0, 0, 8, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, }, +{a: 16, 8, -8, 0, -8, -8, 0, 0, 0, 8, -8, -8, 8, -8, 0, 8, }, +{c: 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, }, +{7: 16, 0, -8, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, -8, }, +{b: 16, -8, 0, 0, -8, 0, 0, -16, 8, 0, 0, 8, 8, -8, 8, -8, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{e: 16, 0, -8, -8, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, 0, -8, }, +{f: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, , x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , x, x, x, , , x, , , x, , x, , , , x, }, +{b: , x, , , x, x, x, x, x, , x, x, , x, x, x, }, +{d: , x, , , x, , x, , , x, , , , x, , x, }, +{e: , , x, x, , x, x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0101,1,}, +{0110,1011,1,}, +{0110,1110,0,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x06,0x09,0x0f,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x06,0x09,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x02,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_079.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_079.txt new file mode 100644 index 0000000..84ddc30 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_079.txt @@ -0,0 +1,440 @@ +079 Sbox: +LUT = { +0x06,0x0d,0x01,0x02,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, }, +{4: 0, 2, 0, 4, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 0, 2, 2, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{a: 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 4, 2, }, +{e: 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:5, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 0, 4, 8, 6, 2, 0, 0, 0, 2, 0, 0, 0, }, +{2: 16, 0, 10, 0, 0, 0, 8, 0, 8, 2, 8, 10, 8, 0, 8, 2, }, +{4: 16, 10, 4, 8, 2, 4, 10, 4, 0, 0, 2, 4, 0, 0, 0, 0, }, +{8: 16, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, }, +{3: 16, 6, 0, 4, 0, 4, 8, 6, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 16, 4, 4, 4, 2, 10, 10, 8, 0, 0, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 4, 0, 0, 6, 8, 4, 0, 2, 0, 6, 0, 0, 2, 0, }, +{9: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{a: 16, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 4, 6, 6, 0, 0, 8, 0, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 6, 0, 2, 0, 0, 0, 4, 0, 4, 6, 8, 2, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 0, 4, 2, 2, 4, 0, 2, 4, 2, }, +{e: 16, 0, 6, 2, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 4, 0, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 6, 0, 2, 6, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:56, 4:30, 6:14, 8:13, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 0, 0, 0, 4, 0, 8, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -16, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, -16, 0, 8, 0, 16, 0, 0, -8, 0, -16, 0, 8, 0, -8, }, +{4: 16, 0, 16, -8, 8, 0, 0, -8, -8, 8, -8, 0, -8, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, 0, 0, 0, 8, 8, -16, -8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, -8, 16, -8, 0, -8, 8, }, +{6: 16, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, 0, 8, 0, 0, 8, 0, 0, 0, -16, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, -8, 0, 0, -8, 8, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, -8, 8, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, , x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , , x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , x, , x, x, , x, , x, , x, x, , x, , x, }, +{b: , , , , , x, x, x, x, , x, , x, x, , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +079 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x05,0x00,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 13, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 13, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, }, +{4: 0, 2, 0, 4, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, }, +{8: 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 4, 4, 0, 2, 0, 0, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 4, }, +{a: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, }, +{c: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 0, }, +{7: 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, 2, }, +{f: 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:5, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 10, 0, 6, 4, 0, 0, 2, 0, 4, 0, 2, 0, 0, }, +{2: 16, 0, 10, 4, 0, 0, 4, 4, 4, 0, 4, 6, 6, 0, 6, 0, }, +{4: 16, 6, 0, 8, 2, 4, 4, 0, 0, 0, 0, 6, 0, 0, 2, 0, }, +{8: 16, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{3: 16, 4, 0, 4, 0, 4, 10, 6, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 6, 0, 4, 2, 6, 8, 4, 0, 2, 0, 0, 0, 0, 0, 0, }, +{9: 16, 2, 8, 0, 2, 0, 0, 0, 4, 0, 0, 2, 4, 4, 2, 4, }, +{a: 16, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, }, +{c: 16, 0, 8, 2, 0, 2, 0, 0, 4, 2, 4, 0, 4, 2, 4, 0, }, +{7: 16, 0, 10, 4, 0, 0, 4, 6, 4, 0, 0, 4, 6, 4, 0, 6, }, +{b: 16, 2, 8, 0, 2, 2, 0, 0, 8, 2, 0, 0, 8, 0, 0, 0, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 8, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 4, 4, 6, }, +{f: 16, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:56, 4:30, 6:14, 8:13, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 8, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 0, -8, 0, 0, -8, 8, -8, 8, -8, }, +{2: 16, 8, -16, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 8, 8, -8, 0, -8, 0, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, -8, -8, 0, 8, }, +{5: 16, 0, 16, -16, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 8, -8, -8, 0, 8, }, +{9: 16, -8, 0, 0, -8, 0, 0, 16, 0, 0, 0, -8, 0, 0, -8, 0, }, +{a: 16, 8, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, -8, 8, -8, -16, 0, 0, 0, 0, 0, 0, 8, 0, }, +{7: 16, 0, -16, 0, 8, 0, 8, 0, 8, -8, 0, -8, -8, 8, 0, -8, }, +{b: 16, -8, 0, 16, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -8, -8, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, , , x, , x, x, , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , , , , x, , x, , x, , x, , x, x, , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0100,1011,0,}, +{0100,1110,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,1101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x05,0x06,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x01,0x0a,0x04,}, {0x04,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x05,0x07,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,}}, +{{0x0d,0x02,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_080.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_080.txt new file mode 100644 index 0000000..45872c8 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_080.txt @@ -0,0 +1,440 @@ +080 Sbox: +LUT = { +0x08,0x0b,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x00,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 2, 0, 4, 4, 0, 0, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 4, 2, 0, 2, 0, 0, }, +{9: 0, 4, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, }, +{a: 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, }, +{b: 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 10, 4, 6, 4, 6, 4, 0, 0, 0, 0, 6, }, +{2: 16, 8, 10, 0, 8, 8, 0, 0, 10, 8, 2, 2, 8, 0, 0, 0, }, +{4: 16, 0, 0, 4, 0, 8, 4, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 6, 4, 6, 0, 10, 4, 6, 4, 4, 0, 4, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 2, 8, 8, 8, 0, 0, 0, 0, 2, 2, 2, 0, }, +{6: 16, 0, 2, 0, 2, 8, 4, 4, 0, 0, 4, 2, 0, 2, 0, 4, }, +{9: 16, 4, 4, 0, 6, 0, 0, 0, 8, 0, 0, 0, 6, 2, 2, 0, }, +{a: 16, 0, 10, 0, 6, 0, 0, 0, 4, 4, 0, 2, 4, 2, 0, 0, }, +{c: 16, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{7: 16, 2, 0, 6, 0, 8, 0, 0, 2, 0, 6, 4, 0, 0, 0, 4, }, +{b: 16, 6, 4, 2, 4, 0, 0, 0, 10, 0, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:56, 4:30, 6:14, 8:13, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, }, +{7: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -16, 0, 8, }, +{2: 16, 0, 0, 8, 0, -8, 0, 0, 8, -16, 0, -16, 0, 16, -8, 0, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, }, +{8: 16, 8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, -8, }, +{3: 16, 0, -8, 8, 8, 0, -8, -8, -8, 0, 0, 0, 8, -16, 0, 8, }, +{5: 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, 0, -8, 0, 0, 0, 0, 0, -16, 0, 0, -8, 0, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, -8, }, +{a: 16, 0, -8, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{c: 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, 0, 8, 8, -8, 8, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , x, x, , x, , , x, x, x, , , x, x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0100,1100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +080 Inverse Sbox: +LUT = { +0x0b,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x01,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{2: 0, 0, 6, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, 0, 0, 4, 0, 0, 0, }, +{3: 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 0, 2, 0, 0, 0, 2, 4, 4, 0, 0, 2, 0, 0, 0, 2, 0, }, +{9: 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 2, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 0, 0, 6, 0, 0, 4, 0, 0, 2, 6, 0, 0, 2, }, +{2: 16, 4, 10, 0, 8, 4, 0, 2, 4, 10, 0, 0, 4, 0, 2, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 0, 0, 2, 6, 2, 2, 2, 0, }, +{8: 16, 0, 8, 0, 4, 0, 2, 2, 6, 6, 0, 0, 4, 0, 0, 0, }, +{3: 16, 10, 8, 8, 0, 10, 8, 8, 0, 0, 0, 8, 0, 2, 0, 2, }, +{5: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 16, 6, 0, 4, 0, 6, 8, 4, 0, 0, 2, 0, 0, 0, 2, 0, }, +{9: 16, 4, 10, 0, 4, 4, 0, 0, 8, 4, 0, 2, 10, 0, 2, 0, }, +{a: 16, 6, 8, 2, 6, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 16, 4, 2, 0, 0, 0, 0, 4, 0, 0, 2, 6, 2, 2, 0, 2, }, +{7: 16, 0, 2, 4, 0, 4, 0, 2, 0, 2, 2, 4, 0, 2, 0, 2, }, +{b: 16, 0, 8, 2, 6, 0, 2, 0, 6, 4, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{f: 16, 6, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:56, 4:30, 6:14, 8:13, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +{2: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{2: 16, 16, -8, 8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 0, 0, -16, 8, -8, 0, 0, 0, }, +{3: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, -8, 0, -8, 0, 0, 8, -8, 0, 0, 8, }, +{9: 16, 0, -8, 8, 0, -8, 0, 0, 8, -8, 0, -8, 0, 16, -8, -8, }, +{a: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -16, 0, 0, }, +{c: 16, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 0, 8, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , x, x, , x, x, , , x, }, +{5: , , x, , x, x, x, x, x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , , x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , , x, x, x, , , , x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , x, , , x, , , x, x, , x, x, , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , x, , x, x, x, , , x, x, , x, }, +{e: , , x, x, x, , , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,0101,1,}, +{1100,0011,0,}, +{1100,1000,1,}, +{1100,1011,1,}, +{1101,0011,1,}, +{1101,1001,0,}, +{1101,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x09,0x0a,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x0a,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x06,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0d,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_081.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_081.txt new file mode 100644 index 0000000..f2b75cf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_081.txt @@ -0,0 +1,440 @@ +081 Sbox: +LUT = { +0x08,0x0d,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x00,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 4, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{5: 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 2, 2, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 2, 2, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, }, +{f: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 10, 6, 0, 0, 2, 0, 0, 0, 0, 2, }, +{2: 16, 0, 10, 0, 0, 0, 4, 0, 6, 0, 6, 6, 4, 4, 4, 4, }, +{4: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{8: 16, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{3: 16, 2, 0, 2, 0, 4, 4, 4, 0, 2, 2, 0, 0, 2, 2, 0, }, +{5: 16, 8, 8, 8, 0, 8, 10, 10, 0, 0, 0, 8, 0, 2, 2, 0, }, +{6: 16, 0, 2, 0, 2, 4, 4, 4, 0, 2, 2, 2, 2, 0, 0, 0, }, +{9: 16, 2, 8, 0, 2, 2, 0, 0, 8, 2, 0, 0, 8, 0, 0, 0, }, +{a: 16, 4, 2, 0, 2, 0, 0, 6, 0, 2, 0, 4, 2, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 2, 8, 2, 0, 0, 4, 0, 4, 2, 0, 4, 4, 0, 0, 2, }, +{b: 16, 0, 8, 4, 2, 2, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 10, 4, 0, 0, 0, 6, 6, 0, 4, 0, 4, 6, 4, 4, }, +{f: 16, 4, 0, 0, 2, 2, 0, 4, 0, 0, 0, 6, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:37, 6:11, 8:12, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 0, 0, 0, 4, 0, 8, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:9, 4:3, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, -8, -8, 0, 8, }, +{2: 16, 0, -8, 0, 0, 0, 8, 0, 8, -8, 8, -16, -8, 8, -8, 0, }, +{4: 16, 0, 8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -8, 0, 8, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, -16, 8, -16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, -8, 0, 16, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 8, -8, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 16, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{e: 16, 8, -8, 0, 0, -16, 0, 0, 8, -8, 8, 0, 0, 8, -8, -8, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, , , x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , x, x, , , , x, x, x, , x, x, , x, , x, }, +{b: , , , , x, x, x, x, x, , x, , x, x, , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0011,0101,1,}, +{0011,1011,0,}, +{0011,1110,1,}, +{0100,0101,1,}, +{0100,1001,0,}, +{0100,1100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x05,0x06,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x01,0x0a,0x04,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x09,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,}}, +{{0x02,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x03,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,}}, +{{0x09,0x0a,}, {0x04,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,}}, +{{0x0d,0x0e,}, {0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +081 Inverse Sbox: +LUT = { +0x0d,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 4, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 6, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 0, 2, 0, 4, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 6, 4, 0, 2, 0, 0, 0, 0, 2, 0, }, +{9: 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, }, +{c: 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 8, 0, 2, 4, 0, 2, 0, 2, 0, 4, }, +{2: 16, 0, 10, 0, 0, 0, 8, 2, 8, 2, 8, 8, 8, 0, 10, 0, }, +{4: 16, 4, 0, 4, 2, 2, 8, 0, 0, 0, 2, 2, 4, 0, 4, 0, }, +{8: 16, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 2, }, +{3: 16, 4, 0, 4, 0, 4, 8, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 16, 10, 4, 8, 2, 4, 10, 4, 0, 0, 2, 4, 0, 0, 0, 0, }, +{6: 16, 6, 0, 4, 0, 4, 10, 4, 0, 6, 0, 0, 4, 0, 6, 4, }, +{9: 16, 0, 6, 2, 2, 0, 0, 0, 8, 0, 0, 4, 4, 0, 6, 0, }, +{a: 16, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, }, +{c: 16, 2, 6, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, }, +{7: 16, 0, 6, 0, 0, 0, 8, 2, 0, 4, 0, 4, 2, 0, 0, 6, }, +{b: 16, 0, 4, 2, 2, 0, 0, 2, 8, 2, 0, 4, 4, 0, 4, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 4, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:37, 6:11, 8:12, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 4, 0, 8, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:9, 4:3, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 16, -16, 0, 0, -16, 0, 0, 0, 0, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 16, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 16, -8, 8, 0, 0, -8, -8, 8, -8, 0, -8, 0, -8, 0, }, +{6: 16, 0, 0, -8, 8, -16, 0, 0, -8, 8, -8, 8, -8, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, 0, 0, 8, 0, -8, -8, -8, 8, 8, -8, -8, }, +{a: 16, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 0, 8, -8, 0, 0, }, +{c: 16, 0, 0, 0, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -16, 0, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, -8, 0, 8, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , , x, x, , x, x, x, , x, x, , x, , x, }, +{6: , , , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , , x, , , x, , x, , x, x, , x, , x, }, +{b: , , , , , , x, , x, , x, , x, x, , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,0x05,0x07,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_082.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_082.txt new file mode 100644 index 0000000..fbdb729 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_082.txt @@ -0,0 +1,440 @@ +082 Sbox: +LUT = { +0x06,0x08,0x0f,0x02,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x01, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 2, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 4, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 2, 4, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, }, +{c: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, }, +{7: 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:2, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 6, 2, 0, 0, 4, 0, 2, 2, 2, }, +{2: 16, 0, 10, 0, 4, 0, 4, 0, 6, 4, 6, 6, 4, 0, 4, 0, }, +{4: 16, 4, 0, 8, 0, 4, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 16, 6, 0, 0, 2, 0, 2, 4, 2, 2, 0, 4, 0, 0, 0, 2, }, +{3: 16, 6, 0, 8, 0, 4, 4, 0, 0, 0, 0, 6, 2, 2, 0, 0, }, +{5: 16, 0, 8, 0, 2, 2, 4, 2, 4, 0, 0, 4, 4, 2, 0, 0, }, +{6: 16, 4, 2, 0, 2, 0, 0, 4, 0, 0, 2, 6, 0, 0, 2, 2, }, +{9: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{a: 16, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, }, +{c: 16, 6, 8, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 6, 0, }, +{7: 16, 10, 8, 8, 0, 8, 8, 8, 0, 2, 2, 10, 0, 0, 0, 0, }, +{b: 16, 4, 10, 0, 4, 4, 0, 2, 10, 4, 0, 0, 8, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 8, 2, 2, 2, 0, 0, 4, 0, 4, 0, 4, 0, 4, 2, }, +{f: 16, 4, 2, 0, 2, 0, 0, 6, 0, 0, 0, 4, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:37, 6:11, 8:12, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{3: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 8, 0, -8, 8, -8, 0, -8, 0, -16, 0, 8, 0, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, -8, 0, 8, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, 0, 0, 0, 0, 8, -8, 0, -8, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, -16, 0, }, +{a: 16, 0, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, 0, 0, 0, -8, -8, -16, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, 0, 8, 0, 0, 8, -16, 0, 0, -16, 0, 0, 16, -8, }, +{b: 16, 0, -8, 8, 0, -8, 0, -8, 16, -8, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, 0, -8, 8, 0, 0, 0, 0, 8, 0, -16, 0, }, +{f: 16, 0, -8, -8, 0, 0, 8, 8, 0, -8, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , , x, x, , x, x, x, x, x, x, , x, x, x, x, }, +{b: , x, x, , x, , x, , x, x, x, x, , x, x, x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , x, x, , , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1001,0111,1,}, +{1001,1011,0,}, +{1001,1100,1,}, +{1110,0111,0,}, +{1110,1001,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x06,0x09,0x0f,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x0c,}, {0x09,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x09,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,0x09,0x0e,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,0x09,0x0e,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x07,0x09,0x0e,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +082 Inverse Sbox: +LUT = { +0x08,0x0f,0x03,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x02, +}; + +ANF of coordinates: +y0 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{8: 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, }, +{a: 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, }, +{c: 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 0, 0, }, +{7: 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 6, 0, 0, 0, 4, }, +{b: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:2, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 6, 6, 0, 4, 0, 0, 6, 10, 4, 0, 0, 4, }, +{2: 16, 0, 10, 0, 0, 0, 8, 2, 8, 0, 8, 8, 10, 0, 8, 2, }, +{4: 16, 0, 0, 8, 0, 8, 0, 0, 2, 2, 0, 8, 0, 2, 2, 0, }, +{8: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 2, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 4, 8, 4, 0, 2, 0, }, +{5: 16, 0, 4, 4, 2, 4, 4, 0, 2, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 6, 0, 0, 4, 0, 2, 4, 0, 0, 0, 8, 2, 0, 0, 6, }, +{9: 16, 2, 6, 0, 2, 0, 4, 0, 4, 0, 0, 0, 10, 0, 4, 0, }, +{a: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 2, 2, 4, 2, 0, 0, }, +{c: 16, 0, 6, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 4, 0, }, +{7: 16, 4, 6, 4, 4, 6, 4, 6, 0, 0, 0, 10, 0, 0, 0, 4, }, +{b: 16, 0, 4, 2, 0, 2, 4, 0, 4, 2, 0, 0, 8, 2, 4, 0, }, +{d: 16, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:37, 6:11, 8:12, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{8: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{f: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 8, 0, 8, -16, -8, 0, -8, 0, 0, 8, -8, }, +{2: 16, 0, -16, 8, 0, 0, 0, -8, 16, 0, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 16, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -16, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -16, -8, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, 0, 0, 0, 8, -8, -8, }, +{a: 16, 8, 0, 0, 0, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{c: 16, 8, 0, -8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, -16, -8, 8, 8, 8, 8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, 0, 0, 0, -16, 0, 8, -8, 8, 0, 0, 0, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , , , x, , x, x, x, x, x, x, , x, x, x, x, }, +{b: , x, , , x, x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, x, x, x, , x, x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0110,1011,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x02,0x09,0x0b,}}, +{{0x03,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x06,0x09,0x0f,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x02,0x09,0x0b,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_083.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_083.txt new file mode 100644 index 0000000..97f9a45 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_083.txt @@ -0,0 +1,440 @@ +083 Sbox: +LUT = { +0x06,0x08,0x0c,0x02,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x01,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, }, +{4: 0, 2, 0, 6, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{3: 0, 2, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 4, }, +{9: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 0, 2, 4, 2, 2, 4, 2, 0, 0, 0, 4, 0, }, +{2: 16, 0, 10, 8, 8, 0, 0, 8, 0, 10, 8, 2, 0, 0, 8, 2, }, +{4: 16, 10, 4, 10, 2, 4, 8, 4, 0, 0, 0, 4, 0, 2, 0, 0, }, +{8: 16, 2, 6, 0, 4, 0, 0, 4, 2, 10, 4, 0, 0, 0, 0, 0, }, +{3: 16, 6, 0, 10, 0, 4, 4, 0, 0, 4, 0, 4, 6, 0, 6, 4, }, +{5: 16, 4, 0, 8, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 4, }, +{6: 16, 0, 6, 8, 0, 0, 0, 4, 0, 0, 0, 2, 6, 0, 2, 4, }, +{9: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{a: 16, 0, 4, 0, 4, 2, 2, 4, 0, 8, 4, 0, 2, 2, 0, 0, }, +{c: 16, 0, 6, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 6, 0, }, +{7: 16, 4, 0, 8, 0, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 2, 0, 2, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:62, 4:40, 6:8, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, -16, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 16, 8, -16, 8, 0, -8, 16, -8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{4: 16, 0, 16, -8, 8, 0, 0, -8, 0, 8, -8, 0, 0, -8, -8, -8, }, +{8: 16, 8, 0, 8, 0, -8, 0, 8, 0, -8, -8, 0, -8, -8, 0, 0, }, +{3: 16, 0, 0, 0, 8, 8, -16, -8, 0, 8, 0, 0, 8, -8, -8, -8, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 0, -16, -8, 0, 0, 0, 8, 8, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{a: 16, 0, 0, 0, -8, 0, 0, -16, -8, 0, 0, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, -8, -8, 8, 0, 0, 8, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -16, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, 0, -8, 0, -8, 8, -8, 0, 0, -8, 8, 0, 0, }, +{d: 16, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, , x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, , x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, , x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , , , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , , , , , , x, x, , , , x, }, +{b: , , , , x, x, , x, , , x, , x, , , x, }, +{d: , x, , x, x, x, , x, , , x, , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,1010,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,}}, +{{0x05,0x0a,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,}, {0x03,0x05,0x06,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +083 Inverse Sbox: +LUT = { +0x08,0x0c,0x03,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x02,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, }, +{a: 0, 0, 6, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 2, 2, 0, 0, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, }, +{f: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 10, 2, 6, 4, 0, 0, 0, 0, 4, 0, 0, 0, 2, }, +{2: 16, 0, 10, 4, 6, 0, 0, 6, 4, 4, 6, 0, 4, 0, 4, 0, }, +{4: 16, 8, 8, 10, 0, 10, 8, 8, 2, 0, 0, 8, 0, 0, 2, 0, }, +{8: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{5: 16, 4, 0, 8, 0, 4, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{6: 16, 2, 8, 4, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, 0, 2, }, +{9: 16, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, }, +{a: 16, 4, 10, 0, 10, 4, 0, 0, 4, 8, 0, 2, 4, 2, 0, 0, }, +{c: 16, 2, 8, 0, 4, 0, 0, 0, 0, 4, 4, 2, 2, 2, 4, 0, }, +{7: 16, 0, 2, 4, 0, 4, 0, 2, 2, 0, 2, 4, 0, 0, 2, 2, }, +{b: 16, 0, 0, 0, 0, 6, 4, 6, 2, 2, 0, 0, 2, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 4, 8, 0, 0, 6, 0, 2, 2, 0, 6, 0, 0, 0, 4, 0, }, +{f: 16, 0, 2, 0, 0, 4, 4, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:62, 4:40, 6:8, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:95, 8:34, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 8, 0, 8, -8, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 0, 0, 0, -8, 8, -8, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 0, 0, 8, 8, -16, -8, 0, 0, 0, 0, 16, -8, -16, 0, }, +{8: 16, 0, 8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, -16, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -16, -8, 0, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, }, +{a: 16, 8, -8, 8, 0, -8, 16, -8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 16, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, 0, }, +{b: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, -16, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, , , x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , x, , x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , , , , , , x, x, , , , x, }, +{b: , , x, , x, , , , , , x, , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0101,0100,1,}, +{0101,1010,0,}, +{0101,1110,1,}, +{0110,0101,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +{1110,0100,1,}, +{1110,1000,1,}, +{1110,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x03,0x04,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x0a,0x04,}, {0x05,}}, +{{0x09,0x0a,0x04,}, {0x05,}}, +{{0x04,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x03,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x0b,}}, +{{0x05,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_084.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_084.txt new file mode 100644 index 0000000..aad533f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_084.txt @@ -0,0 +1,480 @@ +084 Sbox: +LUT = { +0x08,0x05,0x01,0x02,0x03,0x00,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 0, 0, 0, 6, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 2, 0, 6, 6, 0, 0, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 6, 0, 2, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{7: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:78, 6:14, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:12, 2:1, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 8, 0, 10, 8, 8, 0, 0, 0, 8, 0, 2, 0, 2, }, +{2: 16, 8, 10, 8, 0, 8, 8, 8, 2, 0, 2, 10, 0, 0, 0, 0, }, +{4: 16, 8, 8, 10, 0, 8, 10, 8, 0, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 16, 8, 8, 10, 0, 10, 8, 8, 0, 2, 0, 8, 0, 2, 0, 0, }, +{5: 16, 8, 8, 8, 2, 8, 10, 10, 0, 0, 0, 8, 2, 0, 0, 0, }, +{6: 16, 8, 10, 8, 2, 8, 8, 10, 0, 0, 2, 8, 0, 0, 0, 0, }, +{9: 16, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, }, +{a: 16, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, }, +{c: 16, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{7: 16, 10, 8, 8, 0, 8, 8, 8, 2, 0, 0, 10, 0, 0, 0, 2, }, +{b: 16, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{d: 16, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:78, 8:35, 10:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{8: 0, 0, 4, 4, 12, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{7: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{f: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:149, 4:63, 8:42, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 0, -8, 0, 8, 0, 8, 0, 0, -16, 0, -16, 0, 16, 0, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 0, 16, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 8, 8, -8, -16, 0, 0, 0, 0, 16, -16, -8, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, 0, 0, -16, 16, -16, 0, 0, 8, }, +{6: 16, 16, -8, 0, 8, -8, 0, 0, 8, -16, 0, 0, -16, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{7: 16, -16, 0, 0, 8, 0, 0, 16, -8, 0, 0, -16, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, x, , , , x, x, , , x, }, +{5: , , x, x, x, x, x, x, , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, , , x, x, x, x, , , , x, x, , x, }, +{a: , x, , x, , x, x, x, , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , x, x, x, , , x, , , , x, , , , x, }, +{b: , , , , , x, x, x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 22 */ +{0001,0001,1,}, +{0001,0110,0,}, +{0001,0111,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0111,0,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,1000,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1011,0011,0,}, +{1011,0101,1,}, +{1011,0110,1,}, +{1100,0001,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 14, +v=3 15, 1, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x06,0x08,}, {0x01,}}, +{{0x05,0x06,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x01,0x0a,0x0c,}, {0x01,}}, +{{0x09,0x0a,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +084 Inverse Sbox: +LUT = { +0x05,0x02,0x03,0x04,0x06,0x01,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = + x0 + + + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, }, +{3: 0, 6, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 2, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, }, +{c: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:78, 6:14, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:12, 2:1, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 8, 0, 8, 8, 8, 2, 0, 0, 10, 0, 0, 0, 2, }, +{2: 16, 8, 10, 8, 0, 8, 8, 10, 0, 2, 0, 8, 0, 0, 2, 0, }, +{4: 16, 8, 8, 10, 0, 10, 8, 8, 0, 0, 2, 8, 2, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, }, +{3: 16, 10, 8, 8, 0, 10, 8, 8, 2, 0, 0, 8, 2, 0, 0, 0, }, +{5: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 8, 8, 8, 0, 8, 10, 10, 0, 0, 0, 8, 0, 2, 2, 0, }, +{9: 16, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, }, +{a: 16, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, }, +{c: 16, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, }, +{7: 16, 8, 10, 8, 0, 8, 8, 8, 0, 2, 0, 10, 0, 0, 0, 2, }, +{b: 16, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 2, }, +{d: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:78, 8:35, 10:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{9: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 8, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:149, 4:63, 8:42, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 8, 0, 0, 16, -8, 0, 0, -16, 0, 0, 8, -8, }, +{2: 16, 16, -16, 0, 8, -16, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 0, 0, 8, 16, -16, -16, 0, 0, 0, 0, 8, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, }, +{3: 16, -16, 0, 16, 8, 0, -16, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 16, -16, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -16, 8, -16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 8, }, +{9: 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, }, +{a: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, -8, 0, }, +{c: 16, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{7: 16, 0, -16, 0, 8, 0, 16, 0, 0, -8, 0, -16, 0, 8, 0, -8, }, +{b: 16, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{e: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , , , x, x, x, , , , , x, x, , , x, }, +{5: , , , , x, , x, x, , , , x, , x, , x, }, +{6: , , , , x, x, x, x, , , , x, , , x, x, }, +{9: , , x, x, x, , x, x, x, , , , x, x, , x, }, +{a: , , , x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, x, , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , , x, , x, , , , , , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , , , x, x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 22 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0011,0,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0101,0011,1,}, +{0101,0100,1,}, +{0101,0111,0,}, +{0110,0001,0,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0111,0001,1,}, +{0111,0110,0,}, +{0111,0111,1,}, +{1000,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 14, +v=3 15, 1, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x03,0x04,0x08,}, {0x05,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x06,0x08,}, {0x07,}}, +{{0x05,0x06,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x01,0x0a,0x0c,}, {0x07,}}, +{{0x09,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x04,}, {0x03,0x05,0x06,}}, +{{0x0b,0x04,}, {0x03,0x05,0x06,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x05,0x07,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,0x05,0x07,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_085.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_085.txt new file mode 100644 index 0000000..1300669 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_085.txt @@ -0,0 +1,420 @@ +085 Sbox: +LUT = { +0x08,0x0a,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x00,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, }, +{2: 0, 0, 8, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 4, 2, 0, 2, 0, 0, }, +{9: 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 4, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:156, 2:80, 4:18, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 6, 0, 0, 8, 4, 6, 0, 0, 0, 0, 2, 0, 0, 2, }, +{2: 16, 4, 8, 4, 6, 4, 4, 6, 6, 4, 4, 6, 4, 0, 4, 0, }, +{4: 16, 0, 4, 4, 0, 4, 4, 8, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{3: 16, 6, 4, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 16, 0, 4, 0, 0, 4, 8, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{6: 16, 0, 6, 8, 6, 0, 0, 4, 0, 0, 4, 2, 0, 2, 0, 0, }, +{9: 16, 2, 6, 0, 0, 0, 0, 0, 4, 2, 2, 0, 6, 0, 2, 0, }, +{a: 16, 2, 4, 4, 8, 0, 0, 0, 0, 4, 4, 2, 2, 2, 0, 0, }, +{c: 16, 0, 4, 4, 4, 0, 2, 0, 0, 0, 8, 2, 0, 2, 4, 2, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:98, 2:66, 4:40, 6:14, 8:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 8, 8, 0, -8, 0, 0, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 8, 8, -8, 8, 0, 8, -16, 0, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, 0, -8, 0, 0, 0, 0, 0, -16, 0, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, }, +{a: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, 0, -8, 8, -8, }, +{c: 16, 0, 8, -16, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, , x, , x, x, , , x, }, +{5: , , x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , , x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, , x, x, , , x, x, x, }, +{7: , , , x, , , , x, , x, , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , x, , x, x, , x, , x, , , , x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,1100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x03,0x09,0x0a,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +085 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x01,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 2, 8, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{6: 0, 2, 2, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 2, 0, 2, }, +{b: 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:156, 2:80, 4:18, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 6, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 16, 6, 8, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 0, 4, 4, 0, 2, 0, 8, 0, 4, 4, 2, 2, 0, 0, 2, }, +{8: 16, 0, 6, 0, 4, 0, 0, 6, 0, 8, 4, 0, 2, 0, 0, 2, }, +{3: 16, 8, 4, 4, 2, 4, 4, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{5: 16, 4, 4, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{6: 16, 6, 6, 8, 0, 0, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, }, +{9: 16, 0, 6, 0, 2, 2, 2, 0, 4, 0, 0, 2, 6, 0, 0, 0, }, +{a: 16, 0, 4, 2, 6, 2, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{7: 16, 0, 6, 0, 0, 0, 4, 2, 0, 2, 2, 4, 0, 2, 0, 2, }, +{b: 16, 2, 4, 2, 0, 2, 2, 0, 6, 2, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:98, 2:66, 4:40, 6:14, 8:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 8, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -8, 8, 8, -16, 0, 0, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 8, -8, 8, -8, 0, 8, 0, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 8, 8, 0, -8, 0, -8, }, +{5: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 8, -16, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, }, +{9: 16, -8, 0, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, -8, 0, 8, -8, 0, 0, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, -8, 0, 8, 0, 0, -8, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , x, , x, x, , , x, }, +{5: , x, x, , x, , x, x, , x, , x, , x, , x, }, +{6: , x, x, x, , x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , x, x, , , x, x, x, }, +{7: , x, x, , , , , , , x, , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, x, , , , , x, , x, , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x05,0x06,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0c,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x05,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_086.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_086.txt new file mode 100644 index 0000000..4cc5784 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_086.txt @@ -0,0 +1,420 @@ +086 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x05,0x0a,0x07,0x00,0x09,0x04,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 8, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 4, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 4, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:156, 2:80, 4:18, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 6, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{2: 16, 4, 8, 6, 4, 4, 4, 4, 6, 6, 4, 6, 4, 0, 4, 0, }, +{4: 16, 4, 4, 8, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 16, 2, 4, 2, 4, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 2, }, +{3: 16, 8, 4, 4, 0, 4, 4, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 16, 0, 4, 0, 2, 2, 4, 2, 0, 0, 4, 8, 4, 2, 0, 0, }, +{6: 16, 0, 6, 4, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 2, 2, }, +{a: 16, 2, 6, 0, 4, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 4, 6, 6, 0, 0, 8, 0, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 6, 0, 2, 0, 0, 0, 4, 0, 4, 6, 8, 2, 0, 0, }, +{d: 16, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 0, 0, 0, 2, 8, 4, 4, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:96, 2:68, 4:42, 6:12, 8:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 8, 8, -8, 8, -8, 8, -8, 0, -16, 0, 8, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, }, +{a: 16, 0, -8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, 0, 8, 0, 0, 8, 0, 0, 0, -16, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, -8, 0, 0, -8, 8, 8, -8, }, +{d: 16, 0, 0, 0, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 8, 8, -8, 0, 0, 0, 8, 0, 0, -8, }, +{f: 16, 0, 0, 0, 0, 0, -8, 8, -8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , , x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , , x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , , , x, , x, , , , x, }, +{b: , x, x, , x, x, , x, , x, , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x03,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x07,0x08,0x0f,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +086 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x0a,0x05,0x00,0x07,0x01,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{4: 0, 0, 2, 4, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 0, 2, 2, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, }, +{a: 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 4, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 4, 2, }, +{b: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:156, 2:80, 4:18, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 2, 8, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 16, 4, 8, 4, 4, 4, 4, 6, 4, 6, 4, 6, 6, 0, 4, 0, }, +{4: 16, 0, 6, 8, 2, 4, 0, 4, 0, 0, 0, 6, 0, 2, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, }, +{3: 16, 6, 4, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 16, 0, 4, 4, 2, 4, 4, 0, 2, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 2, 4, 4, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{9: 16, 2, 6, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, 0, 0, 2, }, +{a: 16, 0, 6, 2, 4, 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 0, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 0, 0, 4, 0, 4, 2, 8, 2, }, +{7: 16, 0, 6, 0, 0, 0, 8, 2, 0, 0, 0, 4, 6, 0, 4, 2, }, +{b: 16, 0, 4, 2, 0, 2, 4, 0, 4, 2, 0, 0, 8, 2, 4, 0, }, +{d: 16, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:96, 2:68, 4:42, 6:12, 8:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:111, 8:30, 12:1, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -16, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 8, 8, 0, -8, 0, -8, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, -8, 0, 8, }, +{9: 16, -8, 0, 8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, 8, 0, 0, -8, -8, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, 8, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, -8, }, +{b: 16, -8, 0, 0, 0, 0, 0, -16, 0, 8, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, 0, 0, -8, 8, -8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, , x, x, , x, x, , x, , x, , x, , x, }, +{6: , x, , x, , x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, , x, , , , x, , x, , x, , , , x, }, +{b: , , , , x, , , x, , x, , , x, , , x, }, +{d: , , , x, x, , , , , x, , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0110,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x06,0x07,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_087.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_087.txt new file mode 100644 index 0000000..66bf81d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_087.txt @@ -0,0 +1,410 @@ +087 Sbox: +LUT = { +0x08,0x0a,0x01,0x0c,0x03,0x05,0x06,0x07,0x04,0x09,0x00,0x0b,0x02,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, }, +{8: 0, 4, 0, 0, 6, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 2, 0, 2, }, +{6: 0, 0, 4, 0, 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{9: 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 4, 0, }, +{a: 0, 2, 0, 2, 2, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 4, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 4, }, +{b: 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{e: 0, 2, 2, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 0, 8, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, }, +{2: 16, 0, 6, 6, 4, 0, 2, 6, 2, 4, 6, 0, 0, 0, 4, 0, }, +{4: 16, 0, 4, 8, 0, 0, 0, 6, 0, 0, 0, 2, 4, 0, 2, 6, }, +{8: 16, 8, 8, 0, 6, 10, 0, 0, 4, 4, 2, 2, 4, 0, 0, 0, }, +{3: 16, 0, 0, 4, 4, 4, 0, 0, 2, 0, 0, 0, 10, 2, 0, 6, }, +{5: 16, 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 2, 2, 4, 2, }, +{6: 16, 4, 8, 4, 0, 4, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{9: 16, 6, 0, 0, 4, 0, 0, 0, 8, 2, 2, 6, 0, 0, 4, 0, }, +{a: 16, 2, 4, 2, 10, 0, 4, 0, 0, 4, 0, 0, 0, 6, 0, 0, }, +{c: 16, 0, 4, 0, 0, 2, 0, 2, 4, 2, 4, 4, 0, 0, 8, 2, }, +{7: 16, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 2, 6, 2, 0, 4, }, +{b: 16, 0, 0, 0, 8, 6, 6, 0, 0, 2, 2, 0, 4, 4, 0, 0, }, +{d: 16, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, }, +{e: 16, 6, 10, 0, 0, 4, 2, 2, 0, 0, 4, 0, 0, 0, 4, 0, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:54, 4:37, 6:16, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 12, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{e: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, -8, 0, 0, 8, 0, 8, 0, -8, -8, 8, -8, }, +{2: 16, 8, 0, 0, 8, -8, 0, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, -8, -8, 0, 8, -8, 0, 8, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 8, 8, 0, 8, 0, 8, -16, -8, 0, 0, -8, -8, 0, -8, }, +{3: 16, -8, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, -16, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, -8, -8, 8, -8, 0, 0, -8, 8, 8, 0, 0, }, +{a: 16, 0, 8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, -8, -8, 0, 8, 0, 0, -8, -8, 0, -8, 0, 0, 8, 8, }, +{7: 16, -8, 0, -8, -8, 8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 8, -8, 8, 0, -8, -8, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, 8, -8, -8, 0, -8, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , x, x, x, x, , , x, }, +{5: , , x, x, x, x, x, , , x, x, x, , x, , x, }, +{6: , , , x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , , x, x, x, , x, x, , x, }, +{a: , x, , x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , , , , x, , , , , x, x, x, , , , x, }, +{b: , x, , , x, x, , , , , x, , x, , , x, }, +{d: , , x, x, , x, , , , x, x, , , x, , x, }, +{e: , , , x, , x, , , , x, x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0110,1,}, +{1001,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x06,0x09,0x0f,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x06,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +087 Inverse Sbox: +LUT = { +0x0a,0x02,0x0c,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x01,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 4, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{3: 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, }, +{5: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +{6: 0, 2, 2, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 0, 2, 4, 2, 4, 0, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{b: 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 8, 0, 0, 4, 6, 2, 0, 0, 0, 2, 6, 0, }, +{2: 16, 2, 6, 4, 8, 0, 0, 8, 0, 4, 4, 0, 0, 2, 10, 0, }, +{4: 16, 0, 6, 8, 0, 4, 0, 4, 0, 2, 0, 6, 0, 0, 0, 2, }, +{8: 16, 8, 4, 0, 6, 4, 0, 0, 4, 10, 0, 0, 8, 2, 0, 2, }, +{3: 16, 0, 0, 0, 10, 4, 0, 4, 0, 0, 2, 0, 6, 0, 4, 2, }, +{5: 16, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 6, 2, 2, 2, }, +{6: 16, 2, 6, 6, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, }, +{9: 16, 4, 2, 0, 4, 2, 4, 2, 8, 0, 4, 2, 0, 0, 0, 0, }, +{a: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, 4, 2, }, +{7: 16, 0, 0, 2, 2, 0, 4, 0, 6, 0, 4, 2, 0, 2, 0, 2, }, +{b: 16, 2, 0, 4, 4, 10, 2, 0, 0, 0, 0, 6, 4, 0, 0, 0, }, +{d: 16, 4, 0, 0, 0, 2, 2, 2, 0, 6, 0, 2, 4, 2, 0, 0, }, +{e: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 6, 0, 6, 2, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:54, 4:37, 6:16, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 4, 0, 12, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{6: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, -8, -8, 0, 8, -8, 0, 0, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 8, -16, 0, 0, 8, -8, 8, 0, -8, 0, 0, -8, }, +{4: 16, 0, -8, 0, 8, 8, 0, -8, 0, 0, 0, -8, 8, -8, -8, 0, }, +{8: 16, 0, 0, 8, -16, 8, 8, 0, 0, 0, -8, 8, -8, -8, 0, -8, }, +{3: 16, 0, -8, 0, -8, 8, -8, 0, -8, 0, 8, 8, 0, 0, -8, 0, }, +{5: 16, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{6: 16, 8, 0, -8, 8, -8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, -8, 0, 0, 8, -8, 0, 0, 0, -8, -8, 0, 0, 8, -8, 8, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, }, +{7: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, 8, 8, -8, -8, 0, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, -8, 0, -8, 8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , x, x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, x, x, , x, , x, }, +{6: , , , x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, , , x, , , x, x, x, , x, x, , x, }, +{a: , x, x, x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , x, x, , , x, x, x, }, +{7: , , , x, x, x, , , , x, x, x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , x, , , x, , , , x, x, , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0010,1,}, +{1000,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x0e,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x01,0x06,0x07,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x05,0x08,0x0d,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_088.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_088.txt new file mode 100644 index 0000000..11a4eb0 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_088.txt @@ -0,0 +1,410 @@ +088 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x05,0x06,0x03,0x04,0x09,0x0a,0x0b,0x07,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{2: 0, 0, 4, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{9: 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 4, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 2, 0, }, +{b: 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{e: 0, 2, 2, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 6, 0, 10, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{2: 16, 0, 4, 6, 0, 0, 0, 10, 4, 0, 2, 0, 0, 0, 2, 4, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 0, 2, 0, 6, 0, 0, 0, 2, }, +{8: 16, 0, 0, 0, 4, 4, 2, 0, 2, 0, 4, 6, 10, 0, 0, 0, }, +{3: 16, 4, 4, 6, 6, 10, 0, 0, 0, 0, 4, 4, 4, 0, 0, 6, }, +{5: 16, 8, 4, 4, 0, 4, 4, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{6: 16, 4, 8, 4, 0, 4, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{9: 16, 2, 2, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, }, +{a: 16, 2, 2, 0, 4, 0, 4, 0, 0, 2, 2, 0, 2, 4, 2, 0, }, +{c: 16, 0, 0, 0, 2, 6, 0, 6, 4, 0, 4, 0, 0, 2, 0, 8, }, +{7: 16, 0, 0, 6, 0, 4, 0, 2, 0, 0, 6, 8, 4, 0, 2, 0, }, +{b: 16, 0, 0, 2, 8, 6, 4, 0, 0, 2, 0, 0, 4, 6, 0, 0, }, +{d: 16, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, }, +{e: 16, 2, 2, 0, 2, 0, 0, 4, 4, 2, 0, 0, 0, 0, 2, 6, }, +{f: 16, 0, 0, 0, 0, 4, 0, 0, 2, 0, 10, 4, 6, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:107, 2:51, 4:39, 6:18, 8:5, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 0, -8, -8, 0, 8, -8, 0, -8, 0, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 0, 8, -8, -8, 8, -8, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, -8, -8, -8, 0, -8, 8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 8, -8, 0, -8, 0, 8, 0, 0, -16, -8, 0, }, +{5: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, -8, 0, 0, -8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, -8, 8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 8, 0, -8, -8, 0, 8, }, +{7: 16, 0, -8, -8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 8, 8, -8, }, +{b: 16, 0, 0, 8, -8, 8, 0, -8, 0, 0, -8, 8, 0, -8, 0, -8, }, +{d: 16, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, }, +{e: 16, 8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 0, -8, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, , x, , , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , x, x, , , x, x, }, +{9: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, , x, x, x, x, , , x, x, , x, x, x, }, +{7: , x, x, x, , x, x, x, , , x, , , , , x, }, +{b: , x, , , x, x, , , , , x, , x, , , x, }, +{d: , , , , x, x, x, x, , , x, x, , x, , x, }, +{e: , , x, , x, x, x, x, , , x, x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0101,1,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x0e,}}, +{{0x05,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +088 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x07,0x08,0x05,0x06,0x0c,0x00,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 6, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, }, +{3: 0, 0, 0, 2, 0, 6, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 2, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, 4, 0, }, +{9: 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 2, }, +{d: 0, 4, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 8, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{2: 16, 0, 4, 4, 0, 4, 4, 8, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 16, 4, 6, 6, 0, 6, 4, 4, 2, 0, 0, 6, 2, 0, 0, 0, }, +{8: 16, 6, 0, 0, 4, 6, 0, 0, 0, 4, 2, 0, 8, 0, 2, 0, }, +{3: 16, 0, 0, 6, 4, 10, 4, 4, 0, 0, 6, 4, 6, 0, 0, 4, }, +{5: 16, 10, 0, 6, 2, 0, 4, 0, 0, 4, 0, 0, 4, 2, 0, 0, }, +{6: 16, 0, 10, 4, 0, 0, 0, 4, 2, 0, 6, 2, 0, 0, 4, 0, }, +{9: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +{a: 16, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 0, }, +{c: 16, 0, 2, 0, 4, 4, 0, 0, 0, 2, 4, 6, 0, 0, 0, 10, }, +{7: 16, 2, 0, 6, 6, 4, 0, 0, 0, 0, 0, 8, 0, 2, 0, 4, }, +{b: 16, 0, 0, 0, 10, 4, 0, 0, 0, 2, 0, 4, 4, 2, 0, 6, }, +{d: 16, 4, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 6, 2, 0, 0, }, +{e: 16, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 4, 2, 0, 6, 0, 0, 2, 0, 8, 0, 0, 0, 6, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:107, 2:51, 4:39, 6:18, 8:5, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{e: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, 8, -8, 0, 0, }, +{2: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{4: 16, 0, 0, 0, 8, 8, -8, -8, 8, 0, -8, -8, 8, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 8, -8, 0, -8, 0, 0, 8, -8, 0, 0, -8, }, +{3: 16, 0, -8, 0, 8, 8, -16, -8, 0, -8, 0, 8, 0, -8, 0, 8, }, +{5: 16, 0, 8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, -8, 0, 0, }, +{6: 16, 8, -8, -8, 0, -8, -8, 8, 0, -8, 0, 0, 0, 8, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 8, 0, 8, -8, 0, 0, -8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, 0, -8, 8, 8, 0, -8, -8, 0, -8, -8, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 8, 8, 8, 0, 0, 0, -8, 0, -8, 0, -8, }, +{b: 16, -8, -8, 0, -8, 8, 8, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, }, +{e: 16, 0, -8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, , x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, , , , , x, x, , , , x, }, +{b: , , , , x, , x, x, , , , x, x, , , x, }, +{d: , x, , , x, x, , , , , x, , , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0010,1,}, +{0101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x08,}, {0x04,}}, +{{0x03,0x08,}, {0x02,0x05,0x07,}}, +{{0x05,0x08,}, {0x02,0x09,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x06,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_089.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_089.txt new file mode 100644 index 0000000..b9cabad --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_089.txt @@ -0,0 +1,410 @@ +089 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0b,0x06,0x07,0x04,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 4, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{6: 0, 0, 2, 2, 2, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 2, 4, 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 2, 0, 2, 2, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 4, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 2, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 4, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 0, 6, 4, 0, 0, 6, 4, 0, 0, 4, 2, 0, 2, }, +{2: 16, 4, 8, 0, 2, 6, 2, 0, 0, 0, 4, 0, 0, 0, 6, 0, }, +{4: 16, 2, 0, 4, 2, 4, 0, 0, 0, 2, 0, 6, 2, 0, 0, 2, }, +{8: 16, 4, 0, 0, 4, 0, 0, 4, 10, 0, 0, 0, 2, 2, 0, 6, }, +{3: 16, 8, 4, 10, 0, 6, 8, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 10, 4, 0, 0, 0, 2, 0, 2, 4, }, +{6: 16, 0, 2, 2, 2, 6, 4, 4, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 16, 8, 2, 4, 4, 0, 4, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{a: 16, 10, 0, 6, 2, 0, 4, 0, 0, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 0, 0, 0, 0, 10, 4, 4, 2, 6, 2, }, +{7: 16, 0, 0, 4, 0, 4, 2, 2, 2, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 4, 0, 0, 2, 0, 2, 0, 0, 6, 4, 6, 8, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 2, 0, 6, 4, 2, 2, 0, 0, 2, 2, 4, }, +{e: 16, 0, 6, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:51, 4:37, 6:18, 8:6, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 8, 0, 0, 8, -8, -8, -8, 0, -8, }, +{2: 16, 8, 0, 0, 0, 0, 0, -8, -8, -8, 8, 0, -8, 8, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 8, -8, -8, 8, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, -8, 0, 8, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, 0, 0, -8, -8, 0, 0, 0, -8, 8, 0, 8, -8, 8, }, +{6: 16, 8, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 8, 8, -8, -8, }, +{a: 16, 0, 8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, -8, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, -8, }, +{7: 16, -8, -8, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 8, 8, 0, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, -8, 0, -8, 0, -8, 8, 8, 0, }, +{d: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, 8, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, , , x, x, , x, x, , x, x, , , x, }, +{b: , x, , , x, , x, , x, x, , , , , , x, }, +{d: , , x, x, , , x, , x, x, , , x, x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1100,0111,1,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x06,0x09,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x04,0x09,0x0d,}}, +{{0x05,0x02,}, {0x0c,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +089 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0b,0x06,0x07,0x03,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 2, }, +{8: 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 2, 0, 0, 6, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{6: 0, 0, 0, 0, 4, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 4, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 2, 4, 8, 0, 0, 8, 10, 0, 0, 4, 0, 0, 2, }, +{2: 16, 6, 8, 0, 0, 4, 0, 2, 2, 0, 4, 0, 0, 0, 6, 0, }, +{4: 16, 0, 0, 4, 0, 10, 0, 2, 4, 6, 0, 4, 0, 0, 0, 2, }, +{8: 16, 6, 2, 2, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 4, 6, 4, 0, 6, 6, 6, 0, 0, 0, 4, 0, 2, 0, 2, }, +{5: 16, 0, 2, 0, 0, 8, 4, 4, 4, 4, 0, 2, 2, 0, 2, 0, }, +{6: 16, 0, 0, 0, 4, 4, 10, 4, 0, 0, 0, 2, 0, 6, 0, 2, }, +{9: 16, 6, 0, 0, 10, 0, 4, 0, 4, 0, 0, 2, 0, 4, 2, 0, }, +{a: 16, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 6, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 0, 0, 0, 0, 10, 4, 4, 2, 6, 2, }, +{7: 16, 0, 0, 6, 0, 4, 0, 2, 2, 0, 4, 8, 6, 0, 0, 0, }, +{b: 16, 4, 0, 2, 2, 0, 2, 0, 2, 4, 4, 4, 8, 0, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 6, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 2, 6, 0, 4, 0, 0, 0, 2, 0, 0, 4, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:51, 4:37, 6:18, 8:6, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 8, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, -8, 8, 8, -8, 0, -16, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 8, -8, -8, 8, }, +{8: 16, 8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, 0, -8, 0, -8, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, -8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, 8, 0, 0, }, +{6: 16, 0, 0, -8, 0, 0, 8, 8, 0, -8, -8, 8, -8, -8, 0, 0, }, +{9: 16, -8, 8, 0, 0, -8, 0, 8, -8, 0, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, -8, 0, -8, 0, 0, -8, 8, 0, 8, 0, -8, 8, 0, -8, }, +{7: 16, 0, 0, -8, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 8, 0, }, +{b: 16, -8, 0, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 8, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, 0, 8, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , x, , x, , , x, , x, x, , x, x, , , x, }, +{b: , , x, , , x, x, , x, x, , , , , , x, }, +{d: , x, x, , x, , x, , x, x, , , x, x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1100,1011,1,}, +{1101,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_090.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_090.txt new file mode 100644 index 0000000..4fde8dc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_090.txt @@ -0,0 +1,410 @@ +090 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x0b,0x06,0x07,0x00,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, 4, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 4, 2, 0, 2, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, }, +{a: 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 4, 2, 0, }, +{c: 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, }, +{b: 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 6, 6, 0, 0, 6, 4, 2, 0, 4, 0, 0, 2, }, +{2: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 16, 0, 4, 4, 0, 6, 6, 0, 0, 2, 2, 8, 0, 0, 0, 0, }, +{8: 16, 6, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 16, 4, 4, 6, 0, 6, 6, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{5: 16, 0, 0, 2, 0, 4, 4, 10, 0, 0, 0, 0, 4, 6, 0, 2, }, +{6: 16, 0, 4, 0, 2, 4, 8, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 4, 4, 2, 8, 0, 0, 0, 4, 4, 0, 2, 0, 2, 2, 0, }, +{a: 16, 6, 0, 2, 0, 0, 0, 4, 0, 4, 0, 0, 10, 4, 2, 0, }, +{c: 16, 0, 4, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +{7: 16, 2, 0, 4, 0, 6, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, }, +{b: 16, 6, 4, 0, 6, 0, 2, 0, 0, 8, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 6, 4, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:54, 4:43, 6:18, 8:4, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, -8, 8, -8, 0, 8, -8, -8, -8, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, 8, -16, -8, 0, 0, -8, -8, 8, 0, 8, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, 0, -8, 0, 8, 8, -8, -8, 8, }, +{5: 16, -8, 0, -8, 0, 0, 0, -8, 8, 8, -8, 8, -8, 0, 0, 0, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, -8, 8, -8, }, +{c: 16, 0, 0, 0, 0, 0, 8, -8, 0, -8, 8, 0, -8, 0, -8, 0, }, +{7: 16, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, -8, 8, 0, 0, 0, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -16, 8, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, , x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, x, , x, x, , x, x, , x, x, , , x, }, +{b: , x, , , x, , x, , x, x, , , , , , x, }, +{d: , , , x, x, , x, , x, x, , , x, x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,0010,1,}, +{1011,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x0b,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x06,0x09,0x0f,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +090 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x0b,0x06,0x07,0x01,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 2, 4, }, +{9: 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 2, 0, }, +{a: 0, 0, 4, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, }, +{c: 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 6, 4, 0, 0, 4, 6, 0, 2, 6, 0, 0, 2, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 0, 0, 4, 2, 6, 2, 0, 2, 2, 0, 4, 0, 2, 0, 0, }, +{8: 16, 6, 4, 0, 4, 0, 0, 2, 8, 0, 2, 0, 6, 0, 0, 0, }, +{3: 16, 6, 4, 6, 0, 6, 4, 4, 0, 0, 2, 6, 0, 2, 0, 0, }, +{5: 16, 0, 4, 6, 0, 6, 4, 8, 0, 0, 2, 0, 2, 0, 0, 0, }, +{6: 16, 0, 0, 0, 2, 6, 10, 4, 0, 4, 0, 0, 0, 0, 2, 4, }, +{9: 16, 6, 0, 0, 4, 2, 0, 2, 4, 0, 0, 2, 0, 2, 2, 0, }, +{a: 16, 4, 4, 2, 0, 0, 0, 0, 4, 4, 0, 2, 8, 2, 2, 0, }, +{c: 16, 2, 4, 2, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 4, 2, }, +{7: 16, 0, 4, 8, 2, 4, 0, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 4, 0, 0, 2, 0, 4, 0, 0, 10, 0, 0, 4, 2, 0, 6, }, +{d: 16, 0, 0, 0, 0, 2, 6, 0, 2, 4, 2, 0, 0, 2, 2, 4, }, +{e: 16, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:54, 4:43, 6:18, 8:4, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 12, 0, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{f: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 8, 0, -8, -8, -8, 8, -8, }, +{2: 16, 8, -8, 0, 0, 0, -8, -8, 8, -8, 0, 0, -16, 8, 8, 0, }, +{4: 16, 0, 8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{8: 16, 0, 8, 8, -8, 0, -8, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, -8, -8, 8, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, 0, 0, -16, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, 8, -8, -8, -8, 8, }, +{9: 16, -8, 0, 0, 0, -8, -8, 8, 0, -8, 0, 0, 8, 0, 0, 0, }, +{a: 16, 8, -8, 0, 0, -8, 8, -8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{c: 16, 0, 0, 0, 0, 0, 0, -8, 8, 0, 8, -8, -8, 0, 0, -8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{b: 16, -8, 0, 0, -8, 0, 8, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, -8, 0, 0, 0, 8, 0, 0, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , , x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , x, x, x, , x, x, , x, x, , x, x, , , x, }, +{b: , , x, , x, x, x, , x, x, , , , , , x, }, +{d: , , , , x, x, x, , x, x, , , x, x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,0101,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_091.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_091.txt new file mode 100644 index 0000000..0c87bf7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_091.txt @@ -0,0 +1,410 @@ +091 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x09,0x00,0x07,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 2, 4, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, }, +{a: 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, }, +{c: 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 2, 6, 0, 0, 0, 2, }, +{2: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 16, 4, 4, 4, 0, 0, 8, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 16, 0, 0, 6, 4, 4, 0, 2, 2, 0, 0, 0, 10, 0, 0, 4, }, +{3: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{5: 16, 6, 0, 10, 2, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 4, }, +{6: 16, 6, 4, 0, 2, 0, 4, 4, 0, 0, 0, 10, 0, 0, 2, 0, }, +{9: 16, 0, 4, 0, 4, 6, 0, 0, 4, 10, 0, 2, 0, 0, 2, 0, }, +{a: 16, 2, 0, 2, 0, 6, 2, 0, 4, 4, 0, 0, 0, 2, 2, 0, }, +{c: 16, 0, 4, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +{7: 16, 6, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 0, 4, 0, 8, 4, 2, 2, 0, 4, 2, 0, 4, 0, 0, 2, }, +{d: 16, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 0, 4, 2, 2, 4, }, +{e: 16, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:55, 4:46, 6:15, 8:2, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{f: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 8, -8, 0, 8, -8, -8, -8, 8, 0, }, +{2: 16, 8, 0, 0, 0, -8, 8, -16, -8, 0, 0, -8, -8, 8, 0, 8, }, +{4: 16, 0, 0, -8, 0, 8, 0, -8, 0, 0, -8, -8, 8, 0, 8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 8, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 0, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 8, }, +{5: 16, -8, 8, 0, 0, 0, 0, -8, 0, 8, -8, 8, -8, 0, 0, -8, }, +{6: 16, 8, -8, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, -8, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, 8, -8, 0, 0, }, +{c: 16, 0, 0, 0, 0, 0, 8, -8, 0, -8, 8, 0, -8, 0, -8, 0, }, +{7: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, -16, 8, 0, 0, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , , x, x, , , x, }, +{5: , , x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , , , , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{7: , , x, x, , x, x, x, x, , , , , , , x, }, +{b: , x, , , x, , x, x, x, , , x, x, , , x, }, +{d: , , , x, x, , x, x, x, , , x, , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,0010,1,}, +{1011,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x02,0x09,0x0b,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x06,0x09,0x0f,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +091 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x09,0x01,0x07,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, }, +{5: 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, }, +{a: 0, 0, 4, 2, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, }, +{c: 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 4, 6, 6, 0, 2, 0, 6, 0, 0, 0, 2, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 4, 0, 4, 6, 0, 10, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{8: 16, 0, 4, 0, 4, 4, 2, 2, 4, 0, 2, 0, 8, 0, 0, 2, }, +{3: 16, 6, 4, 0, 4, 6, 0, 0, 6, 6, 2, 0, 4, 2, 0, 0, }, +{5: 16, 4, 4, 8, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 6, 0, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, 0, 2, 2, }, +{9: 16, 0, 0, 0, 2, 6, 0, 0, 4, 4, 0, 2, 0, 2, 2, 2, }, +{a: 16, 0, 4, 2, 0, 6, 0, 0, 10, 4, 0, 0, 4, 0, 2, 0, }, +{c: 16, 2, 4, 2, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 4, 2, }, +{7: 16, 6, 4, 4, 0, 0, 0, 10, 2, 0, 0, 4, 0, 0, 2, 0, }, +{b: 16, 0, 0, 2, 10, 6, 4, 0, 0, 0, 0, 0, 4, 4, 0, 2, }, +{d: 16, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 4, 0, 4, 0, 0, 0, 2, 2, 2, 4, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:55, 4:46, 6:15, 8:2, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 12, 0, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{f: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, 0, 8, -8, 8, 0, -8, -8, -8, 8, 0, }, +{2: 16, 8, -8, 0, 0, 0, -8, -8, 8, -8, 0, 0, -16, 8, 8, 0, }, +{4: 16, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 0, 8, -8, 0, -8, }, +{8: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, -8, 0, -8, 0, -8, 8, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, -8, 8, 0, 8, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 0, 0, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, 8, -8, -8, 0, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, 8, 0, -8, 0, }, +{a: 16, 8, -8, 8, 0, -8, 0, -8, 0, 0, 0, -8, 8, 0, -8, 0, }, +{c: 16, 0, 0, 0, 0, 0, 0, -8, 8, 0, 8, -8, -8, 0, 0, -8, }, +{7: 16, 0, 0, -8, 8, 0, -8, 8, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, -8, 0, 0, 0, 8, 0, -8, 0, 8, -8, 8, -8, 0, -8, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 8, -8, 0, 0, 0, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , , , , , x, x, }, +{9: , , x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{7: , x, x, x, , x, x, x, x, , , , , , , x, }, +{b: , , x, , x, x, x, x, x, , , x, x, , , x, }, +{d: , , , , x, x, x, x, x, , , x, , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,0101,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x0a,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_092.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_092.txt new file mode 100644 index 0000000..c0994db --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_092.txt @@ -0,0 +1,410 @@ +092 Sbox: +LUT = { +0x08,0x06,0x01,0x02,0x09,0x05,0x00,0x07,0x04,0x03,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 4, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{8: 0, 0, 0, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 0, 4, }, +{6: 0, 2, 0, 0, 4, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, }, +{9: 0, 0, 2, 2, 2, 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 2, }, +{a: 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 4, 2, 0, 2, }, +{b: 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 0, 10, 4, 4, 0, 0, 2, 8, 0, 0, 2, 0, }, +{2: 16, 8, 6, 2, 10, 4, 0, 0, 8, 4, 0, 0, 4, 0, 2, 0, }, +{4: 16, 8, 0, 4, 6, 2, 6, 0, 4, 0, 0, 0, 0, 0, 2, 0, }, +{8: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{3: 16, 4, 4, 0, 0, 4, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 4, 0, 0, 0, 2, 0, 4, }, +{6: 16, 10, 0, 0, 4, 0, 0, 4, 4, 2, 2, 6, 0, 0, 0, 0, }, +{9: 16, 0, 6, 2, 2, 0, 0, 0, 4, 2, 0, 0, 6, 0, 0, 2, }, +{a: 16, 2, 6, 0, 4, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, }, +{c: 16, 0, 0, 2, 0, 0, 0, 6, 0, 2, 2, 0, 6, 4, 0, 2, }, +{7: 16, 4, 0, 2, 0, 0, 0, 10, 0, 0, 0, 4, 4, 6, 0, 2, }, +{b: 16, 0, 6, 0, 0, 2, 0, 4, 4, 0, 2, 0, 8, 6, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, 2, 2, 4, }, +{e: 16, 0, 0, 4, 0, 6, 0, 2, 2, 0, 0, 4, 0, 2, 2, 2, }, +{f: 16, 0, 2, 4, 2, 4, 0, 0, 0, 0, 2, 6, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:54, 4:37, 6:16, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 8, -16, 0, 8, -8, 0, 0, 8, -8, }, +{2: 16, 8, 0, 8, 0, -8, 0, 0, 8, -8, 0, -8, 0, 8, -16, -8, }, +{4: 16, 0, 8, 0, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, -8, -8, }, +{8: 16, 0, 8, 0, -8, 0, 0, 0, -8, 0, -8, 8, -8, 8, -8, 0, }, +{3: 16, -8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, -8, 8, }, +{5: 16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 0, 0, -8, 0, -8, 8, }, +{6: 16, 8, 0, 0, 0, 0, 0, 8, -8, -8, -8, 0, -8, -8, 8, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 0, 8, 0, -8, -8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 8, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, -8, 8, 0, }, +{7: 16, -8, -8, -8, 0, 8, 0, 0, 8, 0, -8, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 0, -8, -8, 8, -8, 0, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 0, }, +{f: 16, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , , x, x, , , x, }, +{5: , , x, x, , x, x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, , , x, x, x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , x, x, , x, , , x, , , x, , , , x, }, +{b: , x, x, , x, , , x, x, , , , x, , , x, }, +{d: , , , x, , x, , x, , , , , , x, , x, }, +{e: , , , x, x, , , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1001,0001,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x07,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x06,0x09,0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +092 Inverse Sbox: +LUT = { +0x06,0x02,0x03,0x09,0x08,0x05,0x01,0x07,0x00,0x04,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, }, +{4: 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, }, +{8: 0, 0, 2, 2, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, }, +{5: 0, 0, 0, 2, 4, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 0, 2, 0, }, +{9: 0, 0, 4, 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, }, +{7: 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 2, 2, 0, }, +{e: 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:160, 2:72, 4:21, 6:2, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 8, 8, 0, 4, 4, 10, 0, 2, 0, 4, 0, 2, 0, 0, }, +{2: 16, 4, 6, 0, 4, 4, 2, 0, 6, 6, 0, 0, 6, 0, 0, 2, }, +{4: 16, 8, 2, 4, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 4, 4, }, +{8: 16, 0, 10, 6, 4, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 2, }, +{3: 16, 10, 4, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 6, 4, }, +{5: 16, 4, 0, 6, 4, 2, 8, 0, 0, 2, 0, 0, 0, 6, 0, 0, }, +{6: 16, 4, 0, 0, 0, 0, 2, 4, 0, 0, 6, 10, 4, 0, 2, 0, }, +{9: 16, 0, 8, 4, 2, 2, 2, 4, 4, 0, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 4, 0, 8, 2, 4, 2, 2, 4, 2, 0, 0, 4, 0, 0, }, +{c: 16, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, }, +{7: 16, 8, 0, 0, 0, 2, 0, 6, 0, 2, 0, 4, 0, 0, 4, 6, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 6, 0, 6, 4, 8, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 6, 6, 2, 2, 0, }, +{e: 16, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 4, 2, 4, 0, 2, 0, 2, 2, 0, 4, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:54, 4:37, 6:16, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{6: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, -8, -8, 0, 0, 8, 0, -8, 0, -16, 8, -8, }, +{2: 16, 0, -8, 8, 0, -8, 8, -8, 8, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 8, -8, -8, }, +{8: 16, 8, 0, 0, 0, 0, 0, 8, 8, -8, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 0, 0, 8, -8, 0, 0, 8, 8, 0, 0, -8, -8, 0, }, +{5: 16, 0, 8, 0, 0, 0, 8, -8, -8, 0, -8, 8, 0, -8, -8, 0, }, +{6: 16, 0, -8, -8, 0, 0, -8, 0, 0, 0, -8, 8, -8, 8, 8, 0, }, +{9: 16, 0, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 8, -16, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, -8, 0, 0, 8, -8, 8, 8, }, +{c: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, }, +{7: 16, -8, -8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 0, -8, 8, 0, }, +{b: 16, -8, 0, 0, -8, 8, 0, 0, 0, -8, -8, 0, 0, 8, 8, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 8, 8, 0, }, +{e: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, -8, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , , x, x, , , x, }, +{5: , x, , x, x, , x, x, x, , , x, , x, , x, }, +{6: , x, , x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , , x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , x, , x, , , , , x, , , x, , , , x, }, +{b: , x, x, , x, , , x, , , , , x, , , x, }, +{d: , , , x, x, , , x, x, , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1101,0001,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x01,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x03,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_093.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_093.txt new file mode 100644 index 0000000..a633ea2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_093.txt @@ -0,0 +1,422 @@ +093 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x0b,0x04,0x07,0x00,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 6, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, }, +{3: 0, 0, 0, 4, 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, }, +{c: 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{7: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 4, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, 2, 0, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:66, 4:24, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:3, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 8, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 16, 4, 4, 8, 0, 10, 6, 4, 0, 2, 2, 8, 0, 0, 0, 0, }, +{8: 16, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 6, 4, 0, 2, }, +{3: 16, 8, 4, 8, 0, 6, 10, 4, 2, 0, 0, 4, 0, 0, 0, 2, }, +{5: 16, 0, 0, 0, 0, 8, 8, 16, 0, 0, 0, 0, 8, 8, 0, 0, }, +{6: 16, 0, 4, 0, 2, 4, 8, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{a: 16, 2, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, 6, 4, 0, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 4, 0, 8, 0, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 0, 6, 2, 2, 0, 2, 4, 2, 0, 2, 0, 0, 0, }, +{d: 16, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 4, 6, 2, 0, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 4, 6, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:58, 4:44, 6:8, 8:11, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{2: 16, 8, -8, 0, 0, 0, 8, -8, -8, -8, 0, -16, 0, 8, 8, 0, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, -8, 8, -8, 0, 0, 0, -8, 8, }, +{8: 16, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, 0, 0, 0, 0, 8, -8, -16, 8, }, +{5: 16, -8, 0, -8, 0, -8, 0, -8, 8, 0, -8, 16, -8, 0, 8, 0, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{9: 16, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{a: 16, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, -8, }, +{c: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -16, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, -8, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, 0, -8, -8, 8, 0, -8, 0, 0, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, , x, x, x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{7: , , x, x, , x, x, , x, x, , x, x, , , x, }, +{b: , x, x, , x, , x, x, x, x, , , , , , x, }, +{d: , , x, x, x, , x, x, x, x, , , x, x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x04,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,}}, +{{0x09,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +093 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x0b,0x00,0x07,0x01,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 2, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 6, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, }, +{9: 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:66, 4:24, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:3, 4:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 2, 8, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 0, 0, 8, 0, 8, 0, 0, 2, 2, 0, 8, 0, 2, 2, 0, }, +{8: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{3: 16, 8, 4, 10, 0, 6, 8, 4, 0, 0, 2, 4, 2, 0, 0, 0, }, +{5: 16, 4, 4, 6, 0, 10, 8, 8, 0, 0, 2, 4, 2, 0, 0, 0, }, +{6: 16, 4, 0, 4, 4, 4, 16, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{9: 16, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, }, +{a: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 2, 2, 4, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 0, 4, 8, 2, 4, 0, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 0, 0, 0, 6, 0, 8, 0, 2, 6, 0, 0, 2, 4, 0, 4, }, +{d: 16, 0, 0, 0, 4, 0, 8, 0, 0, 4, 2, 0, 0, 6, 2, 6, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:58, 4:44, 6:8, 8:11, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 4, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{f: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 0, 0, -8, -8, 8, -8, 0, 0, -16, 8, 8, 0, }, +{4: 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 16, -8, -8, 0, }, +{8: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 8, 8, 8, -16, -8, -8, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 8, 8, -8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 8, 8, 0, 0, -8, 8, -16, -8, -8, 8, }, +{9: 16, -8, -8, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 8, 0, 0, 0, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{c: 16, 0, -8, 0, 0, 0, 8, -8, 8, 0, 0, -8, 0, 0, 0, -8, }, +{7: 16, 0, -8, 0, 0, 0, 8, 8, 0, -8, 0, -8, 0, 8, -8, -8, }, +{b: 16, -8, 8, 0, -8, -8, 8, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, -8, 8, -8, -8, 8, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, 0, 0, -8, 8, -8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , , x, x, x, x, x, x, x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{7: , x, x, x, , x, x, , x, x, , x, x, , , x, }, +{b: , , x, , x, x, x, , x, x, , , , , , x, }, +{d: , , x, x, x, x, x, x, x, x, , , x, x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0101,0011,1,}, +{0110,0101,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x0b,}}, +{{0x05,0x06,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_094.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_094.txt new file mode 100644 index 0000000..e4cdad7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_094.txt @@ -0,0 +1,422 @@ +094 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x0e,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{8: 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 4, 2, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 0, 2, 0, 4, 4, 0, 0, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 4, 2, }, +{e: 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:66, 4:24, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:11, 2:1, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 4, 4, 8, 2, 2, 0, 4, 0, 2, 2, 0, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 4, 8, 8, 0, 4, 6, 10, 0, 0, 2, 4, 0, 0, 0, 2, }, +{8: 16, 4, 0, 0, 2, 2, 0, 2, 2, 0, 4, 0, 2, 4, 0, 2, }, +{3: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{5: 16, 0, 0, 0, 2, 8, 8, 8, 0, 0, 0, 0, 2, 2, 2, 0, }, +{6: 16, 4, 8, 4, 0, 4, 10, 6, 0, 0, 2, 8, 0, 0, 0, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 4, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 4, 4, }, +{c: 16, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{7: 16, 16, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 4, 6, }, +{e: 16, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 4, 0, 2, 2, 0, 0, 0, 2, 0, 6, 2, 0, 4, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:58, 4:44, 6:8, 8:11, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 12, 4, 0, 0, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, 8, -8, 0, 0, }, +{2: 16, 0, -8, 8, 0, -8, 8, 0, 0, -8, -8, -16, 8, 8, 0, 0, }, +{4: 16, 0, 8, -16, 8, 0, 0, -8, 0, 8, -8, 0, -8, 0, -8, 8, }, +{8: 16, -8, 0, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{3: 16, 0, 0, 8, 0, 8, -8, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 8, -8, 0, 0, -16, 0, 0, 8, }, +{9: 16, 8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, -8, }, +{a: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, -8, -8, 8, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, -8, 0, 8, -16, -8, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 8, -8, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, -8, }, +{e: 16, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, , x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, , , x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, , x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, x, , , , x, x, , x, x, x, , , x, x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , x, x, , x, x, x, , , x, x, , , x, x, x, }, +{e: , x, x, , , x, x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x07,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x07,0x08,0x0f,}}, +{{0x01,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +094 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x0e,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{8: 0, 0, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 6, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 2, 0, 4, 6, 0, 2, 0, 0, 0, 0, 0, 0, }, +{9: 0, 2, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 4, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 4, }, +{e: 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:66, 4:24, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:11, 2:1, 4:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 16, 0, 4, 0, 4, }, +{2: 16, 0, 16, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{4: 16, 0, 4, 8, 0, 4, 0, 4, 0, 0, 2, 4, 0, 2, 2, 2, }, +{8: 16, 0, 4, 0, 2, 2, 2, 0, 4, 2, 0, 0, 6, 0, 0, 2, }, +{3: 16, 4, 0, 4, 2, 4, 8, 4, 0, 2, 2, 0, 0, 0, 2, 0, }, +{5: 16, 4, 4, 6, 0, 8, 8, 10, 0, 0, 2, 4, 0, 0, 2, 0, }, +{6: 16, 8, 4, 10, 2, 4, 8, 6, 0, 2, 0, 4, 0, 0, 0, 0, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 4, 0, 0, 2, 0, 0, 6, 2, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 6, }, +{7: 16, 4, 4, 4, 0, 0, 0, 8, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 2, 0, 0, 4, 0, 2, 0, 0, 0, 2, 4, 2, 2, 2, 4, }, +{e: 16, 2, 0, 0, 0, 0, 2, 0, 2, 4, 2, 4, 0, 4, 2, 2, }, +{f: 16, 0, 0, 2, 2, 0, 0, 2, 2, 4, 0, 4, 0, 6, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:58, 4:44, 6:8, 8:11, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{2: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 8, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 8, 8, -16, 0, -8, -8, 0, -8, 8, -8, }, +{2: 16, 0, -8, 8, 0, -8, -8, 0, 16, -8, -8, 0, -8, 8, 0, 0, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 8, 0, 8, -8, -8, 0, }, +{8: 16, -8, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 8, }, +{3: 16, 0, 0, 8, 0, 0, -8, 0, -16, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 8, 8, -16, 8, 0, -8, -8, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 8, 0, -8, 8, -8, 0, 0, 0, 0, -16, 8, -8, -8, 0, 8, }, +{9: 16, 0, -8, 8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, -8, }, +{a: 16, 0, 0, 8, 0, -8, 0, -8, 0, -8, 8, -8, 0, 0, 0, 0, }, +{c: 16, 0, -8, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, -8, 0, -8, -8, 0, 0, 0, 0, 8, 8, 0, -8, 0, 0, 0, }, +{e: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 0, 8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, , x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , , x, , , , x, x, , x, x, x, , , x, x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, x, , x, , x, , , x, x, , , x, x, x, }, +{e: , x, x, x, x, x, x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1100,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x04,0x09,0x0d,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_095.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_095.txt new file mode 100644 index 0000000..b0fc316 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_095.txt @@ -0,0 +1,422 @@ +095 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x0f,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{2: 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{8: 0, 2, 4, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{6: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{9: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{7: 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{b: 0, 2, 4, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 4, }, +{e: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 2, }, +{f: 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:66, 4:24, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:1, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 4, 4, 8, 2, 0, 2, 4, 2, 0, 2, 0, }, +{2: 16, 0, 16, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{4: 16, 4, 4, 8, 0, 8, 6, 4, 0, 0, 2, 10, 0, 0, 2, 0, }, +{8: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 0, 4, 0, 0, 4, 8, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{6: 16, 4, 4, 0, 0, 0, 4, 4, 0, 0, 2, 8, 0, 2, 2, 2, }, +{9: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{7: 16, 8, 4, 8, 0, 4, 10, 4, 0, 0, 2, 6, 0, 0, 2, 0, }, +{b: 16, 2, 4, 0, 6, 0, 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, }, +{d: 16, 0, 0, 8, 0, 0, 0, 0, 4, 2, 2, 0, 6, 6, 0, 4, }, +{e: 16, 0, 0, 8, 2, 0, 0, 0, 6, 0, 0, 0, 4, 4, 2, 6, }, +{f: 16, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:56, 4:38, 6:10, 8:13, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{7: 0, 4, 4, 4, 0, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 4, 4, 4, 0, 8, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -16, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 16, 8, -8, 8, 0, 0, 16, 0, -8, -8, -8, -8, 0, 0, 0, -8, }, +{4: 16, 0, 8, -16, 8, 0, 0, -8, -8, 8, -8, 0, 0, 8, -8, 0, }, +{8: 16, 0, -8, 8, 0, -8, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -16, -8, 8, 0, -8, 0, 8, 0, -8, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, 8, -8, 8, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, -16, 0, 0, -8, 0, 8, 8, -8, }, +{b: 16, 0, 0, 8, 0, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 8, 0, -8, 8, 8, 0, -8, 0, -8, 0, 0, }, +{e: 16, 0, 8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 8, -8, -8, -8, }, +{f: 16, 0, 0, -8, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , , x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, , x, x, , x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , x, , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, , , x, , x, x, x, x, , x, x, x, x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , x, , x, , , , x, x, x, x, x, , x, x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1001,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x09,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x05,0x09,0x0c,}}, +{{0x09,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0e,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +095 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x0f,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{2: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 2, 0, 4, 4, 0, 0, 2, 0, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 4, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 4, 2, }, +{e: 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 4, 2, 0, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:66, 4:24, 6:2, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:10, 2:1, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 4, 0, 4, 2, 2, 0, 8, 2, 0, 0, 0, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 0, 0, 8, 0, 16, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 4, 0, 8, 0, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{5: 16, 4, 8, 6, 0, 4, 8, 4, 0, 0, 2, 10, 0, 0, 0, 2, }, +{6: 16, 8, 0, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{9: 16, 2, 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 2, 4, 6, 0, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 16, 4, 8, 10, 0, 4, 4, 8, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 6, 4, 0, }, +{d: 16, 0, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 6, 4, 2, }, +{e: 16, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, }, +{f: 16, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, 0, 0, 4, 6, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:56, 4:38, 6:10, 8:13, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, -8, -8, 0, 0, 8, -8, }, +{2: 16, 8, -8, 8, 0, 0, 0, 0, 8, -8, -8, 8, -16, 0, 0, -8, }, +{4: 16, 0, 0, -8, 0, 0, -8, -8, 0, 0, 8, 8, 16, -8, -8, -8, }, +{8: 16, 0, -8, 8, -8, -8, 0, 0, 8, 0, 0, -8, 0, 8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, 8, }, +{5: 16, 0, 8, -16, 8, 8, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 8, -16, 0, 0, 8, }, +{9: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, 8, 0, 0, -8, 0, -16, 0, 8, 0, -8, }, +{b: 16, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, }, +{d: 16, 0, -8, -8, -8, -8, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{f: 16, 0, 8, -8, -8, -8, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , , x, x, x, x, , , x, x, x, x, x, , x, x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{7: , x, x, , , x, , x, x, x, x, , x, x, x, x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, , x, x, , , x, x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0101,1,}, +{0111,0111,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x06,}, {0x04,0x0b,0x0f,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_096.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_096.txt new file mode 100644 index 0000000..eb08271 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_096.txt @@ -0,0 +1,410 @@ +096 Sbox: +LUT = { +0x0f,0x00,0x01,0x03,0x02,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, }, +{2: 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 4, 0, }, +{4: 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{5: 0, 0, 4, 0, 0, 2, 4, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 4, }, +{9: 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, }, +{b: 0, 0, 4, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 6, 0, 0, }, +{e: 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, }, +{f: 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 6, 2, 2, }, +{2: 16, 0, 6, 2, 0, 2, 6, 0, 4, 0, 0, 0, 8, 0, 4, 0, }, +{4: 16, 2, 0, 6, 0, 6, 0, 0, 4, 4, 2, 6, 0, 6, 4, 0, }, +{8: 16, 2, 0, 0, 4, 0, 8, 0, 2, 0, 0, 2, 4, 4, 4, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{5: 16, 0, 4, 0, 8, 2, 4, 2, 2, 4, 2, 0, 0, 4, 0, 0, }, +{6: 16, 2, 0, 0, 0, 2, 0, 6, 6, 2, 0, 2, 0, 0, 0, 4, }, +{9: 16, 0, 4, 6, 0, 0, 0, 6, 6, 2, 0, 0, 4, 4, 2, 6, }, +{a: 16, 0, 0, 6, 0, 2, 4, 0, 0, 4, 2, 0, 6, 0, 8, 0, }, +{c: 16, 4, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 6, 0, 2, }, +{7: 16, 2, 0, 4, 2, 4, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, }, +{b: 16, 0, 8, 2, 6, 0, 0, 0, 4, 4, 0, 2, 6, 0, 0, 0, }, +{d: 16, 4, 2, 4, 6, 0, 6, 0, 6, 0, 4, 0, 2, 6, 0, 0, }, +{e: 16, 2, 6, 6, 4, 0, 0, 0, 0, 8, 0, 2, 0, 0, 4, 0, }, +{f: 16, 0, 0, 0, 0, 2, 0, 4, 6, 0, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:52, 4:37, 6:26, 8:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{7: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 8, 0, -8, -8, 0, -8, }, +{2: 16, 0, -8, 0, 0, 0, -8, -8, 0, 8, 0, 8, 0, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 0, 0, -8, 8, -8, 0, -8, }, +{8: 16, -8, 0, 8, -8, 8, 0, 8, 0, 0, -8, 0, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 8, }, +{6: 16, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, 8, }, +{9: 16, 0, 0, 0, -8, -8, -8, 8, 8, 0, -8, -8, 8, 0, -8, 8, }, +{a: 16, 0, 0, 0, 0, 0, 0, -16, -8, 8, -8, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, 8, -8, }, +{b: 16, 8, -8, 8, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{d: 16, -8, 8, 0, -8, -8, 8, -8, 8, -8, 0, 8, 0, 0, 0, -8, }, +{e: 16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, -8, -16, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, , , x, , x, x, x, , , x, x, x, x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , x, , x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, x, x, x, x, , x, x, x, , x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,1010,1,}, +{1111,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x05,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x0f,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x08,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +096 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x08,0x0c,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x00, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, }, +{2: 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, 2, 0, }, +{4: 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 0, }, +{3: 0, 0, 2, 2, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 4, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 4, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, }, +{e: 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 2, 0, 2, 0, 0, 4, 2, 0, 4, 2, 0, }, +{2: 16, 2, 6, 0, 0, 0, 4, 0, 4, 0, 0, 0, 8, 2, 6, 0, }, +{4: 16, 0, 2, 6, 0, 4, 0, 0, 6, 6, 0, 4, 2, 4, 6, 0, }, +{8: 16, 2, 0, 0, 4, 0, 8, 0, 0, 0, 0, 2, 6, 6, 4, 0, }, +{3: 16, 0, 2, 6, 0, 4, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, }, +{5: 16, 0, 6, 0, 8, 2, 4, 0, 0, 4, 2, 0, 0, 6, 0, 0, }, +{6: 16, 2, 0, 0, 0, 0, 2, 6, 6, 0, 2, 2, 0, 0, 0, 4, }, +{9: 16, 0, 4, 4, 2, 0, 2, 6, 6, 0, 0, 0, 4, 6, 0, 6, }, +{a: 16, 0, 0, 4, 0, 2, 4, 2, 2, 4, 2, 0, 4, 0, 8, 0, }, +{c: 16, 4, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, 0, 4, 0, 2, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 2, 0, 6, 2, 0, 0, }, +{d: 16, 6, 0, 6, 4, 2, 4, 0, 4, 0, 6, 2, 0, 6, 0, 0, }, +{e: 16, 2, 4, 4, 4, 0, 0, 0, 2, 8, 0, 2, 0, 0, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 4, 6, 0, 2, 0, 0, 0, 0, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:52, 4:37, 6:26, 8:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{3: 0, 8, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, -8, }, +{2: 16, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, 8, -8, 8, 0, -8, }, +{4: 16, 8, 0, 0, 0, 0, -8, -8, 8, 8, -8, -8, 8, 0, -8, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, 8, 0, 0, 0, -16, }, +{3: 16, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{6: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 8, -8, -8, 0, 0, 0, -8, 8, }, +{a: 16, 0, -8, 8, -8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 8, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, 8, 0, 8, -8, 0, 8, -8, 0, -8, 0, 0, -8, 0, 0, -8, }, +{d: 16, -8, 8, -8, 0, 0, 0, -8, 0, -8, 8, 0, 8, -8, 8, -8, }, +{e: 16, 0, -8, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, 8, -8, -8, }, +{f: 16, 0, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, -8, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, , , , , x, , , , x, x, , , , x, }, +{b: , x, x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , x, x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, , x, , x, , x, x, x, , x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,0101,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x02,0x05,0x07,}}, +{{0x02,0x0c,}, {0x0d,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x04,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_097.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_097.txt new file mode 100644 index 0000000..e72aeb6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_097.txt @@ -0,0 +1,410 @@ +097 Sbox: +LUT = { +0x08,0x0d,0x01,0x02,0x03,0x05,0x00,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 2, 0, 4, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{8: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{3: 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 4, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 0, }, +{e: 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 6, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{2: 16, 0, 6, 0, 0, 2, 4, 0, 8, 0, 4, 8, 4, 0, 10, 2, }, +{4: 16, 10, 0, 4, 4, 0, 6, 0, 4, 0, 0, 0, 2, 0, 0, 2, }, +{8: 16, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{3: 16, 0, 0, 2, 2, 4, 6, 4, 0, 2, 2, 0, 0, 0, 0, 2, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 0, 0, 0, 4, 0, 2, 2, 0, }, +{6: 16, 0, 2, 0, 2, 8, 4, 4, 4, 4, 0, 2, 0, 2, 0, 0, }, +{9: 16, 6, 4, 0, 6, 4, 2, 0, 6, 6, 0, 0, 4, 0, 0, 2, }, +{a: 16, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 16, 0, 8, 4, 2, 2, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, }, +{d: 16, 4, 0, 0, 4, 0, 0, 0, 8, 2, 2, 4, 2, 2, 4, 0, }, +{e: 16, 0, 10, 4, 0, 0, 0, 6, 2, 0, 4, 0, 0, 2, 4, 0, }, +{f: 16, 0, 0, 0, 2, 4, 0, 0, 10, 4, 0, 4, 0, 0, 6, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:62, 4:40, 6:11, 8:7, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, }, +{2: 16, 0, -8, 8, 0, -8, 0, 0, 8, -8, 8, -8, 0, 8, -16, 0, }, +{4: 16, 0, 8, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, -8, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, -16, 8, -8, 0, 0, 0, 8, -8, 8, -8, 0, }, +{6: 16, 8, -8, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, -8, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 8, 0, 0, -8, -8, 0, 0, -8, 8, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 8, -8, 0, 0, -8, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, -8, -8, 0, -8, 8, 8, 0, 0, 0, 8, -8, }, +{e: 16, 8, 0, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, -8, -8, 0, 0, 8, 0, 8, -8, -8, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, , x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , , x, x, x, , x, x, , x, , x, }, +{b: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{d: , , , x, , x, , x, , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0101,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x01,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x03,0x08,0x0b,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x03,0x05,0x06,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +097 Inverse Sbox: +LUT = { +0x06,0x02,0x03,0x04,0x08,0x05,0x0d,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, }, +{8: 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, }, +{5: 0, 2, 0, 2, 0, 2, 6, 0, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 4, 0, 2, 0, }, +{9: 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 4, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, 4, 2, }, +{f: 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 10, 0, 0, 4, 0, 6, 2, 0, 2, 0, 4, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 8, 2, 4, 2, 4, 4, 8, 0, 10, 0, }, +{4: 16, 4, 0, 4, 2, 2, 8, 0, 0, 0, 2, 2, 4, 0, 4, 0, }, +{8: 16, 0, 0, 4, 2, 2, 0, 2, 6, 0, 0, 0, 2, 4, 0, 2, }, +{3: 16, 2, 2, 0, 2, 4, 4, 8, 4, 0, 0, 0, 2, 0, 0, 4, }, +{5: 16, 6, 4, 6, 0, 6, 6, 4, 2, 2, 0, 4, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 10, 4, 0, 2, 0, 0, 4, 0, 6, 0, }, +{9: 16, 0, 8, 4, 2, 0, 0, 4, 6, 0, 0, 0, 4, 8, 2, 10, }, +{a: 16, 2, 0, 0, 0, 2, 0, 4, 6, 2, 2, 0, 0, 2, 0, 4, }, +{c: 16, 0, 4, 0, 2, 2, 0, 0, 0, 2, 4, 2, 2, 2, 4, 0, }, +{7: 16, 2, 8, 0, 0, 0, 4, 2, 0, 0, 2, 4, 2, 4, 0, 4, }, +{b: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 2, 2, 4, 2, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 10, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 4, 4, 6, }, +{f: 16, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:62, 4:40, 6:11, 8:7, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 0, 0, 0, 0, -8, 8, -8, 0, }, +{4: 16, 8, 0, -8, 0, 8, -8, 0, -8, 0, 0, 0, 8, 0, -8, -8, }, +{8: 16, 0, 0, 0, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, -8, 0, }, +{3: 16, -8, -8, 8, 0, 8, 0, 0, 0, 0, 8, 0, -8, -8, -8, 0, }, +{5: 16, -8, 8, 0, 8, -8, 0, -8, -8, 8, -8, 0, 0, 0, -8, 8, }, +{6: 16, 0, -8, 0, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, 0, 8, 8, -8, 0, -8, 0, 8, -16, 0, }, +{a: 16, 0, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, -8, 8, 8, }, +{c: 16, 0, 0, 0, -8, 8, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 0, 8, 0, 8, 0, 0, 0, -8, -8, 0, 8, 0, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, , x, x, , x, x, x, , x, x, , x, , x, }, +{6: , , , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , , x, , , x, , x, , x, x, , x, , x, }, +{b: , x, x, , x, , , x, , , , , x, , , x, }, +{d: , x, , x, x, , x, x, x, , x, , , , , x, }, +{e: , , , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0010,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x02,0x09,0x0b,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x0f,}}, +{{0x09,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_098.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_098.txt new file mode 100644 index 0000000..424b528 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_098.txt @@ -0,0 +1,410 @@ +098 Sbox: +LUT = { +0x04,0x00,0x01,0x0e,0x02,0x05,0x06,0x07,0x03,0x09,0x08,0x0b,0x0c,0x0d,0x0a,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, }, +{4: 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{3: 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{5: 0, 4, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, }, +{6: 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 2, }, +{a: 0, 0, 2, 0, 2, 0, 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, }, +{c: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, }, +{7: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 4, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 6, 2, }, +{f: 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 2, 2, 0, 0, 6, 0, 2, 4, 0, 0, 2, }, +{2: 16, 0, 6, 6, 4, 0, 2, 6, 0, 4, 4, 0, 2, 0, 6, 0, }, +{4: 16, 0, 6, 4, 0, 0, 2, 6, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 16, 4, 4, 0, 8, 0, 2, 0, 4, 4, 2, 2, 0, 0, 2, 0, }, +{3: 16, 4, 0, 0, 6, 4, 2, 0, 8, 6, 0, 2, 0, 0, 0, 0, }, +{5: 16, 4, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 6, 4, }, +{6: 16, 0, 6, 6, 0, 2, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, 10, 0, 2, 4, 6, 0, 0, 0, 4, 4, 2, }, +{a: 16, 4, 6, 0, 6, 4, 0, 0, 4, 6, 2, 2, 6, 0, 0, 0, }, +{c: 16, 4, 4, 0, 2, 0, 0, 0, 0, 0, 8, 0, 2, 6, 6, 0, }, +{7: 16, 4, 0, 2, 0, 4, 2, 2, 0, 0, 4, 2, 0, 8, 4, 0, }, +{b: 16, 16, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 16, 4, 4, 0, 0, 6, 2, 0, 0, 2, 4, 0, 0, 6, 6, 6, }, +{f: 16, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:54, 4:38, 6:23, 8:4, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 8, 0, -8, -8, 0, 0, -8, 0, }, +{8: 16, 0, 8, 0, -8, 0, 0, 8, -8, -8, -8, 0, 0, 8, -8, 0, }, +{3: 16, -8, 0, 8, 8, 0, 0, 0, -16, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 8, -8, 0, 8, -8, 0, 0, 0, -8, 0, 0, -8, }, +{6: 16, 0, -8, 0, 8, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 8, -8, 0, 8, }, +{a: 16, 8, -8, 8, -8, 0, 8, -8, -8, 0, -8, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, 0, -8, 0, -8, 0, -8, 0, 8, 0, -8, 0, 8, -8, }, +{7: 16, 0, 0, -8, 8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 8, }, +{b: 16, -8, 0, 0, -16, 8, 8, 0, 8, 0, 0, 8, -8, -8, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 0, -8, 8, 8, 8, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, x, x, , x, , x, x, x, , , x, x, }, +{9: , , x, x, x, x, , x, x, , x, , x, x, x, x, }, +{a: , , x, x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , x, x, , , x, , x, }, +{7: , x, , x, x, x, , x, , x, x, x, , , x, x, }, +{b: , , x, , , , , x, , , x, , x, , x, x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , , x, x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1000,1011,1,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x0b,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +098 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x0a,0x09,0x0e,0x0b,0x0c,0x0d,0x03,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, 2, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, }, +{5: 0, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, }, +{6: 0, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 2, 4, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 4, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 6, 0, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 16, 0, 4, 0, }, +{2: 16, 0, 6, 6, 4, 0, 2, 6, 0, 6, 4, 0, 0, 0, 4, 2, }, +{4: 16, 2, 6, 4, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 16, 0, 4, 0, 8, 6, 2, 0, 0, 6, 2, 0, 4, 0, 0, 0, }, +{3: 16, 2, 0, 0, 0, 4, 0, 2, 10, 4, 0, 4, 0, 0, 6, 0, }, +{5: 16, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, }, +{6: 16, 0, 6, 6, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 0, 0, 2, 4, 8, 0, 2, 4, 4, 0, 0, 4, 2, 0, 2, }, +{a: 16, 6, 4, 0, 4, 6, 0, 0, 6, 6, 0, 0, 4, 0, 2, 2, }, +{c: 16, 0, 4, 0, 2, 0, 0, 0, 0, 2, 8, 4, 4, 2, 4, 2, }, +{7: 16, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, }, +{b: 16, 4, 2, 0, 0, 0, 0, 2, 0, 6, 2, 0, 4, 2, 0, 2, }, +{d: 16, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 8, 4, 2, 6, 2, }, +{e: 16, 0, 6, 0, 2, 0, 6, 0, 4, 0, 6, 4, 4, 2, 6, 0, }, +{f: 16, 2, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 4, 2, 6, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:54, 4:38, 6:23, 8:4, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 8, 4, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{f: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, -8, -16, 0, 8, 0, -8, 0, 0, 8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, 0, 0, -8, -8, 0, -8, 0, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 8, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 8, -8, 8, 0, -8, -8, 0, -8, 8, -8, 0, 0, 0, }, +{3: 16, -8, -8, 0, 8, 0, -8, 8, -8, -8, 0, 0, 8, 0, 0, 0, }, +{5: 16, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, }, +{6: 16, 0, 0, -8, 8, -8, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, 8, -8, -8, 0, 0, -8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, 0, -8, 8, 0, -8, 8, -8, 0, 8, }, +{c: 16, 0, 0, -8, -8, 8, 8, 0, -8, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, -8, 0, 0, -16, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 16, 8, 0, -8, -8, -8, 0, 0, -8, 0, 8, 8, 0, 8, -8, -8, }, +{f: 16, -8, 0, 0, -8, 0, -8, 0, 8, 8, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, , x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, , , x, x, , x, , x, x, , x, , x, x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1000,1101,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x01,0x04,0x05,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x02,0x09,0x0b,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_099.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_099.txt new file mode 100644 index 0000000..f6ca028 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_099.txt @@ -0,0 +1,410 @@ +099 Sbox: +LUT = { +0x08,0x00,0x01,0x0f,0x02,0x05,0x03,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 2, 6, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{4: 0, 0, 2, 4, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 4, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 0, 4, 0, 2, 2, 0, 0, 2, }, +{9: 0, 2, 0, 2, 0, 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 6, 0, 2, 0, }, +{d: 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:6, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 0, 0, 8, 0, 0, 0, 6, 0, 2, 6, 0, }, +{2: 16, 2, 6, 0, 0, 0, 4, 0, 6, 0, 4, 4, 6, 0, 6, 2, }, +{4: 16, 0, 2, 4, 4, 8, 2, 0, 0, 2, 0, 4, 4, 2, 0, 0, }, +{8: 16, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 16, 2, 0, 4, 0, 4, 2, 2, 0, 2, 0, 6, 0, 0, 0, 2, }, +{5: 16, 0, 6, 0, 0, 0, 8, 2, 6, 0, 4, 4, 0, 2, 0, 0, }, +{6: 16, 8, 0, 0, 0, 2, 0, 4, 0, 4, 0, 6, 6, 0, 0, 2, }, +{9: 16, 2, 4, 2, 0, 0, 4, 0, 8, 2, 4, 0, 4, 0, 0, 2, }, +{a: 16, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{7: 16, 4, 6, 6, 0, 6, 4, 4, 0, 0, 0, 6, 0, 2, 0, 2, }, +{b: 16, 4, 4, 2, 6, 6, 0, 0, 4, 6, 0, 0, 6, 0, 2, 0, }, +{d: 16, 4, 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 6, 2, 0, 0, }, +{e: 16, 0, 6, 0, 6, 0, 0, 4, 0, 0, 4, 2, 0, 2, 8, 0, }, +{f: 16, 0, 0, 0, 8, 4, 0, 4, 2, 2, 2, 0, 4, 0, 4, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:102, 2:56, 4:37, 6:22, 8:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{a: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{b: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, -16, }, +{2: 16, 0, -8, 8, 0, -8, 0, 0, 8, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 8, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, -8, -8, -8, }, +{8: 16, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, 0, 8, }, +{6: 16, 0, -16, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, 8, }, +{9: 16, -8, 8, 0, 0, -8, 0, 0, 0, 8, -8, -8, 0, 0, -8, 8, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{c: 16, 0, 8, -8, -8, 0, -8, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 8, 8, 8, 0, 0, -8, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 8, -8, 8, 0, 0, 0, -8, }, +{d: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, -8, }, +{e: 16, 8, -8, -8, 0, -8, 0, 8, 0, -8, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -8, 0, -8, 0, -8, 0, 8, 0, 8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , x, x, , x, x, x, , x, x, x, x, }, +{b: , , x, , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0010,0110,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x01,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x0f,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +099 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x08,0x05,0x0f,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, }, +{8: 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, 0, 0, 4, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 4, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, }, +{d: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 4, }, +{f: 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:6, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 0, 2, 2, 0, 8, 2, 0, 0, 4, 4, 4, 0, 0, }, +{2: 16, 0, 6, 2, 0, 0, 6, 0, 4, 2, 4, 6, 4, 0, 6, 0, }, +{4: 16, 2, 0, 4, 2, 4, 0, 0, 2, 0, 2, 6, 2, 0, 0, 0, }, +{8: 16, 4, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 6, 2, 6, 8, }, +{3: 16, 0, 0, 8, 0, 4, 0, 2, 0, 2, 0, 6, 6, 0, 0, 4, }, +{5: 16, 0, 4, 2, 0, 2, 8, 0, 4, 2, 4, 4, 0, 2, 0, 0, }, +{6: 16, 8, 0, 0, 0, 2, 2, 4, 0, 2, 2, 4, 0, 0, 4, 4, }, +{9: 16, 0, 6, 0, 2, 0, 6, 0, 8, 0, 4, 0, 4, 0, 0, 2, }, +{a: 16, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 6, 4, 0, 2, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{7: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 16, 0, 6, 4, 2, 0, 0, 6, 4, 2, 0, 0, 6, 6, 0, 4, }, +{d: 16, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 16, 6, 6, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 8, 4, }, +{f: 16, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:102, 2:56, 4:37, 6:22, 8:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 0, 0, -8, 8, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 0, 0, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 8, -8, 0, 0, 0, -8, -8, 0, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, 0, -16, }, +{3: 16, -8, -16, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, -8, 8, }, +{6: 16, 8, -8, -8, 0, -8, -8, 0, -8, 0, 0, 8, 0, 0, 0, 8, }, +{9: 16, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, -8, -8, 8, -8, 8, }, +{a: 16, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, -8, -8, -8, 8, 0, 0, 8, -8, -8, 0, 0, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 8, 0, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, -8, 0, 0, 8, 0, 8, 8, 0, -8, 0, -8, -8, }, +{f: 16, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{3: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{7: , , , x, , , x, x, x, x, x, , x, x, x, x, }, +{b: , x, , , x, x, , x, , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, , x, x, x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0010,0011,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x05,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x03,0x09,0x0a,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x02,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_100.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_100.txt new file mode 100644 index 0000000..2e7e4e9 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_100.txt @@ -0,0 +1,410 @@ +100 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x0f,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 4, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 2, 0, 6, 2, 2, 0, 0, 0, 0, 2, 0, 2, }, +{6: 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 2, 0, 0, 0, 2, 0, 0, 6, 0, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 4, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 2, 2, }, +{e: 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:3, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 4, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, }, +{2: 16, 6, 8, 0, 0, 4, 6, 0, 2, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 0, 0, 4, 2, 2, 0, 0, 0, 6, 0, 2, 2, 2, 4, 0, }, +{8: 16, 0, 0, 2, 4, 2, 4, 2, 2, 0, 0, 2, 0, 4, 0, 2, }, +{3: 16, 4, 4, 2, 2, 10, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, }, +{5: 16, 0, 4, 0, 6, 0, 6, 2, 2, 4, 0, 4, 0, 6, 0, 6, }, +{6: 16, 2, 0, 2, 0, 0, 0, 6, 4, 2, 0, 2, 0, 0, 2, 4, }, +{9: 16, 0, 2, 2, 0, 0, 0, 4, 6, 2, 0, 0, 2, 0, 2, 4, }, +{a: 16, 6, 2, 4, 0, 0, 6, 0, 0, 6, 0, 2, 6, 0, 4, 4, }, +{c: 16, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 2, 2, 6, }, +{7: 16, 0, 4, 0, 2, 0, 6, 2, 0, 0, 4, 8, 6, 0, 0, 0, }, +{b: 16, 4, 0, 2, 2, 0, 2, 0, 2, 4, 4, 4, 8, 0, 0, 0, }, +{d: 16, 0, 2, 0, 4, 0, 4, 2, 2, 0, 2, 0, 0, 4, 2, 2, }, +{e: 16, 2, 2, 4, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 4, 0, }, +{f: 16, 0, 0, 2, 0, 6, 4, 4, 4, 6, 6, 0, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:54, 4:41, 6:22, 8:4, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{6: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -16, 0, 0, 0, 0, 8, 0, -8, 0, 0, -8, }, +{2: 16, -8, 0, 8, 8, -8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, 0, -8, -8, 0, 0, -8, -8, 0, }, +{3: 16, 0, 8, 0, 0, 8, -8, 0, -8, 0, 8, -8, -8, -8, 0, 0, }, +{5: 16, -8, 8, -8, 0, -8, 8, 0, 0, 0, -8, 8, -8, 0, -8, 8, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{9: 16, 8, -8, 0, 0, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, 0, -8, 8, -8, -8, 8, -8, -8, 0, 0, 8, 0, }, +{c: 16, -8, -8, 0, -8, 8, -8, -8, 0, 0, 8, 8, 0, 0, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 0, -8, -8, -8, 0, -8, 8, 8, 0, }, +{b: 16, -8, 0, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 8, 0, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 8, -8, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, -8, 8, 0, 0, 0, 8, 8, -8, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, , x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, x, , x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , x, , x, , x, x, , x, , x, x, x, x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , x, x, , x, x, , x, x, , x, x, x, , x, x, }, +{e: , x, , , x, x, , x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0001,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x04,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x03,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x01,0x08,}, {0x03,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +100 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x08,0x0a,0x06,0x07,0x0f,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{8: 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, }, +{5: 0, 2, 2, 0, 0, 0, 6, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 2, 0, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 6, 0, 0, 0, 0, 2, 2, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 4, 0, 0, 0, }, +{d: 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 6, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:3, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 6, 0, 0, 4, 0, 2, 0, 6, 0, 0, 4, 0, 2, 0, }, +{2: 16, 4, 8, 0, 0, 4, 4, 0, 2, 2, 0, 4, 0, 2, 2, 0, }, +{4: 16, 0, 0, 4, 2, 2, 0, 2, 2, 4, 0, 0, 2, 0, 4, 2, }, +{8: 16, 0, 0, 2, 4, 2, 6, 0, 0, 0, 0, 2, 2, 4, 2, 0, }, +{3: 16, 4, 4, 2, 2, 10, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, }, +{5: 16, 2, 6, 0, 4, 0, 6, 0, 0, 6, 0, 6, 2, 4, 0, 4, }, +{6: 16, 2, 0, 0, 2, 0, 2, 6, 4, 0, 0, 2, 0, 2, 0, 4, }, +{9: 16, 0, 2, 0, 2, 0, 2, 4, 6, 0, 0, 0, 2, 2, 0, 4, }, +{a: 16, 4, 0, 6, 0, 0, 4, 2, 2, 6, 0, 0, 4, 0, 6, 6, }, +{c: 16, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 2, 2, 6, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 4, 0, 2, 0, 0, 0, 0, 2, 6, 4, 6, 8, 0, 0, 0, }, +{d: 16, 2, 2, 2, 4, 0, 6, 0, 0, 0, 2, 0, 0, 4, 2, 0, }, +{e: 16, 2, 0, 4, 0, 0, 0, 2, 2, 4, 2, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 6, 6, 4, 4, 4, 6, 0, 0, 2, 0, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:54, 4:41, 6:22, 8:4, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{2: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{4: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{b: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, -8, 8, 8, -8, -8, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 0, 0, 8, 0, -16, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, 8, 0, 0, -8, -8, }, +{3: 16, 8, 0, 0, 0, 8, 0, -8, 0, -8, 8, -8, -8, 0, -8, 0, }, +{5: 16, -8, 0, 0, 8, -8, 8, -8, -8, 8, -8, 0, -8, 8, 0, 0, }, +{6: 16, -8, 8, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 8, -8, -8, 8, -8, 0, 0, 0, }, +{a: 16, 8, -8, 0, -8, -8, 0, 0, 0, 8, -8, -8, 8, -8, 0, 8, }, +{c: 16, -8, -8, -8, 0, 8, 0, 0, -8, -8, 8, 0, 8, 0, 0, 0, }, +{7: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, -8, 8, -8, -8, 0, 0, -8, -8, 0, 8, 8, 0, }, +{d: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, -8, 0, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, , x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , , , , x, x, , x, x, , x, x, , x, x, x, }, +{d: , , x, x, , x, , x, x, , x, x, x, , x, x, }, +{e: , x, x, x, , x, , x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0010,1,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x05,0x08,0x0d,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x08,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x0b,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x02,0x05,0x07,}}, +{{0x05,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_101.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_101.txt new file mode 100644 index 0000000..a36a7f2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_101.txt @@ -0,0 +1,410 @@ +101 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 6, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, }, +{8: 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 2, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 4, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{7: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 4, 6, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 4, 0, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, }, +{e: 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:6, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 10, 0, 4, 4, 0, 0, 8, 4, 0, 0, 8, 2, 2, 0, }, +{2: 16, 6, 6, 4, 2, 6, 6, 4, 0, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 2, 4, 4, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, }, +{8: 16, 4, 0, 2, 4, 2, 0, 2, 6, 0, 0, 2, 0, 0, 0, 2, }, +{3: 16, 6, 4, 2, 0, 8, 0, 0, 0, 2, 4, 0, 0, 0, 0, 6, }, +{5: 16, 0, 4, 0, 2, 2, 4, 2, 2, 2, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 8, 6, 0, 0, 0, 4, 6, 2, 0, 2, 4, 0, 0, 0, }, +{9: 16, 4, 0, 2, 4, 0, 0, 2, 4, 2, 0, 0, 2, 2, 2, 0, }, +{a: 16, 6, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 10, 2, 4, 0, }, +{c: 16, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 2, 2, 6, }, +{7: 16, 0, 8, 0, 2, 0, 10, 2, 4, 0, 4, 8, 6, 0, 4, 0, }, +{b: 16, 4, 0, 2, 2, 0, 2, 0, 2, 4, 4, 4, 8, 0, 0, 0, }, +{d: 16, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 4, 2, 4, 2, }, +{e: 16, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 2, 6, 0, 0, 0, 0, 6, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:59, 4:38, 6:15, 8:7, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -16, -8, 8, 0, 0, 8, -8, 0, 0, 0, -8, }, +{2: 16, 0, 0, 8, 8, -8, 8, -8, 0, -8, 8, 0, -8, 0, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, 0, -8, -8, 0, 0, -8, -8, 0, }, +{3: 16, 0, 0, 0, 0, 8, -8, -8, -8, 0, 8, -8, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, 0, 8, -8, 0, 0, 8, -8, -8, -8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, -8, -8, 0, 8, 0, -8, 0, 8, 0, 0, 0, }, +{a: 16, -8, 0, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, -8, -8, -8, 0, 8, 0, 0, -8, -8, 8, 0, 8, 0, 0, 0, }, +{7: 16, -8, -8, 0, 0, 8, 0, 0, 0, 0, -16, 8, -8, 8, 8, -8, }, +{b: 16, 0, 8, 0, -8, 8, -8, -8, 0, 0, -8, 0, -8, 8, 0, 0, }, +{d: 16, 8, -8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , , , , x, x, x, , , x, , , x, , , x, }, +{d: , x, x, x, , x, x, , , x, , , , x, , x, }, +{e: , x, , x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0001,1,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x03,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,}}, +{{0x05,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x01,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +101 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0a,0x06,0x07,0x03,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{8: 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, }, +{9: 0, 4, 0, 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 4, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 6, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:6, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 2, 4, 6, 0, 0, 4, 6, 0, 0, 4, 0, 2, 0, }, +{2: 16, 10, 6, 4, 0, 4, 4, 8, 0, 0, 0, 8, 0, 2, 2, 0, }, +{4: 16, 0, 4, 4, 2, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, 2, }, +{8: 16, 4, 2, 2, 4, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 16, 4, 6, 0, 2, 8, 2, 0, 0, 0, 4, 0, 0, 0, 0, 6, }, +{5: 16, 0, 6, 0, 0, 0, 4, 0, 0, 4, 0, 10, 2, 4, 2, 0, }, +{6: 16, 0, 4, 4, 2, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, }, +{9: 16, 8, 0, 0, 6, 0, 2, 6, 4, 0, 0, 4, 2, 0, 0, 0, }, +{a: 16, 4, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 2, 2, 6, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 8, 0, 2, 0, 0, 0, 4, 2, 10, 4, 6, 8, 4, 0, 0, }, +{d: 16, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 2, 0, 0, 0, 0, 2, 0, 2, 4, 2, 4, 0, 4, 2, 2, }, +{f: 16, 0, 0, 2, 2, 6, 0, 0, 0, 0, 6, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:59, 4:38, 6:15, 8:7, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{2: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -8, -8, 0, -8, 8, 8, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 8, -16, 0, 0, 8, -8, 8, 0, -8, 0, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, 0, -8, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 8, 0, -8, -8, -8, 8, 0, -8, 0, -8, 8, }, +{5: 16, 0, -8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, 8, 0, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, -8, -8, 8, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, 0, -8, -8, 8, 0, 0, -8, 0, -8, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, -8, -8, 0, -8, 8, -8, -8, 0, 0, 8, 8, 0, 0, 0, 0, }, +{7: 16, 8, 0, -8, 0, 8, 0, 0, -8, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, -8, -8, 0, 0, 8, 0, 0, 0, 0, -16, -8, 8, 8, 8, -8, }, +{d: 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, }, +{e: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , , x, , x, x, x, , , x, , , , x, , x, }, +{e: , x, x, , x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0010,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x0a,}}, +{{0x03,0x04,}, {0x0a,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_102.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_102.txt new file mode 100644 index 0000000..f5efb99 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_102.txt @@ -0,0 +1,410 @@ +102 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0d,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x05,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 0, 4, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 6, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 0, 2, 0, 0, 0, 2, 6, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{6: 0, 0, 2, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 2, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 2, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, 0, 0, 2, 2, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 2, 2, }, +{f: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 2, 8, 4, 0, 4, 0, 8, 0, 4, 0, 0, 10, 2, 0, }, +{2: 16, 0, 8, 0, 6, 2, 6, 0, 0, 4, 0, 4, 0, 0, 2, 0, }, +{4: 16, 6, 0, 4, 2, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{8: 16, 4, 4, 0, 6, 6, 0, 2, 6, 4, 0, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 2, 4, 8, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 0, 4, 0, 0, 2, 2, }, +{6: 16, 0, 2, 2, 0, 4, 6, 4, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 16, 6, 2, 2, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 0, }, +{a: 16, 2, 4, 0, 6, 0, 2, 0, 0, 6, 0, 0, 2, 2, 0, 0, }, +{c: 16, 4, 0, 2, 0, 0, 2, 0, 0, 0, 8, 4, 4, 4, 2, 2, }, +{7: 16, 0, 4, 0, 0, 0, 6, 2, 0, 0, 6, 8, 4, 0, 0, 2, }, +{b: 16, 0, 0, 0, 6, 4, 0, 0, 2, 2, 4, 4, 10, 0, 0, 0, }, +{d: 16, 4, 0, 0, 0, 0, 0, 2, 2, 2, 6, 2, 0, 4, 2, 0, }, +{e: 16, 0, 2, 4, 0, 0, 0, 2, 6, 0, 2, 0, 0, 4, 2, 2, }, +{f: 16, 0, 0, 4, 2, 2, 0, 0, 4, 0, 0, 2, 0, 6, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:54, 4:37, 6:22, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 0, 4, 4, }, +{a: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 8, 4, }, +{f: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -16, -8, 8, 0, 0, 8, -8, 0, 0, 0, -8, }, +{2: 16, 8, -8, 8, 0, -8, 8, -8, -8, 0, 0, 0, 0, 0, -8, 0, }, +{4: 16, 0, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 8, -8, 8, 0, 8, 0, -8, -8, 8, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 0, 8, -8, -8, 0, 8, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 8, -8, 0, 0, -8, 8, 0, 8, -8, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, }, +{c: 16, 0, 0, -16, 0, 8, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, }, +{7: 16, -8, -8, -8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 8, 8, 0, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, -8, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 8, -8, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, x, , x, }, +{5: , , , x, x, x, x, , x, , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , , , x, , , , , x, , x, x, , x, , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0001,1,}, +{0100,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x04,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x03,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x09,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +102 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0d,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x05,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, }, +{2: 0, 2, 4, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, }, +{8: 0, 0, 2, 2, 6, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 6, 2, 0, 2, 2, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, }, +{9: 0, 4, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, }, +{a: 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 4, 2, 2, 0, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{b: 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 4, 2, }, +{e: 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 4, 2, 6, 0, 6, 2, 4, 0, 0, 4, 0, 0, }, +{2: 16, 2, 8, 0, 4, 0, 4, 2, 2, 4, 0, 4, 0, 0, 2, 0, }, +{4: 16, 8, 0, 4, 0, 2, 4, 2, 2, 0, 2, 0, 0, 0, 4, 4, }, +{8: 16, 4, 6, 2, 6, 4, 0, 0, 4, 6, 0, 0, 6, 0, 0, 2, }, +{3: 16, 0, 2, 0, 6, 8, 6, 4, 0, 0, 0, 0, 4, 0, 0, 2, }, +{5: 16, 4, 6, 4, 0, 4, 6, 6, 0, 2, 2, 6, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 2, 4, 6, 4, 2, 0, 0, 2, 0, 2, 2, 0, }, +{9: 16, 8, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 2, 6, 4, }, +{a: 16, 0, 4, 0, 4, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 16, 4, 0, 2, 0, 0, 0, 0, 0, 0, 8, 6, 4, 6, 2, 0, }, +{7: 16, 0, 4, 2, 0, 0, 4, 2, 0, 0, 4, 8, 4, 2, 0, 2, }, +{b: 16, 0, 0, 0, 6, 4, 0, 0, 2, 2, 4, 4, 10, 0, 0, 0, }, +{d: 16, 10, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 4, 6, }, +{e: 16, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:54, 4:37, 6:22, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{a: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 8, 4, }, +{e: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 8, 0, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 0, -8, 8, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -8, 8, 0, -16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, }, +{4: 16, 0, 0, -8, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, -8, 8, }, +{8: 16, 8, 0, 8, -8, 8, 8, 0, 0, 0, -8, 0, -8, -8, -8, -8, }, +{3: 16, -8, -8, 8, 0, 8, 0, -8, 0, 0, 0, 8, -8, 0, -8, 0, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, -8, 0, -8, 0, -8, 8, 0, 8, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, -8, -8, 8, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, -8, }, +{a: 16, 0, -8, 8, 0, -8, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, 0, 0, 0, 0, 0, 8, 8, -8, }, +{7: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, -8, -8, 8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 8, 8, 0, 8, -8, 0, -8, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, x, , x, }, +{5: , x, x, x, , x, x, , x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , x, x, x, }, +{9: , x, , x, x, x, , , x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , x, x, , , x, , , x, , x, x, , x, , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0010,1,}, +{0100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x09,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x05,0x08,0x0d,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x09,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_103.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_103.txt new file mode 100644 index 0000000..5caaf03 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_103.txt @@ -0,0 +1,410 @@ +103 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x0b,0x06,0x07,0x03,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 4, 2, }, +{6: 0, 0, 2, 0, 2, 4, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, }, +{a: 0, 2, 2, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, }, +{c: 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 4, 0, 0, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 6, 2, 0, 0, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 2, 4, 8, 0, 0, 8, 10, 0, 0, 4, 0, 0, 2, }, +{2: 16, 4, 8, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, }, +{4: 16, 0, 0, 8, 0, 4, 0, 2, 0, 2, 0, 6, 6, 0, 0, 4, }, +{8: 16, 4, 0, 0, 4, 0, 0, 2, 6, 0, 0, 2, 2, 2, 2, 0, }, +{3: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 2, 4, 0, 2, 0, 0, }, +{5: 16, 0, 2, 0, 0, 4, 8, 6, 0, 0, 0, 0, 6, 0, 4, 2, }, +{6: 16, 0, 2, 0, 2, 8, 4, 4, 4, 4, 0, 2, 0, 2, 0, 0, }, +{9: 16, 4, 2, 2, 4, 2, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, }, +{a: 16, 6, 2, 2, 0, 0, 2, 0, 0, 4, 2, 0, 4, 0, 2, 0, }, +{c: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +{7: 16, 0, 0, 4, 0, 10, 0, 2, 6, 4, 2, 4, 0, 0, 0, 0, }, +{b: 16, 6, 0, 4, 2, 0, 6, 0, 0, 6, 0, 0, 6, 2, 4, 4, }, +{d: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 6, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:57, 4:38, 6:19, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 4, 4, 4, 8, 0, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 8, 0, 8, 0, -16, 0, -8, 0, 0, }, +{2: 16, 8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, -8, -8, 0, 8, 0, 0, 8, 8, -8, -8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, -8, -8, 8, 0, 0, 0, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, -8, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, 8, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, 0, 0, 0, 0, -16, 0, 8, 0, -8, 0, 0, }, +{9: 16, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, -8, 8, 0, -8, 0, }, +{a: 16, 8, 0, 0, 0, -8, 0, -8, -8, 8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, -8, -8, -8, 8, 0, 8, 8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, -8, 8, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , , x, x, x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , x, , x, , , x, , x, x, , x, x, , , x, }, +{b: , , , , x, x, x, , x, x, , , , , , x, }, +{d: , , x, x, , , x, , x, x, , , x, x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0111,0001,1,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +103 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x0b,0x06,0x07,0x03,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 2, 2, 2, 2, 4, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 4, 0, }, +{6: 0, 0, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 4, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 0, }, +{a: 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 4, 2, 0, 2, 0, }, +{c: 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 4, 6, 0, 0, 4, 6, 2, 0, 6, 0, 0, 2, }, +{2: 16, 4, 8, 0, 0, 4, 2, 2, 2, 2, 4, 0, 0, 0, 4, 0, }, +{4: 16, 2, 2, 8, 0, 4, 0, 0, 2, 2, 0, 4, 4, 0, 0, 4, }, +{8: 16, 4, 2, 0, 4, 0, 0, 2, 4, 0, 2, 0, 2, 2, 2, 0, }, +{3: 16, 8, 4, 4, 0, 6, 4, 8, 2, 0, 0, 10, 0, 2, 0, 0, }, +{5: 16, 0, 2, 0, 0, 6, 8, 4, 0, 2, 0, 0, 6, 0, 4, 0, }, +{6: 16, 0, 0, 2, 2, 6, 6, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 8, 2, 0, 6, 0, 0, 4, 4, 0, 0, 6, 0, 2, 0, 0, }, +{a: 16, 10, 0, 2, 0, 0, 0, 4, 0, 4, 0, 4, 6, 0, 2, 0, }, +{c: 16, 0, 4, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 4, 2, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 4, 0, 6, 2, 0, 6, 0, 0, 4, 0, 0, 6, 2, 4, 6, }, +{d: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 2, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:57, 4:38, 6:19, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{5: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 0, -8, 8, 8, -8, -8, -8, 8, 0, }, +{2: 16, 8, 0, 0, 0, -8, 0, -8, 0, -8, 0, -8, -8, 8, 0, 8, }, +{4: 16, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, -16, 0, -8, -8, 0, }, +{8: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, 0, -16, 0, 8, 8, -8, 0, 8, }, +{5: 16, 0, -8, 0, 0, -8, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 8, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, 0, -8, 0, 8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, -8, 8, -8, -8, 8, 0, 8, -8, }, +{c: 16, 0, -8, 0, 0, 0, 8, -8, 0, -8, 8, -8, 0, 0, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, -8, 8, 0, -8, 8, 8, -8, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, -8, 8, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 8, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , x, , x, , , x, , x, x, , x, x, , , x, }, +{b: , , x, , x, x, x, , x, x, , , , , , x, }, +{d: , x, x, , , , x, , x, x, , , x, x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0111,0100,1,}, +{1010,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_104.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_104.txt new file mode 100644 index 0000000..37e77eb --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_104.txt @@ -0,0 +1,410 @@ +104 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x0c,0x06,0x07,0x03,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 0, 4, 0, }, +{6: 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 6, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{c: 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 2, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 6, 0, 4, 0, 6, 2, 4, 0, 0, 4, 2, 0, }, +{2: 16, 0, 8, 6, 2, 0, 2, 4, 6, 0, 0, 0, 4, 0, 0, 0, }, +{4: 16, 8, 4, 6, 0, 4, 4, 8, 0, 0, 2, 10, 0, 0, 0, 2, }, +{8: 16, 10, 0, 0, 4, 2, 0, 4, 6, 0, 0, 4, 2, 0, 0, 0, }, +{3: 16, 2, 0, 4, 2, 8, 2, 0, 4, 4, 2, 4, 0, 0, 0, 0, }, +{5: 16, 4, 2, 4, 2, 0, 8, 2, 0, 0, 2, 0, 4, 0, 4, 0, }, +{6: 16, 0, 6, 6, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 16, 4, 6, 0, 4, 6, 0, 0, 6, 6, 0, 0, 4, 2, 0, 2, }, +{a: 16, 2, 2, 0, 0, 4, 0, 0, 4, 6, 2, 0, 2, 0, 2, 0, }, +{c: 16, 8, 0, 0, 0, 0, 2, 4, 0, 0, 4, 6, 0, 6, 0, 2, }, +{7: 16, 0, 0, 4, 0, 6, 0, 2, 0, 2, 2, 4, 0, 2, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 4, 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 2, 4, 2, 2, }, +{e: 16, 0, 0, 2, 2, 0, 4, 0, 0, 2, 0, 2, 4, 0, 6, 2, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:57, 4:38, 6:19, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, -8, -8, 8, -8, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, -8, 8, -8, -8, }, +{4: 16, 8, 0, -16, 8, 8, -8, 0, 8, 0, -8, -8, 0, -8, 0, 0, }, +{8: 16, -8, 0, 8, 0, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -16, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, 8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 8, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -8, -8, 0, 0, 8, -8, 0, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{c: 16, -8, 8, -8, 0, 0, 0, 0, -8, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 0, -8, -8, 0, 0, 8, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, }, +{d: 16, -8, 0, -8, -8, -8, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, , , x, }, +{5: , , x, , x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, , , x, x, x, , , x, x, , , x, x, }, +{9: , , x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, , x, x, x, , , , x, , , x, x, x, }, +{7: , , x, , , x, x, , , , x, x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , x, x, , , x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0100,0100,1,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +104 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x0c,0x06,0x07,0x03,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 2, 2, 2, 2, 0, 0, 4, 0, 0, 0, }, +{4: 0, 2, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{8: 0, 2, 2, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, }, +{6: 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +{c: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 4, 0, 2, }, +{e: 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 10, 2, 4, 0, 4, 2, 8, 0, 0, 4, 0, 0, }, +{2: 16, 0, 8, 4, 0, 0, 2, 6, 6, 2, 0, 0, 4, 0, 0, 0, }, +{4: 16, 6, 6, 6, 0, 4, 4, 6, 0, 0, 0, 4, 0, 0, 2, 2, }, +{8: 16, 6, 2, 0, 4, 2, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, }, +{3: 16, 0, 0, 4, 2, 8, 0, 2, 6, 4, 0, 6, 0, 0, 0, 0, }, +{5: 16, 4, 2, 4, 0, 2, 8, 0, 0, 0, 2, 0, 4, 2, 4, 0, }, +{6: 16, 0, 4, 8, 4, 0, 2, 4, 0, 0, 4, 2, 0, 2, 0, 2, }, +{9: 16, 6, 6, 0, 6, 4, 0, 0, 6, 4, 0, 0, 4, 2, 0, 2, }, +{a: 16, 2, 0, 0, 0, 4, 0, 0, 6, 6, 0, 2, 2, 0, 2, 0, }, +{c: 16, 4, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, 0, 4, 0, 2, }, +{7: 16, 0, 0, 10, 4, 4, 0, 2, 0, 0, 6, 4, 0, 0, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 4, 0, 0, 0, 0, 0, 2, 2, 0, 6, 2, 2, 4, 0, 2, }, +{e: 16, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 4, 2, 6, 2, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:57, 4:38, 6:19, 8:7, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 8, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 8, 4, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{7: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, -8, 0, -16, 0, 8, -8, -8, -8, 8, 0, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 8, 0, -8, 0, -8, 8, 0, 0, }, +{4: 16, 8, 0, -8, 8, 0, -8, 0, 8, 8, 0, -8, 0, -8, -8, -8, }, +{8: 16, 0, 0, 8, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, -8, }, +{3: 16, 0, -8, 8, 0, 0, 0, 0, -8, -8, -8, 0, 8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, }, +{6: 16, 0, 0, -16, 8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 8, 8, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, -8, -8, 8, 0, 0, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 8, }, +{7: 16, 8, 0, -8, 0, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 0, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, }, +{d: 16, -8, 0, -8, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, 8, 0, }, +{e: 16, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, , , x, x, x, , , x, x, , , x, x, }, +{9: , x, , x, x, x, , , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, x, , , , x, , , x, x, x, }, +{7: , , x, , , x, x, , , , x, x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, , , , x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0100,0110,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x02,0x09,0x0b,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_105.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_105.txt new file mode 100644 index 0000000..1673d38 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_105.txt @@ -0,0 +1,410 @@ +105 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x05,0x06,0x07,0x04,0x0c,0x0a,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, }, +{4: 0, 4, 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, }, +{6: 0, 0, 2, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 0, 4, 0, }, +{a: 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 4, 2, 2, 0, 2, }, +{7: 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 4, 2, 2, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 4, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 2, 6, 6, 0, 4, 2, 6, 0, 4, 0, 0, 4, 0, 0, }, +{2: 16, 0, 8, 0, 6, 2, 6, 0, 0, 4, 0, 4, 0, 0, 2, 0, }, +{4: 16, 8, 0, 4, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 6, }, +{8: 16, 4, 4, 0, 6, 6, 0, 2, 4, 6, 2, 0, 6, 0, 0, 0, }, +{3: 16, 2, 0, 2, 4, 8, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 16, 4, 4, 4, 0, 6, 6, 6, 2, 0, 0, 6, 0, 0, 2, 0, }, +{6: 16, 0, 2, 2, 0, 4, 4, 6, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 16, 8, 2, 2, 4, 0, 0, 0, 4, 2, 2, 0, 0, 0, 4, 4, }, +{a: 16, 0, 4, 2, 6, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 2, }, +{c: 16, 4, 0, 0, 0, 0, 0, 0, 2, 0, 8, 4, 6, 6, 0, 2, }, +{7: 16, 0, 4, 2, 0, 0, 6, 2, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 0, 0, 0, 4, 4, 0, 0, 2, 2, 4, 4, 8, 2, 2, 0, }, +{d: 16, 10, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 6, 4, }, +{e: 16, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:54, 4:37, 6:22, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 8, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 8, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 8, -8, -8, 8, 0, 0, 0, -8, -8, -8, 0, -8, }, +{2: 16, 0, -8, 0, 8, 0, 8, 0, -8, -8, 0, 0, 0, 8, -8, -8, }, +{4: 16, -8, 8, -8, 8, 0, 0, 0, 0, 8, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, 0, 8, -8, 8, 0, 0, -8, -8, -8, 8, -8, -8, 0, 0, }, +{3: 16, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -16, 0, 8, }, +{5: 16, -8, 0, -8, 8, -8, 0, 0, -8, 0, -8, 8, 0, 8, -8, 8, }, +{6: 16, 0, -8, 0, 8, 0, 0, -8, 0, -8, 0, 0, 8, -8, 0, 0, }, +{9: 16, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, -8, 8, 8, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, -8, 0, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 8, 8, 0, }, +{7: 16, 0, -8, 0, 8, 0, 0, -8, 8, 0, -8, 0, -8, 8, 0, -8, }, +{b: 16, 0, 0, 0, -16, 0, -8, -8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{d: 16, -8, 0, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, -8, 0, 0, }, +{e: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, , , x, }, +{5: , , , x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{9: , , x, , x, x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , x, , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , x, , , x, , , x, , x, , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , x, x, x, x, x, , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1000,1011,1,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x05,0x09,0x0c,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +105 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x05,0x06,0x07,0x03,0x0c,0x0a,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 2, 2, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 0, 2, 0, 2, 4, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 6, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{6: 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, }, +{a: 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 4, 0, 2, 2, }, +{7: 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 4, 0, 2, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 4, 0, 2, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:159, 2:75, 4:18, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 4, 2, 4, 0, 8, 0, 4, 0, 0, 10, 0, 2, }, +{2: 16, 2, 8, 0, 4, 0, 4, 2, 2, 4, 0, 4, 0, 0, 2, 0, }, +{4: 16, 6, 0, 4, 0, 2, 4, 2, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 16, 6, 6, 0, 6, 4, 0, 0, 4, 6, 0, 0, 4, 0, 2, 2, }, +{3: 16, 0, 2, 0, 6, 8, 6, 4, 0, 0, 0, 0, 4, 0, 0, 2, }, +{5: 16, 4, 6, 6, 0, 4, 6, 4, 0, 2, 0, 6, 0, 0, 2, 0, }, +{6: 16, 2, 0, 0, 2, 4, 6, 6, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 6, 0, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 2, 2, 0, }, +{a: 16, 0, 4, 0, 6, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, }, +{c: 16, 4, 0, 0, 2, 0, 0, 0, 2, 0, 8, 4, 4, 4, 2, 2, }, +{7: 16, 0, 4, 2, 0, 0, 6, 2, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 0, 0, 0, 6, 4, 0, 0, 0, 2, 6, 4, 8, 0, 2, 0, }, +{d: 16, 4, 0, 2, 0, 0, 0, 2, 0, 2, 6, 0, 2, 4, 0, 2, }, +{e: 16, 0, 2, 4, 0, 0, 2, 0, 4, 0, 0, 0, 2, 6, 2, 2, }, +{f: 16, 0, 0, 6, 0, 2, 0, 0, 4, 2, 2, 0, 0, 4, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:54, 4:37, 6:22, 8:6, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{9: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 8, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, 0, 8, 8, -8, 0, -16, 0, -8, }, +{2: 16, 0, -8, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{4: 16, 0, 0, 0, 8, 0, -8, 0, 0, 0, -8, -8, 8, -8, 0, 0, }, +{8: 16, 8, 0, 8, -8, 0, 8, 8, -8, 0, 0, 0, -8, -8, -8, -8, }, +{3: 16, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, 8, -8, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, -8, 8, -8, 0, 0, 8, -8, 0, }, +{6: 16, -8, 0, 0, 8, 0, 0, 0, -8, -8, 0, 8, 0, -8, 0, 0, }, +{9: 16, -8, 8, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, }, +{c: 16, 0, 0, 0, -16, 8, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, }, +{7: 16, 8, 0, -8, 8, 0, 0, -8, 0, -8, 0, -8, -8, 8, 0, 0, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, -8, 0, 0, 8, 8, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, -8, 8, 0, }, +{e: 16, -8, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 0, 8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{9: , x, , x, x, x, , , x, , x, , x, x, , x, }, +{a: , x, , , x, x, , , x, x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , x, , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, , , x, , , , x, , x, , x, , , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , x, , , , x, , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1000,1100,1,}, +{1101,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x04,}, {0x0a,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x02,0x09,0x0b,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x0f,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_106.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_106.txt new file mode 100644 index 0000000..826efaa --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_106.txt @@ -0,0 +1,422 @@ +106 Sbox: +LUT = { +0x08,0x0f,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x00, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 4, 0, 0, 4, 2, 0, 2, 2, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:12, 2:1, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 4, 4, 10, 0, 0, 0, 6, 0, 0, 2, 2, }, +{2: 16, 0, 10, 0, 0, 0, 4, 0, 6, 0, 6, 6, 4, 4, 4, 4, }, +{4: 16, 0, 0, 4, 4, 16, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, }, +{5: 16, 0, 4, 0, 0, 4, 8, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{6: 16, 8, 2, 0, 4, 0, 0, 4, 6, 0, 2, 6, 0, 0, 0, 0, }, +{9: 16, 6, 4, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 0, 4, 2, 6, 4, 2, 0, 6, 0, 0, 0, 8, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 4, 2, 0, 4, 6, 2, 0, 0, 2, 0, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 0, 8, 4, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:43, 6:21, 8:5, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 0, 8, 0, -8, 8, -8, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 0, 0, 0, 0, -8, 8, -8, 8, -16, 8, -8, 0, 8, 0, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, -16, 0, 16, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -8, 0, 8, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{6: 16, 8, 0, 0, 0, 0, 0, 8, 0, -16, -8, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, -8, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{c: 16, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, -8, -8, 8, -8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, -8, 0, 8, 0, 8, -8, -8, 0, 0, -8, 8, 0, 0, -8, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 8, 0, -8, 0, 0, 8, -8, 0, 8, 0, -8, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, , x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , x, , , , x, x, , x, x, x, , x, x, x, x, }, +{b: , , x, , x, , x, , x, x, x, x, , x, x, x, }, +{d: , x, x, x, x, , x, , x, x, x, x, x, , x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,0100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +106 Inverse Sbox: +LUT = { +0x0f,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x01, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 4, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 4, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 4, 2, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:12, 2:1, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 8, 6, 0, 0, 6, 0, 2, 0, 4, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 4, 2, 8, 4, 4, 0, 10, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 2, 2, 2, 6, 2, 0, 0, 0, }, +{8: 16, 0, 0, 4, 2, 0, 0, 4, 6, 2, 0, 0, 6, 0, 0, 8, }, +{3: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 4, 4, 4, 0, 0, 8, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{6: 16, 10, 0, 4, 2, 0, 4, 4, 0, 0, 0, 6, 0, 0, 2, 0, }, +{9: 16, 0, 6, 4, 2, 0, 0, 6, 6, 0, 0, 0, 6, 4, 2, 4, }, +{a: 16, 0, 0, 4, 2, 2, 2, 0, 6, 2, 0, 0, 0, 6, 0, 0, }, +{c: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{7: 16, 6, 6, 4, 2, 4, 4, 6, 0, 2, 0, 6, 0, 0, 0, 0, }, +{b: 16, 0, 4, 4, 2, 0, 2, 0, 4, 2, 0, 2, 8, 0, 0, 4, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 4, 0, 2, 2, 0, 0, 2, 0, 6, 0, 0, 0, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:43, 6:21, 8:5, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 8, 0, -8, 0, -8, -8, 0, 8, }, +{3: 16, -16, 0, 8, 0, 0, -8, -8, 0, 0, 8, 8, 0, -8, 8, -8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, -8, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 8, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 8, }, +{7: 16, 0, -8, 0, 8, 0, 8, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{e: 16, 0, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, x, , x, x, x, x, x, x, , x, x, x, x, }, +{b: , , x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , x, x, , x, x, , x, x, x, x, x, , x, x, }, +{e: , , x, , x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_107.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_107.txt new file mode 100644 index 0000000..be990b6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_107.txt @@ -0,0 +1,422 @@ +107 Sbox: +LUT = { +0x08,0x00,0x01,0x0d,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x02,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 2, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 4, 0, 0, 4, 2, 0, 2, 2, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, }, +{a: 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:2, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +{2: 16, 0, 10, 0, 0, 0, 4, 0, 6, 0, 6, 6, 4, 4, 4, 4, }, +{4: 16, 16, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{3: 16, 4, 0, 6, 0, 4, 10, 4, 0, 0, 2, 0, 0, 2, 0, 0, }, +{5: 16, 4, 4, 6, 0, 6, 6, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{6: 16, 0, 2, 0, 4, 8, 4, 4, 2, 0, 2, 2, 4, 0, 0, 0, }, +{9: 16, 4, 4, 0, 0, 0, 0, 2, 4, 6, 0, 2, 10, 0, 0, 0, }, +{a: 16, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 4, 4, 4, 2, 0, 8, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 4, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 4, 0, 0, 4, 4, 0, 0, 0, 4, 2, 0, 8, 2, 2, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:52, 4:40, 6:16, 8:8, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{8: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 0, 0, 0, 0, -8, 8, -8, 8, -16, 8, -8, 0, 8, 0, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, -16, 0, 16, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 8, 0, 8, 0, -8, -8, -8, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, 0, 0, 0, 0, 0, 8, 0, -16, -8, 0, -8, 0, 0, 0, }, +{9: 16, -8, 0, 8, 0, -8, -8, 8, 0, 0, -8, -8, 0, 0, 8, 0, }, +{a: 16, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{c: 16, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, -8, -8, 8, -8, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, -8, 0, -8, 0, 0, -8, -8, 0, 8, 0, 8, -8, 0, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , x, , , , , x, x, x, , x, x, , x, , x, }, +{b: , , x, , x, x, x, x, x, , x, , x, x, , x, }, +{d: , x, x, x, x, x, x, x, x, , x, , , , , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,0100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x01,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0b,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +107 Inverse Sbox: +LUT = { +0x01,0x02,0x0d,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, 4, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 0, 2, }, +{5: 0, 0, 0, 4, 0, 2, 6, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 4, 2, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, }, +{c: 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, }, +{7: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 0, }, +{d: 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:2, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 4, 2, 8, 4, 4, 0, 10, 0, }, +{4: 16, 4, 0, 8, 0, 6, 6, 0, 0, 2, 2, 4, 0, 0, 0, 0, }, +{8: 16, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 6, 4, 0, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 8, 0, 0, 0, 0, 6, 4, 0, 2, }, +{5: 16, 4, 4, 8, 0, 10, 6, 4, 0, 2, 2, 8, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 2, 4, 6, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, 2, 4, 0, 2, 0, }, +{a: 16, 0, 0, 8, 2, 0, 0, 0, 6, 2, 0, 0, 6, 4, 0, 4, }, +{c: 16, 2, 6, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, }, +{7: 16, 0, 6, 0, 2, 0, 4, 2, 2, 2, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 8, 2, 0, 0, 4, 10, 2, 0, 0, 6, 8, 0, 4, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:52, 4:40, 6:16, 8:8, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{2: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 8, -8, 0, -8, -8, 8, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{3: 16, -16, 0, 0, 0, 0, 0, -8, 0, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 8, 0, 0, -16, -8, 8, -8, 0, 0, 0, -8, 8, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 8, 0, -8, 0, 0, -8, 8, 0, -8, 0, 8, -8, 0, -8, }, +{c: 16, 0, 0, 0, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, 0, 0, 0, 8, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 8, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, , x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , x, x, , x, x, x, x, , x, , , , , x, }, +{e: , , x, , x, , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_108.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_108.txt new file mode 100644 index 0000000..01908a7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_108.txt @@ -0,0 +1,422 @@ +108 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x0c,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{2: 0, 0, 6, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 6, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 2, 4, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{9: 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{a: 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 0, 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{e: 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 16, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 16, 0, 10, 4, 10, 0, 0, 4, 0, 8, 4, 2, 0, 2, 4, 0, }, +{4: 16, 4, 4, 6, 0, 10, 8, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{8: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 2, 0, 6, 8, 4, 0, 0, 0, }, +{5: 16, 4, 0, 6, 0, 6, 8, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 16, 0, 6, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{9: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{a: 16, 2, 6, 0, 4, 2, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 8, 0, 4, 0, 6, 4, 8, 2, 10, 2, }, +{7: 16, 2, 0, 6, 2, 4, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 16, 0, 4, 2, 6, 2, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 8, 0, 4, 0, 6, 0, 4, 2, 6, 2, }, +{e: 16, 0, 6, 2, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 2, 2, 0, 6, 4, 4, 2, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:52, 4:40, 6:16, 8:8, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 0, 8, 0, -8, 0, }, +{2: 16, 8, -8, 8, 0, -8, 16, -8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 0, 8, -8, 0, 8, -8, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -16, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, 0, 0, -8, 8, 0, -8, 0, 8, }, +{6: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, }, +{a: 16, 0, -8, 8, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, -8, 0, 8, 0, -8, 8, 0, 8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, -8, -8, }, +{d: 16, -8, 0, -8, -8, 0, 0, -8, 0, 8, 0, 8, -8, 8, 0, 0, }, +{e: 16, 8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, x, x, , x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , x, , , , , x, x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,1100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x01,0x04,0x05,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +108 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x0c,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x04,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 4, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{a: 0, 0, 4, 2, 2, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, }, +{b: 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{e: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 0, 0, 0, 6, 2, 0, 2, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 0, 4, 4, 0, 2, 6, 0, 2, 0, }, +{3: 16, 4, 0, 10, 0, 4, 6, 0, 0, 2, 0, 4, 2, 0, 0, 0, }, +{5: 16, 16, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{6: 16, 4, 4, 8, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 16, 4, 0, 0, 2, 2, 0, 2, 2, 0, 4, 0, 2, 4, 0, 2, }, +{a: 16, 0, 8, 2, 6, 0, 2, 0, 6, 4, 0, 0, 4, 0, 0, 0, }, +{c: 16, 4, 4, 0, 0, 6, 0, 0, 0, 2, 6, 2, 0, 6, 4, 6, }, +{7: 16, 0, 2, 4, 0, 8, 0, 2, 0, 2, 4, 4, 0, 0, 2, 4, }, +{b: 16, 4, 0, 0, 2, 4, 0, 0, 2, 2, 8, 0, 2, 4, 0, 4, }, +{d: 16, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{e: 16, 4, 4, 0, 0, 0, 0, 2, 0, 0, 10, 2, 0, 6, 4, 0, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:52, 4:40, 6:16, 8:8, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{e: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, -8, 0, 8, -8, 0, 8, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, -8, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, -8, 8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, -8, 8, -8, 0, -8, 8, }, +{9: 16, -8, 0, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{a: 16, 8, 0, 8, 0, -8, 8, -8, 0, 0, -8, -8, 0, 0, -8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, }, +{7: 16, 0, -16, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, -8, 0, 8, 8, -8, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 8, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , , , x, x, x, , , x, }, +{5: , x, , , x, , x, x, , , x, x, , x, , x, }, +{6: , x, , x, x, x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, , , , , , , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , x, , x, , , x, }, +{d: , , , , x, , , x, , , x, , , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_109.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_109.txt new file mode 100644 index 0000000..8d76d86 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_109.txt @@ -0,0 +1,422 @@ +109 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x0e,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 0, 2, }, +{8: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 4, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 4, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, }, +{7: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 4, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 4, 0, }, +{e: 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 4, 2, 6, 6, 4, 4, 6, 0, 0, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 0, 8, 4, 0, 0, 6, 6, 0, 0, 2, 4, 0, 0, 0, 2, }, +{8: 16, 2, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, }, +{3: 16, 0, 0, 2, 4, 8, 4, 6, 2, 0, 0, 0, 6, 0, 0, 0, }, +{5: 16, 0, 0, 2, 0, 4, 4, 6, 0, 2, 0, 0, 2, 2, 2, 0, }, +{6: 16, 4, 8, 4, 0, 4, 10, 6, 0, 0, 2, 8, 0, 0, 0, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 6, 6, 0, 0, 4, 2, 2, 0, }, +{a: 16, 8, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 6, 0, 6, 4, }, +{c: 16, 4, 0, 2, 2, 2, 2, 0, 0, 0, 4, 2, 0, 6, 0, 0, }, +{7: 16, 10, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 6, 4, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 8, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{e: 16, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:50, 4:37, 6:19, 8:9, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 0, 4, 0, 4, 12, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 0, -8, 0, 8, -8, 0, -8, 8, 0, }, +{2: 16, 0, 0, 8, 0, -16, 8, -8, 0, 0, -8, -8, 0, 8, -8, 8, }, +{4: 16, 0, 0, -16, 8, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, }, +{8: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, 0, 0, 8, 0, 8, -8, 0, 0, -8, -8, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, 0, 8, -8, 8, 0, 0, 0, 0, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 8, -8, 0, 0, -16, 0, 0, 8, }, +{9: 16, 8, 0, 8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, -8, -8, }, +{a: 16, 0, -8, 8, 0, -8, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, }, +{7: 16, -8, -8, -8, 0, 8, 0, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 8, 0, 0, 0, -16, 8, 0, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 16, 0, 0, -8, }, +{e: 16, -8, 0, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, , x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, , , x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, , x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, x, , , , x, x, , x, x, x, , , x, x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, , , x, x, x, x, , x, x, , , x, x, x, }, +{e: , x, x, , , x, x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0100,0100,1,}, +{1011,0110,1,}, +{1011,1011,1,}, +{1011,1101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x04,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +109 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x0e,0x06,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 4, 4, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 2, 2, 6, 0, 2, 0, 0, 0, 0, 2, 0, }, +{9: 0, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 2, 4, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 6, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 4, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 2, 0, 0, 4, 0, 8, 4, 10, 4, 8, 2, 0, }, +{2: 16, 0, 16, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{4: 16, 0, 4, 4, 2, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, 2, }, +{8: 16, 0, 4, 0, 6, 4, 0, 0, 4, 0, 2, 0, 10, 0, 0, 2, }, +{3: 16, 2, 0, 0, 4, 8, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, }, +{5: 16, 0, 4, 6, 0, 4, 4, 10, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 16, 4, 4, 6, 0, 6, 6, 6, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 4, 2, 2, 0, }, +{a: 16, 6, 4, 0, 0, 0, 2, 0, 6, 4, 0, 0, 8, 2, 0, 0, }, +{c: 16, 6, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 2, }, +{7: 16, 4, 4, 4, 0, 0, 0, 8, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 16, 4, 4, 0, 6, 6, 2, 0, 4, 6, 0, 0, 6, 0, 0, 2, }, +{d: 16, 6, 0, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 4, 2, 2, }, +{e: 16, 0, 0, 0, 0, 0, 2, 0, 2, 6, 0, 6, 0, 4, 2, 2, }, +{f: 16, 0, 0, 2, 2, 0, 0, 2, 0, 4, 0, 4, 2, 4, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:50, 4:37, 6:19, 8:9, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, 0, 8, -16, 8, 0, -8, 0, -8, 8, -8, }, +{2: 16, 0, -8, 8, 0, -8, -8, 0, 16, -8, -8, 0, -8, 8, 0, 0, }, +{4: 16, 0, 8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, }, +{8: 16, -8, 0, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, }, +{3: 16, 0, 0, 8, 0, 8, 0, 0, -16, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 8, 0, -8, 8, -8, 0, -8, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 8, -8, -8, 8, -8, -8, 0, 0, 0, -8, 8, 0, -8, 0, 8, }, +{9: 16, 0, 0, 8, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, -8, -8, }, +{a: 16, 0, 0, 8, 0, -16, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, 8, 0, }, +{7: 16, 0, 0, -16, 0, 8, 0, 0, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, -8, 0, -8, -8, -8, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , , x, , , , x, x, , x, x, x, , , x, x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, , x, x, , x, x, , , x, x, x, }, +{e: , x, x, x, x, x, x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,1010,1,}, +{0100,0111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0a,0x04,}, {0x03,0x05,0x06,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_110.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_110.txt new file mode 100644 index 0000000..e2ee1c1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_110.txt @@ -0,0 +1,422 @@ +110 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x0b,0x06,0x07,0x04,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 4, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 2, 0, 4, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:1, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 8, 10, 0, 0, 4, 4, 0, 0, 8, 2, 0, 2, }, +{2: 16, 4, 10, 0, 0, 4, 2, 0, 2, 0, 8, 0, 0, 4, 10, 4, }, +{4: 16, 0, 0, 4, 6, 8, 2, 0, 0, 2, 0, 6, 4, 0, 0, 0, }, +{8: 16, 4, 0, 0, 4, 0, 0, 2, 6, 0, 2, 2, 2, 0, 0, 2, }, +{3: 16, 8, 4, 10, 0, 6, 8, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{5: 16, 0, 0, 2, 4, 8, 4, 6, 2, 0, 0, 0, 6, 0, 0, 0, }, +{6: 16, 0, 2, 0, 2, 4, 4, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 16, 10, 0, 4, 6, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 16, 8, 2, 6, 0, 0, 4, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 4, 4, 6, }, +{7: 16, 2, 0, 4, 0, 4, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 16, 4, 0, 0, 2, 0, 2, 2, 0, 6, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 4, 0, 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:50, 4:38, 6:16, 8:9, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:5, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, 0, 8, -8, 0, 8, 0, -8, -16, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 16, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, -8, 0, 8, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, 0, 8, 0, -8, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 0, 8, -8, 8, -8, 8, -8, 0, 0, 0, -8, }, +{7: 16, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, , x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, , , x, x, , x, x, , x, x, , , x, }, +{b: , x, , , x, , x, , x, x, , , , , , x, }, +{d: , , , x, x, , x, , x, x, , , x, x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,1010,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x03,0x05,0x06,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x04,0x09,0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x04,0x09,0x0d,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +110 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x0b,0x06,0x07,0x00,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 4, 2, 2, 0, 0, 0, 0, 0, }, +{8: 0, 4, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 2, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:1, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 4, 8, 0, 0, 10, 8, 0, 2, 4, 0, 0, 2, }, +{2: 16, 4, 10, 0, 0, 4, 0, 2, 0, 2, 8, 0, 0, 4, 10, 4, }, +{4: 16, 0, 0, 4, 0, 10, 2, 0, 4, 6, 2, 4, 0, 0, 0, 0, }, +{8: 16, 8, 0, 6, 4, 0, 4, 2, 6, 0, 0, 0, 2, 0, 0, 0, }, +{3: 16, 10, 4, 8, 0, 6, 8, 4, 0, 0, 0, 4, 0, 2, 0, 2, }, +{5: 16, 0, 2, 2, 0, 8, 4, 4, 4, 4, 0, 0, 2, 2, 0, 0, }, +{6: 16, 0, 0, 0, 2, 4, 6, 4, 0, 0, 0, 2, 2, 0, 2, 2, }, +{9: 16, 4, 2, 0, 6, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 16, 4, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 6, 2, 0, 0, }, +{c: 16, 0, 8, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 4, 6, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{d: 16, 2, 4, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 6, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:50, 4:38, 6:16, 8:9, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:5, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 8, -8, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 8, 0, 0, 0, -8, -8, 0, 0, -8, -8, 8, 0, -8, 8, }, +{8: 16, 0, 8, 8, 0, 0, -8, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, -16, 0, 0, 8, 0, 0, -8, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 0, 0, 0, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, 0, -8, 0, 8, -8, 8, -8, 8, 0, -8, 0, 0, -8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , , x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, x, , x, x, , x, x, , x, x, , , x, }, +{b: , , x, , , x, x, , x, x, , , , , , x, }, +{d: , , , , x, x, x, , x, x, , , x, x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0b,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x08,0x09,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_111.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_111.txt new file mode 100644 index 0000000..204e845 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_111.txt @@ -0,0 +1,422 @@ +111 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x05,0x0e,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x04,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{2: 0, 0, 6, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 0, 0, 2, 2, 2, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, }, +{9: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{7: 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, }, +{b: 0, 2, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 6, 4, 0, 0, 8, 2, 0, 6, 0, }, +{2: 16, 0, 10, 4, 10, 0, 0, 4, 0, 8, 4, 2, 0, 2, 4, 0, }, +{4: 16, 4, 4, 8, 0, 0, 4, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{8: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 4, 0, 4, 0, 4, 16, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 16, 4, 6, 6, 2, 4, 4, 6, 0, 0, 0, 6, 0, 0, 0, 2, }, +{9: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{a: 16, 2, 6, 0, 4, 2, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 2, 4, 0, 4, 2, 8, 0, 0, 2, 4, 0, }, +{7: 16, 8, 0, 6, 0, 0, 4, 6, 0, 0, 0, 4, 0, 2, 0, 2, }, +{b: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 6, 2, 6, 0, }, +{e: 16, 0, 6, 0, 0, 0, 4, 0, 6, 0, 4, 6, 4, 2, 6, 2, }, +{f: 16, 0, 0, 0, 2, 0, 4, 0, 10, 0, 4, 4, 0, 0, 6, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:43, 6:21, 8:5, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{e: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 8, -8, 8, 0, -8, 16, -8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{4: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 8, -16, -8, 8, 0, -8, 0, 8, 0, -8, 0, }, +{5: 16, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 8, 8, -8, -8, 0, -8, -8, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{a: 16, 0, -8, 8, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, -8, 8, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, 0, -8, 0, -8, 0, 8, -8, 8, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 0, 8, 0, 8, 8, -8, -8, }, +{f: 16, 0, 0, -8, -8, 8, 0, 8, -8, -8, 0, -8, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , x, , x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , x, , x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , , , , x, , x, x, x, , , x, x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x03,0x05,0x06,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x05,0x09,0x0c,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +111 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x0e,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x06,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 4, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, 4, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, }, +{b: 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 4, 0, 4, 2, 2, 0, 8, 2, 0, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 0, 4, 8, 0, 4, 0, 6, 0, 0, 2, 6, 0, 2, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 2, 4, 4, 0, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 4, 2, 2, 2, 0, 2, 0, 0, 0, }, +{5: 16, 0, 0, 4, 0, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 16, 6, 4, 4, 2, 4, 6, 6, 0, 0, 0, 6, 0, 2, 0, 0, }, +{9: 16, 4, 0, 0, 2, 4, 0, 0, 2, 0, 4, 0, 0, 0, 6, 10, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 4, 2, 0, 0, 2, 8, 0, 2, 0, 4, 4, }, +{7: 16, 8, 2, 0, 0, 0, 0, 6, 0, 2, 0, 4, 0, 0, 6, 4, }, +{b: 16, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 6, 4, 0, }, +{d: 16, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 16, 6, 4, 2, 0, 4, 0, 0, 2, 0, 4, 0, 0, 6, 6, 6, }, +{f: 16, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:43, 6:21, 8:5, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 4, 0, 4, 12, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{7: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, -8, -8, 0, 0, 8, -8, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, -8, 0, -8, 0, 0, 8, -8, 0, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 8, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 8, 0, }, +{9: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, }, +{7: 16, 0, -16, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 8, 8, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , , x, x, x, x, , x, x, }, +{5: , x, , , x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, , x, , x, , x, x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , x, , , , , , , , x, x, x, , , x, x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , , x, , , x, , x, x, , , x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_112.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_112.txt new file mode 100644 index 0000000..e9d7625 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_112.txt @@ -0,0 +1,422 @@ +112 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x0d,0x00,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, }, +{2: 0, 0, 4, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{8: 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{5: 0, 2, 0, 2, 0, 0, 6, 0, 0, 0, 2, 2, 2, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 4, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 4, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:3, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 2, 2, 4, 2, 0, 4, 0, 0, 0, }, +{2: 16, 0, 16, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{4: 16, 4, 4, 4, 0, 0, 8, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{8: 16, 2, 4, 2, 6, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 0, 0, 0, 0, 6, 4, 10, 8, 4, 4, 0, 2, 0, 2, 8, }, +{5: 16, 6, 4, 6, 0, 4, 6, 4, 0, 0, 2, 6, 2, 0, 0, 0, }, +{6: 16, 0, 4, 0, 0, 4, 10, 4, 0, 0, 2, 6, 0, 0, 2, 0, }, +{9: 16, 0, 4, 2, 4, 6, 0, 0, 4, 10, 0, 0, 0, 2, 0, 0, }, +{a: 16, 6, 4, 0, 4, 6, 0, 0, 4, 6, 0, 0, 6, 2, 2, 0, }, +{c: 16, 0, 0, 0, 2, 6, 0, 6, 4, 0, 4, 0, 0, 2, 0, 8, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 4, 4, 0, 6, 0, 0, 0, 0, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, }, +{f: 16, 0, 0, 0, 2, 4, 0, 4, 4, 0, 4, 0, 2, 2, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:105, 2:53, 4:36, 6:16, 8:11, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{7: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -16, 0, 0, 0, 0, 0, -8, 0, 8, 0, }, +{2: 16, 8, 0, 8, 0, -8, 16, -8, -8, 0, -8, 0, -8, 0, -8, 0, }, +{4: 16, 0, 0, -16, 0, 8, 0, 0, 0, 0, 0, -8, 8, 0, 0, -8, }, +{8: 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, -8, -8, }, +{3: 16, -8, -8, 8, 0, 0, -16, 0, 0, -8, 0, 8, 8, 0, -8, 8, }, +{5: 16, -8, 8, -8, 8, 0, 0, -8, -8, 8, -8, 0, -8, 8, 0, 0, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, }, +{9: 16, 0, 8, 8, -8, 0, 0, 0, 0, -8, -8, 0, 8, -8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, -8, 8, 0, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 8, 0, -8, -8, 0, 8, }, +{7: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, -16, 0, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 8, 8, 0, 0, 8, -8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{5: , , x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, , x, x, , x, x, , x, , , x, x, x, }, +{9: , x, x, x, x, x, , x, x, , x, x, x, , , x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, , x, x, , , x, x, }, +{7: , , x, , , x, , x, x, , x, , , x, , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, , , x, x, , x, x, , , , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1011,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x05,0x09,0x0c,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +112 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x0d,0x01,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{2: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{8: 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, }, +{5: 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{6: 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 4, }, +{9: 0, 2, 0, 0, 2, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 4, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, }, +{c: 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 0, }, +{b: 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, }, +{e: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 0, 0, 4, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:3, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 4, 0, 4, 2, 0, 6, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{8: 16, 0, 8, 0, 6, 0, 0, 0, 4, 4, 2, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 6, 4, 4, 6, 6, 6, 0, 0, 2, 0, 4, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 0, 0, 0, 4, 0, 2, 2, 0, }, +{6: 16, 2, 0, 0, 0, 10, 4, 4, 0, 0, 6, 0, 0, 0, 2, 4, }, +{9: 16, 2, 0, 0, 2, 8, 0, 0, 4, 4, 4, 2, 0, 0, 2, 4, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 10, 6, 0, 0, 8, 2, 2, 0, }, +{c: 16, 2, 0, 2, 0, 4, 2, 2, 0, 0, 4, 0, 2, 2, 0, 4, }, +{7: 16, 0, 8, 4, 0, 0, 6, 6, 0, 0, 0, 4, 0, 2, 2, 0, }, +{b: 16, 4, 0, 0, 2, 2, 2, 0, 0, 6, 0, 0, 6, 0, 0, 2, }, +{d: 16, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, }, +{e: 16, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 2, 2, 8, 0, 0, 0, 0, 8, 2, 2, 0, 0, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:105, 2:53, 4:36, 6:16, 8:11, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{7: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 12, 0, 0, 4, }, +{d: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 0, -8, 8, -8, 0, -8, 0, 8, -8, }, +{2: 16, 8, -8, 8, 0, 0, 0, 0, 8, -8, -8, 8, -16, 0, 0, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 8, -8, 0, -8, -8, 8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, -8, 8, 0, 8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -16, 8, -8, 0, 0, 0, 8, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 0, 0, -8, 8, 0, 0, 8, 0, -8, -8, 0, 8, }, +{9: 16, -8, 0, 8, 0, 0, -8, 8, -8, -8, 0, 0, 8, 0, -8, 0, }, +{a: 16, 8, -8, 8, -8, -16, 8, -8, 0, 0, 0, -8, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -16, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, }, +{b: 16, -8, 0, 8, 0, 0, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, }, +{f: 16, 0, 0, -8, -8, 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{5: , x, x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{9: , , x, x, x, x, , x, x, , x, x, x, , , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, x, , x, x, , , x, x, }, +{7: , x, x, , , x, , x, x, , x, , , x, , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, x, x, , x, x, , x, x, , , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0101,1,}, +{0011,1010,1,}, +{0011,1111,0,}, +{0100,0111,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x0a,0x04,}, {0x03,}}, +{{0x09,0x0a,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,}}, +{{0x01,0x02,}, {0x0b,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x03,0x05,0x06,}}, +{{0x0d,0x06,}, {0x0d,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_113.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_113.txt new file mode 100644 index 0000000..2b9cf5d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_113.txt @@ -0,0 +1,422 @@ +113 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x07,0x00,0x0f,0x0a,0x0b,0x0c,0x0d,0x0e,0x09, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, }, +{2: 0, 0, 4, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{3: 0, 0, 0, 2, 0, 4, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 4, 0, 2, 0, 0, 2, }, +{7: 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 2, 2, }, +{d: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 4, 0, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 6, 0, 4, 6, 6, 4, 4, 0, 2, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 0, 8, 6, 0, 0, 6, 4, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 0, 0, 2, 4, 4, 0, 0, 2, 0, 0, 2, 6, 0, 2, 2, }, +{3: 16, 0, 0, 2, 4, 8, 4, 6, 2, 0, 0, 0, 6, 0, 0, 0, }, +{5: 16, 2, 0, 2, 0, 4, 6, 6, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 0, 0, 10, 0, 0, 2, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 10, 0, 0, 0, 2, 0, 0, 0, 4, 6, 0, 4, 4, 2, 0, }, +{c: 16, 4, 0, 0, 2, 2, 2, 0, 0, 2, 4, 0, 2, 4, 0, 2, }, +{7: 16, 8, 0, 2, 0, 2, 0, 4, 2, 0, 4, 4, 0, 4, 2, 0, }, +{b: 16, 4, 8, 0, 8, 4, 0, 0, 4, 10, 0, 0, 6, 0, 2, 2, }, +{d: 16, 8, 0, 2, 2, 0, 2, 0, 2, 0, 8, 0, 0, 8, 0, 0, }, +{e: 16, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:105, 2:53, 4:36, 6:16, 8:11, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{5: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{c: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 8, -8, 0, 8, -8, -8, -8, 8, 0, }, +{2: 16, 8, 0, 0, 8, -8, 8, -16, 0, 8, -8, -8, 0, 0, -8, 0, }, +{4: 16, 0, 0, -8, 8, 0, 8, -8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{5: 16, -8, 0, 0, 8, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, }, +{6: 16, 8, -16, -8, 8, -8, 0, 8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, -8, 0, 8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, 0, -8, 8, 0, -8, -8, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, -16, 8, -8, 0, 0, -8, 8, 8, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 16, -8, -8, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{6: , , , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , , , , x, x, , x, x, x, , x, x, x, }, +{d: , , , x, , , x, x, , x, x, x, x, , x, x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{0010,1011,1,}, +{0010,1101,0,}, +{0110,0010,1,}, +{1000,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x0a,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x06,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x06,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +113 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x01,0x0f,0x0a,0x0b,0x0c,0x0d,0x0e,0x09, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 2, 0, }, +{2: 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 4, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 4, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, }, +{a: 0, 0, 4, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 0, }, +{c: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, }, +{7: 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 0, 2, 4, 0, 10, 4, 8, 4, 8, 2, 0, }, +{2: 16, 0, 16, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{4: 16, 0, 4, 6, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 16, 0, 4, 0, 4, 4, 0, 0, 4, 0, 2, 0, 8, 2, 2, 2, }, +{3: 16, 2, 0, 0, 4, 8, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, }, +{5: 16, 0, 4, 6, 0, 4, 6, 8, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, 2, 2, }, +{a: 16, 4, 4, 0, 0, 0, 0, 0, 6, 4, 2, 0, 10, 0, 2, 0, }, +{c: 16, 6, 0, 2, 0, 0, 0, 0, 0, 6, 4, 4, 0, 8, 0, 2, }, +{7: 16, 6, 4, 4, 2, 0, 0, 10, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 4, 4, 0, 6, 6, 2, 0, 6, 4, 2, 0, 6, 0, 0, 0, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 0, 4, 4, 4, 0, 8, 2, 2, }, +{e: 16, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 2, }, +{f: 16, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:105, 2:53, 4:36, 6:16, 8:11, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 4, 8, 0, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, 0, 8, -16, 8, 0, -8, 0, 0, 8, -8, }, +{2: 16, 8, -8, 0, 8, 0, -8, -8, 16, 0, -8, 0, -8, 0, 0, -8, }, +{4: 16, 0, 0, 0, 8, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -16, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 0, 8, 0, 0, -8, -16, 0, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, 0, 0, 8, 0, 0, -16, 0, -8, 8, 0, 0, 0, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, -8, 8, 0, 0, 0, 8, -8, -8, 0, 8, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 0, 8, 0, -8, 0, }, +{a: 16, 8, -8, 8, -8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, 0, 0, 8, -8, 0, -8, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, -8, 0, -8, }, +{b: 16, -8, 0, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 8, 0, 0, }, +{d: 16, 0, 0, -8, -8, -8, 8, -8, 0, 8, 0, 0, 8, -8, 0, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{6: , x, , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , x, x, , x, x, x, , x, x, x, , x, x, x, }, +{c: , x, , x, , x, x, x, , x, x, x, x, , x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , , x, , , x, x, x, , x, x, x, , x, x, x, }, +{d: , , , , , x, x, x, , x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,0101,1,}, +{1000,1000,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x06,0x09,0x0f,}}, +{{0x09,0x02,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_114.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_114.txt new file mode 100644 index 0000000..b9d23d2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_114.txt @@ -0,0 +1,422 @@ +114 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x07,0x00,0x09,0x0a,0x0e,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, }, +{5: 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{a: 0, 2, 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, }, +{7: 0, 2, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, }, +{d: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 4, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:3, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 2, 2, 4, 2, 0, 4, 0, 0, 0, }, +{2: 16, 0, 16, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{4: 16, 4, 4, 6, 0, 0, 10, 0, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 2, 4, 2, 4, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, }, +{3: 16, 0, 0, 2, 0, 6, 4, 8, 10, 4, 4, 0, 0, 0, 2, 8, }, +{5: 16, 6, 4, 6, 0, 4, 6, 6, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 0, 4, 0, 0, 6, 8, 4, 0, 0, 0, 6, 2, 0, 0, 2, }, +{9: 16, 0, 4, 0, 4, 4, 0, 0, 4, 8, 2, 0, 0, 2, 2, 2, }, +{a: 16, 6, 4, 0, 6, 4, 0, 2, 4, 6, 0, 0, 6, 0, 2, 0, }, +{c: 16, 0, 0, 0, 2, 6, 2, 0, 2, 2, 4, 0, 0, 2, 0, 4, }, +{7: 16, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 16, 4, 4, 0, 6, 0, 0, 0, 0, 10, 2, 0, 4, 0, 2, 0, }, +{d: 16, 0, 0, 2, 2, 0, 2, 4, 4, 2, 0, 0, 0, 2, 2, 4, }, +{e: 16, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 2, 2, 2, 2, 4, }, +{f: 16, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 2, 2, 2, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:50, 4:37, 6:19, 8:9, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 0, -8, 0, 8, -8, 16, -8, -8, 0, -8, -8, 0, 8, 0, 0, }, +{4: 16, -8, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, }, +{3: 16, 0, -8, 0, 8, 0, -16, 0, 0, -8, 0, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{6: 16, 0, -16, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 0, -16, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, 0, -8, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 8, }, +{7: 16, 0, -8, 0, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, -8, }, +{b: 16, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{e: 16, -8, -8, -8, -8, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, -8, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, , , x, x, , x, x, , , x, x, }, +{5: , , x, , x, x, x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, x, , x, x, x, , , x, }, +{9: , x, x, x, , x, , x, x, , x, , , x, x, x, }, +{a: , x, x, x, x, , , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , x, , , , , x, x, , x, , , , x, x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, x, , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1000,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x05,0x09,0x0c,}}, +{{0x06,0x08,}, {0x02,0x09,0x0b,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +114 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x01,0x09,0x0a,0x0e,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, }, +{5: 0, 0, 4, 2, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 4, 2, 4, 0, 2, 0, 0, 0, 0, 2, 0, }, +{9: 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, }, +{a: 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 2, 0, 2, 2, 0, 0, }, +{c: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, }, +{7: 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 4, 0, 2, 2, }, +{d: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 4, DDT1_spectrum: {0:8, 2:3, 4:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{2: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 16, 4, 0, 6, 2, 2, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 2, 0, 6, 2, 0, 0, }, +{3: 16, 2, 0, 0, 0, 6, 4, 6, 4, 4, 6, 2, 0, 0, 0, 6, }, +{5: 16, 4, 8, 10, 0, 4, 6, 8, 0, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 0, 8, 6, 4, 0, 2, 0, 0, 0, 4, 6, 0, }, +{9: 16, 2, 0, 0, 0, 10, 0, 0, 4, 4, 2, 0, 0, 4, 6, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 8, 6, 2, 0, 10, 2, 0, 0, }, +{c: 16, 2, 0, 2, 2, 4, 0, 0, 2, 0, 4, 0, 2, 0, 0, 6, }, +{7: 16, 0, 8, 4, 0, 0, 4, 6, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 16, 4, 0, 0, 2, 0, 2, 2, 0, 6, 0, 0, 4, 0, 2, 2, }, +{d: 16, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:106, 2:50, 4:37, 6:19, 8:9, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, 0, 0, -8, 8, -8, -8, 0, -8, 0, -8, }, +{2: 16, 0, -16, 0, 8, 0, 0, 0, 8, -8, -8, 0, -8, 8, 8, -8, }, +{4: 16, -8, 8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, }, +{8: 16, 0, 8, 8, -16, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, -8, 0, 8, 8, -8, 0, -8, -8, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, -8, 0, -8, 0, 0, 8, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, -8, -8, 0, 0, -8, 8, 0, 8, 0, 0, 0, }, +{a: 16, 8, -8, 8, -8, -8, 8, -16, 0, 0, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, 0, -8, 8, -8, 0, 0, 0, 0, -8, -8, 0, 0, 0, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, -8, -8, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, x, , x, x, , , x, x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, x, , x, x, x, , , x, }, +{9: , x, x, x, , x, , x, x, , x, , , x, x, x, }, +{a: , x, , , , x, , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, , , , x, x, , x, , x, x, , x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , x, , , , x, , x, x, , x, , , , x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0110,0101,1,}, +{0110,1010,1,}, +{0110,1111,0,}, +{1000,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x03,0x05,0x06,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_115.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_115.txt new file mode 100644 index 0000000..4ff90d8 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_115.txt @@ -0,0 +1,422 @@ +115 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x09,0x04,0x07,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 2, 2, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, }, +{7: 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 2, 8, 8, 10, 0, 0, 0, 4, 0, 0, 0, 2, }, +{2: 16, 4, 10, 0, 0, 4, 2, 0, 2, 0, 8, 0, 0, 4, 10, 4, }, +{4: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{8: 16, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 6, 0, 0, 2, }, +{3: 16, 10, 4, 0, 4, 6, 0, 0, 4, 8, 0, 0, 8, 2, 0, 2, }, +{5: 16, 4, 0, 6, 2, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{6: 16, 4, 2, 0, 2, 0, 0, 4, 2, 2, 0, 6, 0, 0, 2, 0, }, +{9: 16, 0, 0, 2, 2, 4, 0, 0, 4, 6, 0, 2, 0, 0, 2, 2, }, +{a: 16, 0, 2, 2, 0, 8, 4, 4, 4, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 4, 4, 6, }, +{7: 16, 8, 0, 2, 0, 0, 0, 6, 2, 4, 0, 4, 6, 0, 0, 0, }, +{b: 16, 0, 0, 0, 4, 10, 6, 4, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 2, 4, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:50, 4:38, 6:16, 8:9, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:5, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 8, -8, 0, 8, 0, -8, -16, 0, 0, }, +{2: 16, 8, 0, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 16, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, -8, 8, 0, 0, 0, -8, -8, 0, 8, 0, 8, -16, 0, 8, }, +{5: 16, -8, 8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, -8, 0, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 0, 8, -8, 8, -8, 8, -8, 0, 0, 0, -8, }, +{7: 16, -8, 0, 0, 8, 0, -8, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, , x, x, x, x, x, , , x, x, , , x, }, +{5: , , x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , , , , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{7: , , x, , , x, x, x, x, , , , , , , x, }, +{b: , x, , , x, , x, x, x, , , x, x, , , x, }, +{d: , , , x, x, , x, x, x, , , x, , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,1010,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x03,0x05,0x06,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x04,0x09,0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x04,0x09,0x0d,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +115 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x09,0x00,0x07,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, 4, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:69, 4:21, 6:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 0, 10, 4, 4, 0, 0, 0, 8, 0, 2, 0, 2, }, +{2: 16, 4, 10, 0, 0, 4, 0, 2, 0, 2, 8, 0, 0, 4, 10, 4, }, +{4: 16, 4, 0, 4, 0, 0, 6, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 16, 2, 0, 2, 4, 4, 2, 2, 2, 0, 0, 0, 4, 0, 0, 2, }, +{3: 16, 8, 4, 0, 4, 6, 2, 0, 4, 8, 0, 0, 10, 2, 0, 0, }, +{5: 16, 8, 2, 6, 0, 0, 4, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{6: 16, 10, 0, 0, 2, 0, 0, 4, 0, 4, 0, 6, 4, 0, 2, 0, }, +{9: 16, 0, 2, 0, 2, 4, 2, 2, 4, 4, 0, 2, 0, 0, 2, 0, }, +{a: 16, 0, 0, 6, 0, 8, 0, 2, 6, 4, 0, 4, 2, 0, 0, 0, }, +{c: 16, 0, 8, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 4, 6, }, +{7: 16, 4, 0, 2, 2, 0, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 0, 4, 6, 8, 2, 0, 0, 2, 0, 6, 4, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 4, 0, 2, 2, 0, 0, 2, 0, 6, 0, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:106, 2:50, 4:38, 6:16, 8:9, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:5, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 8, 0, 0, 8, -8, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -16, 0, 8, 8, 0, -8, -8, -8, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, 0, 0, 0, -8, 8, 0, 0, -8, 8, -8, 0, 8, -8, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, 0, 0, -8, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, 0, 0, -8, 0, 8, -8, 8, -8, 8, 0, -8, 0, 0, -8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, , x, x, x, x, , , x, x, , , x, }, +{5: , , x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , , , , , x, x, }, +{9: , , x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{c: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{7: , , x, x, , x, x, x, x, , , , , , , x, }, +{b: , , x, , , x, x, x, x, , , x, x, , , x, }, +{d: , , , , x, x, x, x, x, , , x, , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0b,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x08,0x09,}}, +{{0x01,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_116.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_116.txt new file mode 100644 index 0000000..6e4bd82 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_116.txt @@ -0,0 +1,410 @@ +116 Sbox: +LUT = { +0x0f,0x00,0x01,0x0a,0x02,0x05,0x06,0x07,0x04,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, }, +{2: 0, 0, 6, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{4: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 6, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, 2, 0, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 4, }, +{9: 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 6, 0, 2, 0, }, +{d: 0, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 4, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:78, 4:15, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, 6, 2, 0, 2, }, +{2: 16, 0, 6, 2, 0, 0, 6, 0, 4, 2, 4, 6, 4, 0, 6, 0, }, +{4: 16, 4, 0, 6, 6, 2, 6, 0, 4, 0, 4, 2, 0, 6, 0, 0, }, +{8: 16, 2, 2, 0, 4, 4, 0, 0, 2, 0, 0, 0, 6, 0, 2, 2, }, +{3: 16, 2, 0, 2, 8, 4, 4, 0, 0, 2, 0, 0, 4, 4, 0, 2, }, +{5: 16, 0, 6, 0, 0, 0, 4, 2, 2, 2, 2, 4, 2, 0, 0, 0, }, +{6: 16, 2, 0, 0, 0, 2, 0, 6, 6, 2, 0, 2, 0, 0, 0, 4, }, +{9: 16, 0, 4, 6, 0, 0, 0, 6, 6, 2, 0, 0, 4, 4, 2, 6, }, +{a: 16, 8, 0, 0, 0, 2, 2, 0, 0, 4, 4, 0, 6, 6, 0, 0, }, +{c: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{7: 16, 0, 4, 2, 4, 0, 8, 2, 0, 0, 2, 4, 0, 4, 2, 0, }, +{b: 16, 4, 4, 2, 6, 6, 0, 0, 4, 6, 0, 0, 6, 0, 2, 0, }, +{d: 16, 2, 2, 4, 0, 0, 0, 0, 6, 0, 2, 0, 2, 6, 0, 0, }, +{e: 16, 4, 6, 0, 2, 0, 0, 0, 0, 0, 8, 2, 0, 6, 4, 0, }, +{f: 16, 0, 0, 0, 0, 2, 0, 4, 6, 0, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:52, 4:35, 6:30, 8:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{c: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 0, 0, 0, -8, 0, 8, -8, -8, }, +{4: 16, -8, 8, -8, 0, 0, 8, -8, 0, -8, 0, 8, 8, -8, 0, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, 0, -8, -8, }, +{3: 16, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, -8, 8, 0, 8, }, +{6: 16, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, 8, }, +{9: 16, 0, 0, 0, -8, -8, -8, 8, 8, 0, -8, -8, 8, 0, -8, 8, }, +{a: 16, 0, 0, 0, -8, 0, 0, -16, -8, 0, 0, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 8, }, +{7: 16, 8, 0, -8, 0, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 8, -8, 8, 0, 0, 0, -8, }, +{d: 16, 0, 8, 0, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, 0, -8, }, +{e: 16, 0, 0, 0, 0, -8, 0, 8, -8, 0, 8, 0, 0, 0, 0, -16, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, , , , x, x, x, , x, , x, x, x, x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , x, , x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, x, x, x, , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,1010,1,}, +{1111,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x05,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x0b,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x08,}}, +{{0x05,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +116 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0a,0x08,0x05,0x06,0x07,0x0f,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x00, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 4, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 4, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 2, 0, 0, 2, 2, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 6, 2, 0, 0, }, +{d: 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:78, 4:15, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:6, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 0, 2, 0, 8, 0, 0, 4, 2, 4, 0, }, +{2: 16, 0, 6, 0, 2, 0, 6, 0, 4, 0, 6, 4, 4, 2, 6, 0, }, +{4: 16, 0, 2, 6, 0, 2, 0, 0, 6, 0, 0, 2, 2, 4, 0, 0, }, +{8: 16, 2, 0, 6, 4, 8, 0, 0, 0, 0, 0, 4, 6, 0, 2, 0, }, +{3: 16, 0, 0, 2, 4, 4, 0, 2, 0, 2, 2, 0, 6, 0, 0, 2, }, +{5: 16, 0, 6, 6, 0, 4, 4, 0, 0, 2, 2, 8, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 0, 0, 2, 6, 6, 0, 2, 2, 0, 0, 0, 4, }, +{9: 16, 0, 4, 4, 2, 0, 2, 6, 6, 0, 0, 0, 4, 6, 0, 6, }, +{a: 16, 4, 2, 0, 0, 2, 2, 2, 2, 4, 0, 0, 6, 0, 0, 0, }, +{c: 16, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 8, 2, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 6, 4, 0, 6, 4, 2, 0, 4, 6, 0, 0, 6, 2, 0, 0, }, +{d: 16, 2, 0, 6, 0, 4, 0, 0, 4, 6, 2, 4, 0, 6, 6, 0, }, +{e: 16, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, 4, 2, }, +{f: 16, 2, 0, 0, 2, 2, 0, 4, 6, 0, 2, 0, 0, 0, 0, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:52, 4:35, 6:30, 8:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:7, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 0, 0, -8, 8, -8, 0, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, -8, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, -8, 0, -8, 0, 0, 0, 0, -16, }, +{3: 16, 0, -8, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 8, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, }, +{6: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 8, -8, -8, 0, 0, 0, -8, 8, }, +{a: 16, 0, -8, 8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, -8, -8, 0, 8, -8, -8, 0, 0, -8, 0, 0, 8, 8, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, 8, 8, -8, 0, 0, -8, -8, 0, 8, 0, -8, 8, -8, 0, -8, }, +{e: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 8, -8, -8, }, +{f: 16, 0, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, -8, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, , , , x, , , , x, , x, , , , x, }, +{b: , x, x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , x, x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, , x, , , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0110,0101,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_117.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_117.txt new file mode 100644 index 0000000..1bc5338 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_117.txt @@ -0,0 +1,410 @@ +117 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0f,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, }, +{2: 0, 0, 4, 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +{8: 0, 0, 4, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{9: 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 2, 2, }, +{7: 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 2, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 4, 0, 2, }, +{e: 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:78, 4:15, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 2, 0, 0, 0, 0, 4, 2, 4, 6, 4, 6, 6, 0, 0, }, +{2: 16, 0, 8, 0, 6, 2, 10, 0, 0, 4, 0, 8, 0, 4, 2, 4, }, +{4: 16, 2, 0, 4, 6, 4, 0, 0, 0, 0, 0, 10, 0, 0, 2, 4, }, +{8: 16, 0, 4, 0, 6, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 6, 0, 8, 0, 0, 4, 6, 0, 4, 0, 0, 0, 2, }, +{5: 16, 0, 4, 0, 0, 2, 4, 2, 2, 0, 0, 4, 0, 2, 2, 2, }, +{6: 16, 4, 2, 2, 4, 0, 0, 4, 0, 2, 2, 8, 0, 0, 0, 4, }, +{9: 16, 0, 2, 2, 0, 4, 0, 0, 6, 6, 0, 0, 2, 0, 2, 0, }, +{a: 16, 6, 4, 0, 6, 4, 2, 0, 4, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 4, 0, 0, 4, 0, 4, 2, 0, 0, 4, 2, 0, 8, 2, 2, }, +{7: 16, 6, 4, 4, 0, 4, 6, 6, 0, 0, 0, 6, 2, 0, 2, 0, }, +{b: 16, 6, 0, 0, 2, 0, 0, 2, 2, 6, 2, 0, 4, 0, 0, 0, }, +{d: 16, 4, 0, 2, 0, 0, 0, 2, 0, 2, 6, 0, 2, 4, 0, 2, }, +{e: 16, 0, 2, 2, 4, 0, 4, 0, 2, 0, 2, 0, 0, 6, 2, 0, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:57, 4:36, 6:23, 8:5, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{9: 0, 8, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 0, 0, 0, 8, -8, -8, 0, 8, -8, }, +{2: 16, 8, 0, 8, 0, 0, 8, 0, -8, -8, 0, 8, -8, 0, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 8, 0, 8, 0, -8, 0, -8, -8, -8, }, +{8: 16, 0, -8, 8, 0, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, -8, 8, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 0, 0, -8, -8, -8, 0, 0, 8, 0, }, +{9: 16, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 8, -8, -8, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -16, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 0, 8, -8, 0, -8, 0, 0, 8, 8, -8, }, +{b: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, -8, 8, 0, }, +{e: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, x, , x, , x, x, x, x, , x, x, x, x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , x, , , , , x, x, x, x, x, x, , x, x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0100,1100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x07,0x09,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x0d,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +117 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0f,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{2: 0, 2, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{8: 0, 0, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 2, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 0, 4, 2, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 2, 2, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{f: 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:78, 4:15, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 2, 0, 2, 0, 4, 0, 6, 4, 6, 6, 4, 0, 0, }, +{2: 16, 2, 8, 0, 4, 0, 4, 2, 2, 4, 0, 4, 0, 0, 2, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 2, 2, 0, 0, 4, 0, 2, 2, 2, }, +{8: 16, 0, 6, 6, 6, 0, 0, 4, 0, 6, 4, 0, 2, 0, 4, 2, }, +{3: 16, 0, 2, 4, 2, 8, 2, 0, 4, 4, 0, 4, 0, 0, 0, 2, }, +{5: 16, 0, 10, 0, 0, 0, 4, 0, 0, 2, 4, 6, 0, 0, 4, 2, }, +{6: 16, 4, 0, 0, 2, 0, 2, 4, 0, 0, 2, 6, 2, 2, 0, 0, }, +{9: 16, 2, 0, 0, 2, 4, 2, 0, 6, 4, 0, 0, 2, 0, 2, 0, }, +{a: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 6, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 6, 2, 2, }, +{7: 16, 4, 8, 10, 0, 4, 4, 8, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 6, 0, 0, 2, 0, 0, 0, 2, 6, 0, 2, 4, 2, 0, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{f: 16, 0, 4, 4, 2, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:57, 4:36, 6:23, 8:5, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, -8, 8, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, 0, 8, 0, -8, 0, 8, 0, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 0, }, +{8: 16, 8, -8, 8, 0, 0, 8, -8, 8, 0, 0, -8, -8, 0, -8, -8, }, +{3: 16, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, 8, }, +{5: 16, 0, -8, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 8, -8, 0, 8, 0, }, +{9: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 0, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -16, 8, 8, 0, 8, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, }, +{f: 16, 0, 8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{7: , x, , , , , , x, x, x, x, , x, x, x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, x, x, x, , , x, x, x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0100,0111,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x0a,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x09,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x03,0x05,0x06,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_118.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_118.txt new file mode 100644 index 0000000..8550f99 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_118.txt @@ -0,0 +1,410 @@ +118 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x0f,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 4, }, +{8: 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 2, 4, 0, 2, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 6, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{c: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 2, 2, 0, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2, 4, 0, }, +{f: 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:78, 4:15, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 2, 4, 0, 0, 4, 6, 2, 0, 6, 0, 0, 0, 0, }, +{2: 16, 0, 6, 0, 2, 0, 6, 0, 6, 0, 4, 4, 6, 2, 4, 0, }, +{4: 16, 0, 0, 8, 0, 4, 2, 2, 0, 0, 0, 4, 4, 2, 2, 4, }, +{8: 16, 4, 0, 0, 6, 2, 0, 0, 6, 0, 0, 2, 2, 0, 2, 0, }, +{3: 16, 2, 0, 4, 2, 8, 2, 0, 4, 4, 2, 4, 0, 0, 0, 0, }, +{5: 16, 2, 6, 0, 0, 0, 4, 2, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 4, 0, 0, 0, 2, 0, 8, 0, 0, 0, 6, 6, 4, 0, 2, }, +{9: 16, 4, 6, 0, 4, 6, 0, 0, 6, 6, 0, 0, 4, 2, 0, 2, }, +{a: 16, 2, 2, 0, 0, 4, 0, 0, 4, 6, 2, 0, 2, 0, 2, 0, }, +{c: 16, 2, 4, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 2, }, +{7: 16, 4, 4, 6, 0, 6, 6, 4, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 16, 0, 6, 6, 2, 0, 0, 4, 4, 2, 0, 0, 6, 4, 0, 6, }, +{d: 16, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, 6, 6, 0, 0, }, +{e: 16, 0, 4, 0, 2, 0, 2, 2, 0, 2, 6, 0, 0, 2, 4, 0, }, +{f: 16, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 2, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:52, 4:35, 6:30, 8:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, 0, 8, -8, 0, -8, -8, 0, -8, 0, -8, }, +{2: 16, 0, 0, 8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -16, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, -8, 0, }, +{8: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, -8, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -16, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, }, +{6: 16, -8, -8, -8, 0, 0, 0, 0, 8, -8, 0, 8, 0, -8, 8, 0, }, +{9: 16, -8, 0, 8, -8, -8, 0, 0, 8, -8, 0, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, }, +{7: 16, -8, -8, -8, 8, 8, 8, 0, -8, 0, -8, -8, 8, 0, 0, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 8, 8, -8, 0, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 8, 0, }, +{e: 16, 8, 0, -8, -8, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, }, +{f: 16, 8, 0, -8, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{5: , x, x, , x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{c: , x, x, , x, x, x, , x, x, x, x, x, x, , x, }, +{7: , , x, , , , x, , x, x, x, , x, x, x, x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , x, x, , , , x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0100,0100,1,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x04,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x04,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0c,}, {0x02,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +118 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x0f,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, }, +{4: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, }, +{8: 0, 4, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 4, 2, 2, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 6, 0, 2, 0, 0, }, +{b: 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:158, 2:78, 4:15, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 0, 4, 2, 2, 4, 4, 2, 2, 4, 0, 0, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 6, 0, 6, 2, 4, 4, 6, 0, 4, 2, }, +{4: 16, 2, 0, 8, 0, 4, 0, 0, 0, 0, 0, 6, 6, 2, 0, 4, }, +{8: 16, 4, 2, 0, 6, 2, 0, 0, 4, 0, 2, 0, 2, 0, 2, 0, }, +{3: 16, 0, 0, 4, 2, 8, 0, 2, 6, 4, 0, 6, 0, 0, 0, 0, }, +{5: 16, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 4, 0, 2, 0, 0, 2, 8, 0, 0, 0, 4, 4, 4, 2, 2, }, +{9: 16, 6, 6, 0, 6, 4, 0, 0, 6, 4, 0, 0, 4, 2, 0, 2, }, +{a: 16, 2, 0, 0, 0, 4, 0, 0, 6, 6, 0, 2, 2, 0, 2, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 6, 4, 4, 2, 4, 6, 6, 0, 0, 0, 6, 0, 2, 0, 0, }, +{b: 16, 0, 6, 4, 2, 0, 0, 6, 4, 2, 0, 0, 6, 6, 0, 4, }, +{d: 16, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 4, 6, 2, 0, }, +{e: 16, 0, 4, 2, 2, 0, 2, 0, 0, 2, 6, 0, 0, 0, 4, 2, }, +{f: 16, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 6, 0, 0, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:104, 2:52, 4:35, 6:30, 8:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, 0, 0, -16, 0, 0, 0, -8, -8, 0, 0, }, +{2: 16, 0, -8, 8, 0, -8, 8, -8, 8, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, -8, 0, -8, 0, 8, 0, 0, 8, 8, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 8, 0, -8, 0, 0, -8, }, +{3: 16, 0, -8, 8, 0, 0, 0, 0, -8, -8, -8, 0, 8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -16, 0, -8, 0, 0, 8, 0, 0, 8, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 8, 8, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, -8, -8, 8, 0, 0, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 8, 0, 8, 8, -8, -8, -8, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 8, 0, -8, 8, -8, 0, 8, -8, }, +{d: 16, 8, 0, -8, 0, -8, -8, 0, 8, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, -8, -8, 0, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, , x, x, x, , , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{7: , , x, , , , x, , x, x, x, , x, x, x, x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, , , , , x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0100,0110,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x04,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x02,0x09,0x0b,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_119.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_119.txt new file mode 100644 index 0000000..7d32837 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_119.txt @@ -0,0 +1,422 @@ +119 Sbox: +LUT = { +0x06,0x08,0x01,0x0b,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x02,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 2, 2, 0, 6, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 2, 0, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, }, +{f: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 6, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, }, +{2: 16, 4, 10, 0, 4, 6, 4, 0, 4, 6, 0, 4, 6, 0, 0, 0, }, +{4: 16, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 16, 4, 4, 0, 0, }, +{8: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 6, 6, 6, 0, 6, 4, 4, 2, 0, 0, 4, 0, 2, 0, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 16, 0, 4, 0, 0, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 6, 0, 6, 0, 4, 0, 0, 6, 2, 4, 0, 6, 0, 4, }, +{c: 16, 0, 0, 2, 0, 2, 4, 0, 0, 6, 2, 0, 0, 0, 2, 6, }, +{7: 16, 2, 0, 6, 2, 4, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +{b: 16, 0, 6, 2, 2, 0, 4, 0, 6, 0, 6, 4, 6, 0, 4, 0, }, +{d: 16, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 6, 2, 6, 0, }, +{e: 16, 0, 0, 2, 2, 0, 0, 2, 2, 4, 0, 4, 0, 6, 2, 0, }, +{f: 16, 2, 0, 0, 0, 0, 0, 2, 2, 0, 6, 4, 4, 2, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:48, 4:45, 6:27, 10:1, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{c: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, -16, 8, 8, 0, 8, -8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{4: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, 0, -8, 8, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 8, }, +{6: 16, 8, -16, -8, 0, -8, 0, 8, 8, 0, 8, 0, -8, 0, -8, 0, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, -8, 0, 0, -8, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, -8, 8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 8, 0, -8, 0, -8, 8, 0, -8, }, +{d: 16, 0, 0, -8, 0, -8, 0, -8, 0, 8, -8, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 0, 8, 0, 0, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{5: , x, , , x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , , x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , x, , , , x, , , x, x, , x, x, , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0100,0100,1,}, +{0110,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x02,}}, +{{0x0a,0x0c,}, {0x01,0x02,0x03,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +119 Inverse Sbox: +LUT = { +0x08,0x02,0x0b,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x03,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +{3: 0, 2, 2, 0, 0, 6, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 2, 0, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, }, +{b: 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 6, 2, 0, 0, }, +{d: 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, 2, 0, }, +{f: 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 6, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 16, 4, 10, 4, 4, 6, 0, 4, 4, 6, 0, 0, 6, 0, 0, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 0, 0, 2, 6, 2, 2, 2, 0, }, +{8: 16, 2, 4, 0, 4, 0, 0, 0, 2, 6, 0, 2, 2, 0, 2, 0, }, +{3: 16, 6, 6, 4, 0, 6, 6, 4, 2, 0, 2, 4, 0, 0, 0, 0, }, +{5: 16, 0, 4, 4, 0, 4, 4, 16, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 16, 2, 0, 0, 2, 4, 6, 4, 0, 0, 0, 0, 0, 2, 2, 2, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 6, 4, 6, 0, 0, 4, 0, 6, 6, 0, 0, 2, 4, 0, }, +{c: 16, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, 6, 0, 0, 6, }, +{7: 16, 0, 4, 16, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 16, 0, 6, 4, 2, 0, 2, 4, 6, 0, 0, 0, 6, 6, 0, 4, }, +{d: 16, 0, 0, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 2, 6, 2, }, +{e: 16, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 4, 6, 2, 0, }, +{f: 16, 0, 0, 0, 2, 0, 2, 4, 2, 4, 6, 2, 0, 0, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:48, 4:45, 6:27, 10:1, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{c: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{7: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 8, -8, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, -8, -8, 8, 0, 0, 0, -8, 8, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, -8, 0, 0, -8, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, 0, 8, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, }, +{7: 16, 0, -16, -8, 0, 0, 8, 8, 0, 0, 8, -8, 0, 8, -8, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 8, 0, -8, 8, -8, 8, 0, -8, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, 8, -8, -8, 0, }, +{e: 16, 0, 0, -8, 0, -8, -8, 8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , , x, x, , x, x, , , x, }, +{5: , x, , , x, , x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , , x, x, , , , x, x, , , , x, x, , x, }, +{a: , , , x, x, x, , , x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , , , , , , x, x, , x, x, , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, x, x, , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x02,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_120.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_120.txt new file mode 100644 index 0000000..c8ba717 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_120.txt @@ -0,0 +1,422 @@ +120 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x0a,0x06,0x07,0x00,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 0, }, +{8: 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 2, 2, 0, }, +{a: 0, 4, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 6, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, }, +{d: 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 4, 10, 0, 0, 8, 8, 2, 0, 4, 0, 2, 0, }, +{2: 16, 8, 10, 8, 0, 8, 10, 8, 0, 2, 0, 8, 0, 2, 0, 0, }, +{4: 16, 0, 10, 4, 0, 0, 6, 4, 0, 0, 2, 4, 2, 0, 0, 0, }, +{8: 16, 10, 0, 4, 4, 0, 4, 0, 6, 0, 0, 2, 0, 0, 0, 2, }, +{3: 16, 4, 4, 2, 0, 8, 0, 2, 2, 0, 4, 0, 2, 0, 0, 4, }, +{5: 16, 0, 4, 2, 0, 0, 4, 2, 0, 2, 0, 4, 2, 2, 2, 0, }, +{6: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 4, 0, 0, 6, 0, 0, 2, 4, 2, 0, 2, 0, 2, 2, 0, }, +{a: 16, 8, 0, 4, 0, 2, 6, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 0, 0, 2, 6, 6, 4, 4, 4, 6, 0, 0, 2, 0, 6, }, +{7: 16, 2, 4, 0, 2, 2, 4, 0, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 4, 2, 2, 2, 0, 0, 0, 0, 4, 2, 0, 4, 2, 0, 2, }, +{d: 16, 0, 2, 2, 0, 4, 0, 0, 6, 4, 2, 0, 0, 2, 2, 0, }, +{e: 16, 2, 0, 0, 0, 4, 4, 4, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:59, 4:40, 6:12, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 0, 4, 0, 4, 12, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:10, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -16, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +{2: 16, 0, 0, 0, 8, -16, 16, -16, 0, 0, 0, 0, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 0, 0, -8, -8, 0, 8, 0, -8, }, +{8: 16, 0, 8, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, -8, -8, -8, }, +{3: 16, 0, 0, 0, 0, 8, -16, -8, 0, -8, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, 0, 8, -8, 8, 0, 0, 0, 0, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 0, -8, -8, 0, 8, 0, 0, 0, }, +{a: 16, -8, 0, 8, 0, -8, 0, -8, -8, 8, 0, 0, 0, -8, 8, 0, }, +{c: 16, -8, 0, 0, 0, 8, 0, -8, -8, -8, 8, 8, 0, -8, -8, 8, }, +{7: 16, -8, -8, 0, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 8, 0, 0, 0, -8, 0, 0, -8, }, +{d: 16, 8, 0, 0, -8, -8, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, , x, x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , x, x, x, , , x, , , x, , x, , , , x, }, +{b: , , , , x, x, x, , , x, , , x, , , x, }, +{d: , x, , x, x, x, x, , , x, , , , x, , x, }, +{e: , x, x, x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x05,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +120 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x0a,0x06,0x07,0x01,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 0, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 6, 2, 0, 0, 0, 0, }, +{5: 0, 0, 6, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 4, 2, }, +{9: 0, 4, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, 2, 0, }, +{c: 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 8, 0, 10, 4, 0, 0, 4, 8, 0, 2, 4, 0, 2, 0, }, +{2: 16, 4, 10, 10, 0, 4, 4, 8, 0, 0, 0, 4, 2, 2, 0, 0, }, +{4: 16, 0, 8, 4, 4, 2, 2, 4, 0, 4, 0, 0, 2, 2, 0, 0, }, +{8: 16, 4, 0, 0, 4, 0, 0, 2, 6, 0, 2, 2, 2, 0, 0, 2, }, +{3: 16, 10, 8, 0, 0, 8, 0, 0, 0, 2, 6, 2, 0, 4, 4, 4, }, +{5: 16, 0, 10, 6, 4, 0, 4, 4, 0, 6, 6, 4, 0, 0, 4, 0, }, +{6: 16, 0, 8, 4, 0, 2, 2, 4, 2, 0, 4, 0, 0, 0, 4, 2, }, +{9: 16, 8, 0, 0, 6, 2, 0, 2, 4, 0, 4, 0, 0, 6, 0, 0, }, +{a: 16, 8, 2, 0, 0, 0, 2, 0, 2, 4, 4, 0, 4, 4, 2, 0, }, +{c: 16, 2, 0, 2, 0, 4, 0, 0, 0, 0, 6, 0, 2, 2, 0, 6, }, +{7: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 4, 0, 2, 0, 2, 2, 0, 0, 6, 0, 2, 4, 0, 0, 2, }, +{d: 16, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, }, +{e: 16, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:59, 4:40, 6:12, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +{b: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:10, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, 0, 8, -16, 8, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 0, -8, 16, -8, 0, 0, -8, 0, 0, -8, }, +{4: 16, 0, 8, 0, 0, 8, 0, -8, 0, 0, -8, 8, 0, -8, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, 0, 0, 0, 8, -8, -8, -16, -8, 8, -8, 0, 0, 8, 8, }, +{5: 16, 8, 0, 0, 8, -8, 8, -16, 0, 0, 0, -8, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 8, 0, 0, -8, 8, }, +{9: 16, -8, 8, 8, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, }, +{a: 16, 0, 0, 0, -8, -16, 8, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{c: 16, -8, 0, 0, 0, 8, -8, -8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{b: 16, -8, -8, 0, 0, 8, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, }, +{e: 16, -8, 0, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , x, x, , , x, , , x, , x, , , , x, }, +{b: , x, x, , x, , x, , , x, , , x, , , x, }, +{d: , x, , , x, , x, , , x, , , , x, , x, }, +{e: , x, x, , x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,1010,1,}, +{0110,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_121.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_121.txt new file mode 100644 index 0000000..441e02a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_121.txt @@ -0,0 +1,422 @@ +121 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x0f,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, }, +{2: 0, 0, 6, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, }, +{8: 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 2, 2, 0, }, +{9: 0, 2, 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 4, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 2, 2, 0, 4, 0, 4, 6, 4, 6, 6, 0, 0, }, +{2: 16, 0, 10, 0, 4, 0, 6, 0, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 0, 0, 4, 2, 4, 2, 0, 0, 0, 0, 6, 2, 0, 2, 2, }, +{8: 16, 0, 8, 0, 6, 0, 0, 0, 4, 4, 2, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 6, 0, 8, 0, 0, 4, 6, 0, 4, 0, 0, 0, 2, }, +{5: 16, 0, 4, 2, 0, 2, 4, 2, 2, 0, 0, 6, 0, 0, 0, 2, }, +{6: 16, 4, 2, 0, 0, 0, 0, 4, 0, 2, 2, 6, 0, 2, 2, 0, }, +{9: 16, 2, 0, 2, 2, 4, 0, 0, 6, 6, 0, 0, 0, 0, 2, 0, }, +{a: 16, 4, 10, 0, 4, 4, 2, 0, 8, 6, 0, 0, 8, 2, 0, 0, }, +{c: 16, 8, 0, 2, 0, 0, 0, 6, 0, 0, 4, 4, 0, 6, 0, 2, }, +{7: 16, 8, 4, 4, 0, 4, 4, 10, 0, 0, 0, 10, 0, 0, 2, 2, }, +{b: 16, 10, 0, 0, 2, 2, 0, 4, 0, 6, 0, 4, 4, 0, 0, 0, }, +{d: 16, 4, 4, 2, 0, 0, 2, 0, 0, 2, 8, 0, 2, 4, 4, 0, }, +{e: 16, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 4, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:50, 4:37, 6:21, 8:7, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, -8, 0, -8, 0, 8, 0, -8, -8, 8, -8, }, +{2: 16, 8, 0, 8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 8, -8, 0, -8, -8, 8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, -8, 8, }, +{5: 16, -8, 0, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, 8, -8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 8, -16, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 0, 16, -8, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, 0, 0, -8, 0, 0, 0, -8, 8, -8, -8, 8, 0, }, +{d: 16, 0, 8, -8, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, 8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, x, , x, , x, x, x, x, , x, x, x, x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, , , x, x, x, x, x, x, , x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,1100,1,}, +{0110,0111,0,}, +{0110,1010,1,}, +{0110,1101,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x01,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x06,0x09,0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +121 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x0f,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{2: 0, 0, 6, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{8: 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 0, 2, 0, }, +{9: 0, 0, 2, 0, 4, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 4, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 6, 0, 0, 0, 0, }, +{b: 0, 2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 4, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 4, 2, 4, 8, 8, 10, 4, 0, 0, }, +{2: 16, 0, 10, 0, 8, 0, 4, 2, 0, 10, 0, 4, 0, 4, 2, 4, }, +{4: 16, 0, 0, 4, 0, 6, 2, 0, 2, 0, 2, 4, 0, 2, 2, 0, }, +{8: 16, 2, 4, 2, 6, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 4, 0, 8, 2, 0, 4, 4, 0, 4, 2, 0, 0, 2, }, +{5: 16, 0, 6, 2, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 2, }, +{6: 16, 4, 0, 0, 0, 0, 2, 4, 0, 0, 6, 10, 4, 0, 2, 0, }, +{9: 16, 0, 6, 0, 4, 4, 2, 0, 6, 8, 0, 0, 0, 0, 2, 0, }, +{a: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 6, 4, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 8, 0, 6, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 6, 4, 2, 6, 0, 0, 0, 0, 8, 0, 0, 4, 2, 0, 0, }, +{d: 16, 6, 0, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 4, 2, 2, }, +{e: 16, 0, 6, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 2, 4, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:50, 4:37, 6:21, 8:7, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 8, -8, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 16, -8, 8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, -8, -8, }, +{3: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, -8, -8, 0, 0, -8, 0, 0, 0, -8, 8, -8, 8, 8, 0, }, +{9: 16, 0, 0, 8, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -16, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 0, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, 0, -8, 8, 0, -8, -8, 8, 0, }, +{7: 16, 0, 0, -16, 8, 8, 0, 0, -8, -8, -8, -8, 0, 8, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 0, 8, -8, 0, 0, -8, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 8, 8, 0, 0, -8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , , x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, , , x, , x, x, x, x, , x, x, x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , x, x, x, , x, x, x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,0111,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x02,0x09,0x0b,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_122.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_122.txt new file mode 100644 index 0000000..113715d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_122.txt @@ -0,0 +1,422 @@ +122 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x0b,0x07,0x00,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 0, 2, 0, 4, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, }, +{5: 0, 2, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 4, }, +{9: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 4, 0, }, +{c: 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{f: 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 0, 0, 10, 0, 2, 2, 0, 6, 0, 0, 4, 4, 4, }, +{2: 16, 4, 10, 0, 10, 4, 2, 0, 4, 8, 0, 0, 4, 0, 0, 2, }, +{4: 16, 0, 0, 4, 0, 4, 2, 0, 2, 2, 2, 6, 0, 2, 0, 0, }, +{8: 16, 2, 8, 4, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 4, 8, 10, 0, 6, 4, 8, 2, 0, 0, 4, 0, 0, 2, 0, }, +{5: 16, 2, 0, 0, 2, 4, 4, 6, 2, 0, 0, 0, 2, 2, 0, 0, }, +{6: 16, 0, 2, 0, 0, 8, 4, 4, 0, 0, 4, 2, 2, 0, 2, 4, }, +{9: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 0, 2, 4, 2, 2, 0, }, +{a: 16, 2, 8, 0, 4, 0, 0, 0, 0, 4, 4, 2, 2, 2, 4, 0, }, +{c: 16, 4, 0, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 6, 0, 2, }, +{7: 16, 2, 0, 6, 0, 8, 0, 0, 0, 2, 4, 4, 0, 0, 0, 6, }, +{b: 16, 0, 10, 4, 6, 0, 0, 6, 4, 4, 6, 0, 4, 0, 4, 0, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, }, +{f: 16, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:59, 4:40, 6:12, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, -16, 0, -8, -8, 8, -8, -8, 0, 8, 8, }, +{2: 16, 8, -8, 8, 0, -8, 16, -8, 0, 0, 0, -8, -8, 0, -8, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 8, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, -8, -8, -8, }, +{3: 16, 0, -8, 0, 8, 0, -16, 0, 0, -8, 0, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, }, +{6: 16, 0, -16, -8, 0, 0, 0, 8, 8, 0, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, -8, 8, 0, 0, 8, 0, 8, -8, }, +{c: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, }, +{7: 16, -8, -8, 0, 8, 8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 0, }, +{b: 16, 8, -8, 8, 0, 0, 0, -8, 8, -8, 0, 0, -16, 8, 0, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, x, x, x, , , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{b: , , x, , x, , , x, x, x, , , , , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, , , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1011,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x05,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x02,}, {0x05,}}, +{{0x09,0x02,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +122 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x0b,0x07,0x01,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 2, }, +{4: 0, 0, 0, 4, 4, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, }, +{5: 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{6: 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{9: 0, 2, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 4, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 2, 0, }, +{c: 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 4, 0, 2, 2, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 2, 4, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 8, 10, 0, 8, 8, 0, 2, 8, 8, 0, 0, 10, 0, 0, 2, }, +{4: 16, 0, 0, 4, 4, 10, 0, 0, 2, 0, 0, 6, 4, 2, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 2, 0, 4, 4, 2, 0, 6, 0, 0, 0, }, +{3: 16, 10, 4, 4, 0, 6, 4, 8, 0, 0, 2, 8, 0, 0, 2, 0, }, +{5: 16, 0, 2, 2, 2, 4, 4, 4, 0, 0, 2, 0, 0, 2, 0, 2, }, +{6: 16, 2, 0, 0, 4, 8, 6, 4, 0, 0, 0, 0, 6, 0, 0, 2, }, +{9: 16, 2, 4, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, 2, 0, }, +{a: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 0, 2, 4, 2, 2, 0, }, +{c: 16, 6, 0, 2, 0, 0, 0, 4, 0, 4, 6, 4, 6, 6, 0, 2, }, +{7: 16, 0, 0, 6, 0, 4, 0, 2, 2, 2, 0, 4, 0, 0, 2, 2, }, +{b: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 2, 2, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 4, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 4, 2, 2, 2, }, +{f: 16, 4, 2, 0, 2, 0, 0, 4, 0, 0, 2, 6, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:59, 4:40, 6:12, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{8: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 12, 0, 0, 4, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 0, -16, 0, 0, -8, -8, 0, 8, 0, }, +{2: 16, 0, -16, 8, 0, 0, 0, -8, 16, 0, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, 0, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, -8, 0, 0, 0, 0, -8, -8, 0, -8, 8, -8, 0, }, +{3: 16, -8, -8, 0, 8, 8, -8, 0, -16, -8, 8, 0, 8, 0, 0, 0, }, +{5: 16, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 8, -8, -8, 0, 8, }, +{9: 16, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 8, -8, 0, 0, -8, 8, -8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{c: 16, -8, 8, 0, 0, 0, -8, 0, 0, 8, 8, -8, -8, -8, 8, -8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 8, }, +{f: 16, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, , , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{7: , , , x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , , x, x, , x, x, x, , , , , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , x, , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x03,0x09,0x0a,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x01,0x04,0x05,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_123.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_123.txt new file mode 100644 index 0000000..2118113 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_123.txt @@ -0,0 +1,422 @@ +123 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x0d,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, }, +{8: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 0, 0, 0, 6, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{a: 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 4, 0, }, +{f: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 2, 2, 4, 2, 0, 4, 0, 0, 0, }, +{2: 16, 0, 10, 0, 4, 0, 6, 0, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 8, 0, 4, 0, 0, 6, 0, 0, 0, 4, 2, 0, 6, 0, 2, }, +{8: 16, 2, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, }, +{3: 16, 0, 0, 2, 4, 8, 4, 6, 2, 0, 0, 0, 6, 0, 0, 0, }, +{5: 16, 10, 4, 4, 0, 4, 6, 8, 0, 0, 0, 8, 2, 0, 0, 2, }, +{6: 16, 0, 2, 0, 0, 4, 4, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{9: 16, 0, 10, 0, 4, 0, 2, 0, 4, 6, 0, 0, 4, 2, 0, 0, }, +{a: 16, 6, 0, 0, 0, 2, 0, 4, 0, 6, 4, 4, 6, 6, 2, 0, }, +{c: 16, 0, 4, 0, 2, 2, 0, 0, 0, 0, 4, 2, 0, 2, 6, 2, }, +{7: 16, 2, 4, 2, 0, 2, 6, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{f: 16, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 0, 4, 0, 4, 12, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{5: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 8, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, -8, 0, -8, 8, 8, }, +{2: 16, 8, -8, 8, 0, -16, 8, -8, 0, 0, 0, -8, 0, 8, -8, 0, }, +{4: 16, 0, 8, -16, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, 0, 0, 8, 0, 8, -8, 0, 0, -8, -8, 8, 0, -8, -8, 0, }, +{5: 16, -8, 0, -8, 8, -8, 0, 0, 0, 8, -8, 8, -16, 0, 0, 8, }, +{6: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, 8, 0, 0, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, -8, 0, 8, 0, -8, -8, 0, -8, 8, 8, 0, 0, -8, 8, -8, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 8, 0, 0, 0, -16, 8, 0, -8, }, +{d: 16, 8, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 16, 0, 0, -8, }, +{f: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, , x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, , x, , , x, x, x, }, +{7: , x, x, , , , x, x, x, , x, x, , x, , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, , , x, x, x, x, x, , x, , , , , x, }, +{e: , x, x, , , x, x, x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0100,0100,1,}, +{1011,0101,1,}, +{1011,1011,1,}, +{1011,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x0b,}}, +{{0x01,0x0a,0x04,}, {0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +123 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x0d,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 6, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{8: 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 4, 4, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 6, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 4, 4, 0, 0, 0, 0, 0, 2, 0, 2, }, +{9: 0, 2, 2, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{c: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 4, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 8, 2, 0, 10, 0, 0, 6, 0, 2, 4, 0, 4, 4, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 10, 0, 4, 4, 8, 2, 4, 0, }, +{4: 16, 4, 0, 4, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +{8: 16, 0, 4, 0, 6, 4, 0, 0, 4, 0, 2, 0, 10, 0, 0, 2, }, +{3: 16, 2, 0, 0, 4, 8, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, }, +{5: 16, 4, 6, 6, 0, 4, 6, 4, 2, 0, 0, 6, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 0, 6, 8, 4, 0, 4, 0, 0, 0, 2, 0, 6, }, +{9: 16, 2, 6, 0, 2, 2, 0, 2, 4, 0, 0, 0, 4, 0, 2, 0, }, +{a: 16, 4, 4, 0, 0, 0, 0, 0, 6, 6, 0, 0, 8, 2, 2, 0, }, +{c: 16, 2, 4, 4, 0, 0, 0, 0, 0, 4, 4, 2, 2, 2, 8, 0, }, +{7: 16, 0, 4, 2, 0, 0, 8, 2, 0, 4, 2, 4, 0, 0, 2, 4, }, +{b: 16, 4, 4, 0, 6, 6, 2, 0, 4, 6, 0, 0, 6, 0, 0, 2, }, +{d: 16, 0, 0, 6, 0, 0, 0, 2, 2, 6, 2, 0, 0, 2, 4, 0, }, +{e: 16, 0, 6, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 8, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 8, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, 8, 0, -16, 8, -8, -8, 0, -8, 8, 0, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 16, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, -8, -8, }, +{8: 16, -8, 0, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, }, +{3: 16, 0, 0, 8, 0, 8, 0, 0, -16, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 8, -8, 8, -8, 8, -8, 0, 0, -8, 0, 0, 8, -8, 0, }, +{6: 16, -8, 0, -8, 8, -8, 0, 0, 0, 0, 0, 8, -8, -8, 0, 8, }, +{9: 16, 0, 0, 8, 0, -8, -8, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, 0, -16, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, }, +{c: 16, 0, 8, -8, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, 8, -8, }, +{7: 16, 0, -8, -16, 0, 8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, -8, 8, -8, 8, 0, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, 8, 0, -8, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 8, -8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , x, , , , x, x, x, , x, x, , x, , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, , x, x, x, , x, , , , , x, }, +{e: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,1010,1,}, +{0100,0111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_124.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_124.txt new file mode 100644 index 0000000..bc52b6d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_124.txt @@ -0,0 +1,422 @@ +124 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x0a,0x00,0x09,0x07,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{5: 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 4, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 4, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 0, 0, 10, 0, 2, 2, 0, 6, 0, 0, 4, 4, 4, }, +{2: 16, 4, 10, 4, 0, 4, 8, 4, 0, 2, 0, 10, 0, 0, 0, 2, }, +{4: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 2, 0, 2, 4, 4, 2, 2, 2, 0, 0, 0, 4, 0, 0, 2, }, +{3: 16, 4, 8, 0, 4, 6, 0, 2, 8, 4, 0, 0, 10, 0, 2, 0, }, +{5: 16, 2, 8, 2, 2, 0, 4, 0, 4, 0, 0, 4, 4, 2, 0, 0, }, +{6: 16, 0, 10, 4, 0, 0, 4, 4, 4, 0, 4, 6, 6, 0, 6, 0, }, +{9: 16, 0, 0, 2, 2, 4, 2, 0, 4, 6, 0, 0, 0, 2, 2, 0, }, +{a: 16, 2, 0, 0, 0, 8, 0, 0, 4, 4, 4, 2, 2, 2, 0, 4, }, +{c: 16, 4, 0, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 6, 0, 2, }, +{7: 16, 2, 8, 2, 0, 0, 4, 0, 0, 2, 4, 4, 0, 0, 4, 2, }, +{b: 16, 0, 2, 0, 6, 8, 0, 2, 0, 0, 6, 0, 4, 0, 0, 4, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:60, 4:41, 6:11, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, -16, 0, -8, -8, 8, -8, -8, 0, 8, 8, }, +{2: 16, 0, -8, 0, 8, -8, 16, -8, 0, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 8, -8, 0, 8, 0, 0, 0, -8, -8, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 0, 0, -16, 0, 0, -8, 0, 8, 8, 0, -8, 8, }, +{5: 16, -8, 8, 0, 0, 0, 0, -8, 0, 8, -8, 8, -8, 0, 0, -8, }, +{6: 16, 8, -16, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 8, 0, -8, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, -8, -8, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -8, 8, 0, }, +{c: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, -8, 8, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, 8, 0, 0, 0, -16, 0, 0, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, }, +{f: 16, 8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , , , x, , x, }, +{6: , x, , x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{7: , x, , x, , x, x, x, , x, , , , , , x, }, +{b: , , x, , x, , x, x, , x, , x, x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, , , x, x, , x, , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1011,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x05,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x01,0x02,0x03,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +124 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x0a,0x01,0x09,0x07,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, }, +{5: 0, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, }, +{9: 0, 2, 0, 2, 2, 4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 2, }, +{c: 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 2, 4, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 8, 10, 8, 0, 8, 8, 10, 0, 0, 0, 8, 2, 0, 0, 2, }, +{4: 16, 0, 4, 4, 2, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, }, +{8: 16, 0, 0, 2, 4, 4, 2, 0, 2, 0, 2, 0, 6, 0, 0, 2, }, +{3: 16, 10, 4, 0, 4, 6, 0, 0, 4, 8, 2, 0, 8, 0, 2, 0, }, +{5: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 2, 4, 4, 2, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, }, +{9: 16, 2, 0, 2, 2, 8, 4, 4, 4, 4, 0, 0, 0, 2, 0, 0, }, +{a: 16, 0, 2, 0, 0, 4, 0, 0, 6, 4, 0, 2, 0, 2, 2, 2, }, +{c: 16, 6, 0, 2, 0, 0, 0, 4, 0, 4, 6, 4, 6, 6, 0, 2, }, +{7: 16, 0, 10, 4, 0, 0, 4, 6, 0, 2, 0, 4, 0, 0, 2, 0, }, +{b: 16, 0, 0, 0, 4, 10, 4, 6, 0, 2, 0, 0, 4, 0, 0, 2, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 4, 0, 0, 0, 2, 0, 6, 2, 0, 0, 4, 0, 2, 2, 2, }, +{f: 16, 4, 2, 0, 2, 0, 0, 0, 0, 4, 2, 2, 4, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:60, 4:41, 6:11, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 8, 8, 4, 4, 4, 0, 0, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 12, 0, 0, 4, }, +{d: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 0, -16, 0, 0, -8, -8, 0, 8, 0, }, +{2: 16, 8, -16, 0, 8, -8, 0, 0, 16, -8, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, -8, 8, 0, 0, -8, -8, -16, 0, 8, 0, 8, -8, 0, 8, }, +{5: 16, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, 8, -8, -8, 0, 0, }, +{9: 16, -8, 8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 8, -8, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, -8, 8, 0, 0, 0, }, +{c: 16, -8, 8, 0, 0, 0, -8, 0, 0, 8, 8, -8, -8, -8, 8, -8, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, -8, -8, 0, 0, 0, 0, -8, 0, 8, -8, 8, -8, 0, 0, 8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, -8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , , , x, , x, }, +{6: , x, , x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{a: , x, , x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{7: , , , x, , x, x, x, , x, , , , , , x, }, +{b: , x, , , x, x, x, x, , x, , x, x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , x, , x, x, , x, , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x06,0x09,0x0f,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_125.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_125.txt new file mode 100644 index 0000000..f9e0f6d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_125.txt @@ -0,0 +1,422 @@ +125 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x0d,0x04,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{2: 0, 0, 6, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, }, +{8: 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 2, 0, 4, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 2, 2, 0, }, +{9: 0, 2, 0, 4, 2, 2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, }, +{b: 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 2, }, +{e: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 10, 0, 4, 0, 6, 0, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 4, 0, 4, 2, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 2, }, +{8: 16, 0, 8, 0, 6, 0, 0, 0, 4, 4, 2, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 6, 4, 4, 6, 6, 4, 0, 0, 0, 2, 6, }, +{5: 16, 4, 4, 10, 0, 8, 6, 4, 0, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 0, 2, 0, 0, 4, 4, 4, 0, 2, 2, 2, 0, 2, 2, 0, }, +{9: 16, 2, 0, 4, 2, 10, 0, 0, 4, 6, 0, 4, 0, 0, 0, 0, }, +{a: 16, 4, 10, 0, 4, 4, 2, 0, 8, 6, 0, 0, 8, 2, 0, 0, }, +{c: 16, 0, 0, 6, 0, 8, 0, 2, 0, 0, 4, 4, 0, 2, 0, 6, }, +{7: 16, 2, 4, 2, 0, 0, 6, 2, 0, 0, 0, 4, 2, 2, 0, 0, }, +{b: 16, 4, 0, 0, 2, 2, 0, 2, 0, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 2, 4, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 6, 2, }, +{e: 16, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 4, 0, 2, 4, 0, 2, 2, 0, 8, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 8, -8, -8, 8, -8, }, +{2: 16, 8, 0, 8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 8, -8, 0, -8, -8, 8, -8, 0, }, +{3: 16, -8, -8, 8, 0, 0, -8, 0, -8, 0, 8, 0, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 8, 0, 0, -16, -8, 0, 0, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, 0, 0, -8, 0, 0, 0, -8, -8, 8, -8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 8, -16, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, -8, -8, 8, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, -8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{5: , , x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , x, , , x, x, x, }, +{9: , x, x, x, x, x, , x, x, , x, x, x, , , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, , x, x, , , x, x, }, +{7: , , x, x, , x, , x, x, , x, , , x, , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, , , x, x, , x, x, , , , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,1100,1,}, +{0110,0101,1,}, +{0110,1010,1,}, +{0110,1111,0,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +125 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x0d,0x00,0x09,0x0a,0x0b,0x0c,0x07,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, }, +{2: 0, 0, 6, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{8: 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 6, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{6: 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 2, 2, }, +{9: 0, 0, 2, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 4, 0, 0, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{b: 0, 4, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 10, 0, 8, 0, 4, 2, 0, 10, 0, 4, 0, 4, 2, 4, }, +{4: 16, 4, 0, 4, 0, 0, 10, 0, 4, 0, 6, 2, 0, 0, 2, 0, }, +{8: 16, 2, 4, 2, 6, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 6, 8, 4, 10, 4, 8, 0, 2, 0, 0, 4, }, +{5: 16, 4, 6, 6, 0, 4, 6, 4, 0, 2, 0, 6, 0, 0, 2, 0, }, +{6: 16, 2, 0, 0, 0, 4, 4, 4, 0, 0, 2, 2, 2, 0, 2, 2, }, +{9: 16, 0, 6, 0, 4, 6, 0, 0, 4, 8, 0, 0, 0, 0, 2, 2, }, +{a: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 4, 0, 2, 4, 2, 2, 0, 0, 4, 0, 2, 4, 0, 8, }, +{7: 16, 0, 4, 2, 0, 0, 8, 2, 4, 0, 4, 4, 0, 2, 0, 2, }, +{b: 16, 4, 4, 2, 6, 0, 0, 0, 0, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 6, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 6, 2, 4, }, +{f: 16, 0, 0, 2, 2, 6, 0, 0, 0, 0, 6, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 8, 0, 0, 4, 4, }, +{7: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, -8, 8, 8, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, -8, -8, }, +{3: 16, -16, 0, 8, 8, 0, -8, -8, -8, 0, 0, 8, 0, 0, -8, 8, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, -8, 8, -8, 0, 0, 8, -8, 0, }, +{6: 16, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, -16, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 0, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 8, 0, }, +{7: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, 0, 0, 0, 0, -8, 8, -8, -8, 0, -8, 8, -8, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , , x, x, x, x, , x, x, , x, , x, x, , x, }, +{5: , , x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, x, , x, , , x, x, x, }, +{9: , , x, x, x, x, , x, x, , x, x, x, , , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, x, , x, x, , , x, x, }, +{7: , , x, , , x, , x, x, , x, , , x, , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , x, x, x, , x, x, , x, x, , , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,0111,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x02,0x09,0x0b,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_126.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_126.txt new file mode 100644 index 0000000..76cc525 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_126.txt @@ -0,0 +1,422 @@ +126 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x0c,0x0a,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 4, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 0, 0, 0, 4, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 4, 0, 2, }, +{7: 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 2, 2, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:2, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 10, 8, 2, 4, 2, 4, 0, 8, 0, 0, 4, 0, 0, }, +{2: 16, 0, 10, 0, 4, 0, 10, 0, 2, 4, 0, 8, 0, 4, 2, 4, }, +{4: 16, 6, 4, 4, 0, 0, 8, 0, 0, 0, 0, 6, 2, 2, 0, 0, }, +{8: 16, 4, 4, 4, 10, 4, 0, 0, 6, 6, 4, 0, 6, 0, 0, 0, }, +{3: 16, 2, 0, 2, 4, 8, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 16, 4, 4, 6, 0, 6, 6, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{6: 16, 0, 6, 0, 0, 4, 8, 6, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 16, 4, 0, 4, 10, 0, 0, 0, 4, 2, 6, 0, 0, 0, 2, 0, }, +{a: 16, 0, 6, 0, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +{c: 16, 6, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 8, 0, 6, }, +{7: 16, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 0, 0, 0, 4, 6, 0, 2, 0, 2, 2, 0, 4, 2, 2, 0, }, +{d: 16, 6, 0, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 4, 2, 2, }, +{e: 16, 0, 6, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, 4, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:50, 4:37, 6:21, 8:7, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 8, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 8, 0, -8, 8, -8, 0, 0, 0, -8, -16, 0, -8, }, +{2: 16, 0, -8, 0, 8, -8, 8, 0, 0, -8, 0, -8, 0, 16, -8, -8, }, +{4: 16, -8, 8, -8, 8, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, }, +{8: 16, 8, 8, 8, -16, 8, 0, 0, -8, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -16, 0, 8, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 0, -16, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, }, +{9: 16, 8, 8, 0, -8, 0, -8, 0, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{c: 16, -8, 8, -8, -8, 0, 0, 0, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, 0, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, -8, }, +{b: 16, 0, -8, 0, -8, 0, -8, -8, 0, 0, 0, 8, 0, 0, 8, 0, }, +{d: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, , , x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, x, , x, x, , , x, x, }, +{9: , , x, , , x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, , x, , , x, x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , x, , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , x, , , x, , , x, , x, , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, , x, , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{1000,1000,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +126 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x0c,0x0a,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 4, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 4, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:2, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 4, 2, 4, 0, 4, 0, 6, 2, 0, 6, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 4, 6, 0, 6, 4, 4, 0, 0, 6, 0, }, +{4: 16, 10, 0, 4, 4, 2, 6, 0, 4, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 8, 4, 0, 10, 4, 0, 0, 10, 4, 0, 0, 4, 0, 2, 2, }, +{3: 16, 2, 0, 0, 4, 8, 6, 4, 0, 0, 0, 0, 6, 0, 0, 2, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 6, 6, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 16, 4, 2, 0, 6, 0, 2, 0, 4, 0, 2, 0, 0, 2, 2, 0, }, +{a: 16, 0, 4, 0, 6, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, }, +{c: 16, 8, 0, 0, 4, 0, 0, 0, 6, 0, 4, 0, 2, 6, 0, 2, }, +{7: 16, 0, 8, 6, 0, 0, 4, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 0, 0, 2, 6, 4, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, }, +{d: 16, 4, 4, 2, 0, 0, 2, 0, 0, 2, 8, 0, 2, 4, 4, 0, }, +{e: 16, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 0, 4, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:105, 2:50, 4:37, 6:21, 8:7, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, -8, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 0, -8, 0, -8, 0, 8, 0, -8, }, +{4: 16, -8, 8, 0, 8, 0, -8, 0, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 8, -8, 0, 0, 16, -8, 0, 0, 0, -8, -8, -8, -8, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 8, -8, -8, 0, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, }, +{c: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 8, -8, 0, -8, -8, 0, 0, 0, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 0, -8, 0, 8, 0, 8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , x, , x, x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, x, , x, x, , , x, x, }, +{9: , x, x, x, x, , , , x, , x, , x, x, , x, }, +{a: , x, , , x, x, , , x, x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , x, , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , , x, , , , x, , x, , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , x, , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0110,0101,1,}, +{0110,1000,0,}, +{0110,1101,1,}, +{1000,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x05,0x06,0x08,}, {0x06,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x06,0x09,0x0f,}}, +{{0x03,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_127.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_127.txt new file mode 100644 index 0000000..f32e429 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_127.txt @@ -0,0 +1,422 @@ +127 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x07,0x00,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{4: 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 6, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 4, 2, 0, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, 0, 2, }, +{c: 0, 0, 0, 0, 4, 2, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, }, +{7: 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 2, 2, 4, 2, 0, 4, 0, 0, 0, }, +{2: 16, 0, 10, 0, 0, 0, 8, 0, 4, 2, 4, 10, 4, 0, 4, 2, }, +{4: 16, 4, 4, 6, 0, 0, 10, 0, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 2, 0, 2, 4, 4, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, }, +{3: 16, 0, 0, 2, 8, 8, 4, 6, 2, 0, 0, 0, 10, 4, 4, 0, }, +{5: 16, 6, 4, 6, 0, 4, 6, 6, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 0, 4, 0, 0, 4, 8, 6, 0, 0, 0, 6, 0, 0, 2, 2, }, +{9: 16, 0, 4, 0, 2, 0, 0, 4, 4, 2, 2, 0, 8, 4, 2, 0, }, +{a: 16, 6, 0, 0, 0, 2, 0, 4, 0, 4, 0, 0, 8, 6, 0, 2, }, +{c: 16, 0, 4, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 0, 8, 2, }, +{7: 16, 2, 6, 2, 0, 2, 4, 0, 0, 2, 0, 4, 0, 0, 2, 0, }, +{b: 16, 4, 6, 0, 6, 4, 0, 0, 6, 4, 0, 2, 6, 0, 0, 2, }, +{d: 16, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, }, +{e: 16, 0, 6, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 6, 0, 0, 6, 0, 2, 2, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 0, -8, 0, 8, -8, 16, -8, 0, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, -8, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, -8, }, +{8: 16, 0, 8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, -8, -8, }, +{3: 16, 0, -8, 0, 8, 0, -16, 0, 8, -8, -8, 8, 0, -8, 0, 8, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{6: 16, 0, -16, 0, 8, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, }, +{9: 16, 0, 8, 0, -16, -8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, }, +{a: 16, -8, -8, 8, -8, 0, 0, -8, 0, 8, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, 0, -8, 8, 0, 0, -8, -8, 0, 0, -8, 0, -8, 8, }, +{7: 16, 0, -8, 0, 8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 8, 0, -8, 0, -8, 8, 0, -8, }, +{d: 16, 0, 8, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{e: 16, 8, -8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 8, -8, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, , x, x, x, , x, x, , x, x, x, }, +{5: , , x, , x, x, x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, , x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , x, , , , x, x, x, , x, x, , x, x, x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, x, , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1000,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x05,}}, +{{0x06,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x09,0x0c,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x05,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +127 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x01,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 0, }, +{4: 0, 4, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 2, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 2, }, +{c: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 2, }, +{7: 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{d: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{2: 16, 0, 10, 4, 0, 0, 4, 4, 4, 0, 4, 6, 6, 0, 6, 0, }, +{4: 16, 4, 0, 6, 2, 2, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 4, 0, 6, 2, 0, 6, }, +{3: 16, 2, 0, 0, 4, 8, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, }, +{5: 16, 4, 8, 10, 0, 4, 6, 8, 0, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 0, 6, 6, 6, 4, 4, 4, 0, 0, 0, 2, 6, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 2, 0, 6, 2, 0, 0, }, +{a: 16, 4, 2, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 2, }, +{c: 16, 2, 4, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 6, 2, }, +{7: 16, 0, 10, 4, 0, 0, 4, 6, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 4, 4, 0, 4, 10, 2, 0, 8, 8, 0, 0, 6, 2, 0, 0, }, +{d: 16, 0, 0, 2, 2, 4, 2, 0, 4, 6, 0, 0, 0, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 4, 0, 2, 2, 0, 8, 2, 0, 0, 4, 4, }, +{f: 16, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, 0, 0, -8, 8, -8, -8, 0, -8, 0, -8, }, +{2: 16, 8, -16, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, -8, 8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, 0, -8, 0, 8, 0, -8, 0, -8, -8, 0, 0, 0, -8, 8, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, -8, 0, -8, 0, 8, 8, 0, -8, -8, 8, }, +{9: 16, -8, 8, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, -8, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, }, +{7: 16, 0, -8, -8, 8, 8, 0, 0, 8, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 0, 0, -16, 0, 8, -8, 8, 0, 0, 8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, , x, x, , x, x, x, }, +{a: , x, , x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , , x, x, x, , x, x, x, x, , x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , x, , , , x, x, x, x, , x, x, , x, x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0110,0101,1,}, +{0110,1011,1,}, +{0110,1110,0,}, +{1000,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x01,0x06,0x07,}}, +{{0x01,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_128.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_128.txt new file mode 100644 index 0000000..3be28ea --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_128.txt @@ -0,0 +1,422 @@ +128 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x09,0x07,0x00,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{9: 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 6, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, }, +{7: 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, }, +{d: 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 10, 8, 8, 0, 0, 2, 4, 0, 0, 2, 0, }, +{2: 16, 8, 10, 0, 8, 8, 2, 0, 8, 10, 0, 0, 8, 2, 0, 0, }, +{4: 16, 4, 0, 4, 2, 0, 6, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{3: 16, 4, 4, 2, 0, 8, 0, 2, 2, 0, 4, 0, 2, 0, 0, 4, }, +{5: 16, 10, 0, 4, 0, 0, 4, 2, 0, 6, 0, 0, 4, 2, 0, 0, }, +{6: 16, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, 6, 0, 2, 2, 2, }, +{9: 16, 0, 10, 0, 4, 0, 0, 2, 4, 6, 0, 0, 4, 0, 2, 0, }, +{a: 16, 2, 4, 2, 4, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, }, +{c: 16, 0, 0, 0, 2, 6, 6, 4, 4, 4, 6, 0, 0, 2, 0, 6, }, +{7: 16, 8, 0, 2, 2, 2, 0, 4, 0, 4, 0, 4, 4, 0, 0, 2, }, +{b: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 2, 2, 4, 0, 0, 2, }, +{d: 16, 0, 2, 2, 0, 4, 4, 4, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 16, 2, 0, 0, 0, 4, 0, 0, 4, 6, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:60, 4:41, 6:11, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 0, 4, 0, 4, 12, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{b: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -8, -16, 8, -8, 0, 8, 0, -8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 0, -16, 16, -16, 0, 0, 0, -8, 0, 0, 0, 0, }, +{4: 16, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 8, -16, -8, 0, -8, 0, 0, 0, 0, 0, 8, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 8, -8, 8, -8, 0, 8, 0, }, +{6: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 8, 0, 8, -8, -8, 0, 8, 0, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, -8, 8, 0, 0, 8, -8, 0, 0, }, +{c: 16, -8, 0, 0, 0, 8, 0, -8, -8, -8, 8, 8, 0, -8, -8, 8, }, +{7: 16, -8, 0, 0, 8, 8, 0, 8, -8, 0, 0, -8, 0, -8, 0, -8, }, +{b: 16, 0, -8, 0, 0, 8, 0, -8, 8, 0, 0, -8, -8, 8, 0, -8, }, +{d: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{e: 16, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, -8, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , x, x, x, , , , x, x, , , x, , , , x, }, +{b: , , , , x, x, , x, x, , , , x, , , x, }, +{d: , x, , x, x, x, , x, x, , , , , x, , x, }, +{e: , x, x, x, , x, , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x04,0x09,0x0d,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +128 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x09,0x07,0x01,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 6, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{6: 0, 4, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, }, +{9: 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 2, 4, 0, }, +{a: 0, 0, 6, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, }, +{c: 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 8, 4, 0, 4, 10, 4, 0, 2, 0, 8, 0, 0, 2, 0, }, +{2: 16, 4, 10, 0, 4, 4, 0, 2, 10, 4, 0, 0, 8, 2, 0, 0, }, +{4: 16, 4, 0, 4, 2, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{8: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 2, 2, 4, 0, 0, 2, }, +{3: 16, 10, 8, 0, 0, 8, 0, 0, 0, 2, 6, 2, 0, 4, 4, 4, }, +{5: 16, 8, 2, 6, 0, 0, 4, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{6: 16, 8, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 0, 4, 0, 2, }, +{9: 16, 0, 8, 0, 2, 2, 0, 2, 4, 0, 4, 0, 4, 2, 4, 0, }, +{a: 16, 0, 10, 0, 4, 0, 6, 0, 6, 4, 4, 4, 4, 0, 6, 0, }, +{c: 16, 2, 0, 2, 0, 4, 0, 0, 0, 0, 6, 0, 2, 2, 0, 6, }, +{7: 16, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 8, 2, 2, 2, 4, 0, 4, 0, 0, 4, 4, 0, 0, 2, }, +{d: 16, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:60, 4:41, 6:11, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{b: 0, 8, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{e: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, 0, 8, -16, 8, 0, -8, 0, 0, 8, -8, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 16, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 8, -8, -8, -16, -8, 8, -8, 0, 0, 8, 8, }, +{5: 16, 0, 8, -8, 0, -8, 8, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, -8, 0, 0, 8, -8, -8, 8, 0, 0, 0, 0, -8, -8, 0, 8, }, +{9: 16, 0, 0, 0, -8, -8, -8, 8, 0, -8, 0, 8, 8, 0, -8, 0, }, +{a: 16, 8, -8, 8, 0, -16, 8, -8, 0, 0, 0, -8, 0, 8, -8, 0, }, +{c: 16, -8, 0, 0, 0, 8, -8, -8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, 0, 0, 0, 8, 0, -8, 0, 8, -8, 8, -8, 0, -8, 0, }, +{d: 16, 8, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , , x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, , , , x, x, , x, }, +{a: , x, x, , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , x, x, , , , x, x, , , x, , , , x, }, +{b: , x, x, , x, , , x, x, , , , x, , , x, }, +{d: , x, , , x, , , x, x, , , , , x, , x, }, +{e: , x, x, , x, x, , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,1010,1,}, +{0110,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x06,0x09,0x0f,}}, +{{0x09,0x02,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0a,}, {0x01,0x02,0x03,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_129.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_129.txt new file mode 100644 index 0000000..3a43bbb --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_129.txt @@ -0,0 +1,422 @@ +129 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0e,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, }, +{4: 0, 4, 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{7: 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 10, 0, 4, 0, 10, 0, 2, 4, 0, 8, 0, 4, 2, 4, }, +{4: 16, 4, 4, 6, 2, 0, 8, 0, 0, 0, 0, 6, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 0, 4, 2, 8, 4, 0, 2, 2, 0, 2, }, +{3: 16, 2, 0, 2, 0, 6, 4, 10, 4, 8, 8, 0, 0, 0, 0, 4, }, +{5: 16, 4, 4, 6, 0, 6, 6, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{6: 16, 0, 6, 0, 0, 6, 8, 4, 0, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 2, 0, 2, 2, 4, 0, 0, 4, 4, 2, 0, 0, 0, 2, 2, }, +{a: 16, 4, 6, 0, 6, 4, 2, 0, 4, 6, 0, 0, 6, 0, 2, 0, }, +{c: 16, 0, 4, 2, 0, 4, 0, 0, 2, 2, 4, 2, 0, 4, 0, 8, }, +{7: 16, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 4, 0, 0, 2, 0, 0, 4, 0, 10, 6, 0, 4, 0, 2, 0, }, +{d: 16, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 6, 2, 4, }, +{f: 16, 0, 0, 0, 0, 6, 0, 0, 0, 0, 6, 2, 2, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 8, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 4, 8, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -16, 0, -8, }, +{2: 16, 0, -8, 0, 8, -8, 8, 0, 0, -8, 0, -8, 0, 16, -8, -8, }, +{4: 16, -8, 8, 0, 8, 0, 0, 0, -8, 8, -8, 0, -8, 0, 0, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, 0, -8, 8, 8, 0, -8, -8, -8, 0, 0, 0, 8, -16, 0, 8, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 0, -16, -8, 8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, }, +{a: 16, 8, -8, 8, -8, -8, 8, -8, -8, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, 0, -8, 0, -8, 8, 0, 8, 0, }, +{7: 16, 0, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, -8, }, +{b: 16, 8, -8, 0, -8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, , , x, x, , x, x, , , x, x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, x, , x, x, x, , , x, }, +{9: , x, x, x, , x, , x, x, , x, , , x, x, x, }, +{a: , x, x, x, , , , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, , x, , x, x, , x, , x, x, , x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , x, , , , , x, x, , x, , , , x, x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, , , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{1000,1000,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +129 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0e,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{4: 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 4, 0, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:161, 2:72, 4:18, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 4, 6, 0, 6, 4, 4, 0, 0, 6, 0, }, +{4: 16, 4, 0, 6, 0, 2, 6, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 16, 2, 4, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 2, 0, 0, }, +{3: 16, 2, 0, 0, 0, 6, 6, 6, 4, 4, 4, 0, 0, 0, 2, 6, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 4, 10, 6, 4, 0, 0, 0, 2, 4, 0, 0, 0, }, +{9: 16, 0, 2, 0, 2, 4, 2, 0, 4, 4, 2, 0, 0, 2, 2, 0, }, +{a: 16, 4, 4, 0, 8, 8, 0, 0, 4, 6, 2, 0, 10, 2, 0, 0, }, +{c: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 4, 0, 6, 2, 0, 6, }, +{7: 16, 0, 8, 6, 0, 0, 4, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 4, 0, 2, 2, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, 2, }, +{d: 16, 2, 4, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 0, 4, 0, 2, 4, 0, 2, 2, 0, 8, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:53, 4:39, 6:19, 8:8, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, 0, 0, 0, -8, 8, -8, 0, -8, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 0, -8, 0, -8, 0, 8, 0, -8, }, +{4: 16, -8, 8, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 8, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -16, -8, 0, 0, 0, 8, -8, 8, 8, }, +{c: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 8, -8, 0, -8, -8, 0, 0, 0, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, x, , x, x, , , x, x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, x, , x, x, x, , , x, }, +{9: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{a: , x, , , x, x, , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, , , , x, x, , x, , x, x, , x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , , x, x, , x, x, , x, , , , x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0110,0101,1,}, +{0110,1010,1,}, +{0110,1111,0,}, +{1000,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_130.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_130.txt new file mode 100644 index 0000000..18edbd5 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_130.txt @@ -0,0 +1,410 @@ +130 Sbox: +LUT = { +0x04,0x00,0x01,0x0a,0x02,0x05,0x03,0x07,0x06,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, }, +{2: 0, 2, 8, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 4, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, }, +{3: 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{5: 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, 2, 2, 0, 0, 0, }, +{6: 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{9: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 4, 2, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{d: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:159, 2:74, 4:21, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 0, 10, 0, 0, 0, 0, 0, 6, 2, 0, 0, 2, }, +{2: 16, 6, 8, 4, 4, 4, 6, 4, 4, 6, 4, 4, 4, 0, 6, 0, }, +{4: 16, 0, 6, 4, 0, 0, 2, 8, 0, 6, 4, 0, 0, 2, 0, 0, }, +{8: 16, 6, 6, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 2, 2, 0, }, +{3: 16, 8, 4, 0, 4, 4, 2, 2, 4, 0, 0, 0, 0, 2, 2, 0, }, +{5: 16, 2, 6, 0, 0, 0, 4, 2, 2, 0, 0, 6, 2, 0, 0, 0, }, +{6: 16, 0, 4, 10, 2, 6, 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{9: 16, 0, 6, 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 2, 0, 2, }, +{a: 16, 0, 4, 0, 4, 2, 0, 4, 0, 8, 4, 2, 2, 0, 0, 2, }, +{c: 16, 0, 4, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 2, }, +{7: 16, 0, 4, 6, 2, 4, 6, 0, 2, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 4, 0, 0, 0, 8, 0, 2, 0, 4, 2, 2, 2, }, +{d: 16, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 16, 0, 4, 0, 0, 0, 2, 4, 0, 4, 8, 2, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:57, 4:42, 6:15, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{5: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 8, -8, 0, 0, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 0, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 8, 0, -8, 8, -8, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 8, 8, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 8, -8, -8, 0, -8, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, -8, 8, 8, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -8, 8, 0, -8, -8, 0, 0, -8, 0, 0, 8, 8, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{7: 16, -8, 0, 0, 8, 8, 0, 0, -8, -8, -8, 0, 8, 0, -8, 0, }, +{b: 16, 0, 0, 0, -16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, -8, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, x, , x, , x, , x, , x, }, +{6: , , , x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , , x, x, , , x, , x, , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0011,0010,1,}, +{1000,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +130 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x05,0x08,0x07,0x0a,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 4, 2, 0, 0, }, +{3: 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 4, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 2, }, +{a: 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 4, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 4, 0, 0, 2, 0, }, +{b: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:159, 2:74, 4:21, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 6, 0, 6, 8, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 4, 4, 4, 0, 0, 0, 10, 0, 0, 2, 6, 0, 2, 0, 0, }, +{8: 16, 0, 4, 0, 8, 4, 0, 2, 0, 4, 2, 2, 4, 2, 0, 0, }, +{3: 16, 10, 4, 0, 0, 4, 0, 6, 0, 2, 0, 4, 0, 2, 0, 0, }, +{5: 16, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 0, 4, 8, 0, 2, 2, 4, 2, 4, 0, 0, 0, 0, 4, 2, }, +{9: 16, 0, 4, 0, 4, 4, 2, 0, 4, 0, 0, 2, 8, 2, 0, 2, }, +{a: 16, 0, 6, 6, 4, 0, 0, 0, 2, 8, 0, 0, 0, 0, 4, 2, }, +{c: 16, 0, 4, 4, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 8, 2, }, +{7: 16, 6, 4, 0, 0, 0, 6, 4, 0, 2, 0, 8, 0, 0, 2, 0, }, +{b: 16, 2, 4, 0, 0, 0, 2, 0, 4, 2, 2, 0, 4, 2, 0, 2, }, +{d: 16, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +{e: 16, 0, 6, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:57, 4:42, 6:15, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, 0, 0, -8, 0, 8, 0, -8, -8, -8, 0, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 0, 0, -8, -8, 8, -8, 0, 8, -8, }, +{3: 16, -8, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, -8, 8, 0, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 8, 0, -8, 0, 8, 0, -8, 0, 0, -8, -8, 8, }, +{9: 16, -8, 8, 0, -8, 0, 8, 8, 0, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 8, -8, 0, -8, -8, 0, 0, 0, 8, 0, -8, 8, 0, -8, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{7: 16, 0, -8, -8, 8, -8, 0, 8, -8, 0, -8, 0, 0, 0, 8, 0, }, +{b: 16, -8, 0, 0, -8, 0, 0, -8, 0, 8, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{1000,1100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x04,}, {0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x0a,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_131.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_131.txt new file mode 100644 index 0000000..3d78ee1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_131.txt @@ -0,0 +1,410 @@ +131 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x0a,0x07,0x00,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{5: 0, 2, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 4, 2, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, }, +{d: 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:158, 2:77, 4:18, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 6, 0, 2, 2, 0, 6, 0, 0, 4, 0, 0, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 0, 4, 0, }, +{4: 16, 0, 4, 4, 2, 0, 2, 4, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 16, 2, 4, 4, 4, 0, 0, 0, 2, 8, 0, 2, 0, 0, 4, 2, }, +{3: 16, 4, 4, 2, 0, 8, 0, 2, 2, 0, 4, 0, 2, 0, 0, 4, }, +{5: 16, 2, 4, 0, 2, 0, 4, 2, 2, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 0, 6, 8, 0, 0, 0, 4, 0, 6, 0, 2, 0, 0, 4, 2, }, +{9: 16, 0, 4, 2, 2, 0, 2, 0, 4, 2, 0, 0, 4, 2, 2, 0, }, +{a: 16, 2, 6, 0, 4, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 4, 4, 0, 2, 6, 2, 0, 0, 0, 6, 0, 0, 6, 4, 6, }, +{7: 16, 2, 6, 2, 0, 2, 4, 0, 0, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 6, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 0, 2, 2, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 8, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:95, 2:61, 4:46, 6:17, 8:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 4, 12, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{5: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, -8, 8, 0, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, -8, -8, -8, }, +{3: 16, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, -8, 8, }, +{5: 16, -8, 8, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, 0, 0, 0, }, +{6: 16, 8, -16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, -8, -8, 8, 0, -8, 0, 0, 8, }, +{7: 16, -8, -8, 0, 8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 8, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, -8, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, 0, 0, 8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , , x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , , , x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , , , x, , , , x, , x, , x, , , , x, }, +{b: , x, x, , x, x, , x, , x, , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0010,0110,1,}, +{0011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +131 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x0a,0x07,0x01,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 4, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{6: 0, 2, 2, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, }, +{9: 0, 2, 2, 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 4, 0, }, +{c: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, }, +{d: 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:158, 2:77, 4:18, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 2, 4, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 4, 8, 4, 4, 4, 4, 6, 4, 6, 4, 6, 6, 0, 4, 0, }, +{4: 16, 0, 4, 4, 4, 2, 0, 8, 2, 0, 0, 2, 0, 2, 4, 0, }, +{8: 16, 0, 4, 2, 4, 0, 2, 0, 2, 4, 2, 0, 2, 0, 0, 2, }, +{3: 16, 6, 4, 0, 0, 8, 0, 0, 0, 2, 6, 2, 0, 0, 0, 4, }, +{5: 16, 0, 6, 2, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 2, 0, }, +{6: 16, 2, 6, 4, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, }, +{9: 16, 2, 6, 0, 2, 2, 2, 0, 4, 0, 0, 0, 4, 2, 0, 0, }, +{a: 16, 0, 6, 0, 8, 0, 0, 6, 2, 4, 0, 0, 0, 2, 4, 0, }, +{c: 16, 6, 4, 2, 0, 4, 0, 0, 0, 0, 6, 0, 2, 6, 4, 6, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 4, 2, 0, 2, 2, 0, 4, 2, 0, 2, 4, 0, 0, 2, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 4, 0, 4, 0, 0, 4, 2, 0, 4, 0, 2, 2, 8, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:95, 2:61, 4:46, 6:17, 8:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:109, 4:118, 8:26, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 8, -16, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, 0, -8, }, +{4: 16, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, 0, 8, -8, -8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 0, 0, 8, 0, 0, -8, 0, 8, -8, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, 8, }, +{9: 16, -8, 8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, -8, 0, -8, -16, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 8, -8, -8, 0, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, 0, 8, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 8, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, -8, 8, 8, 0, 0, 8, 0, 0, 0, 0, }, +{f: 16, 0, -8, 0, 0, 8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, x, , x, , x, , x, , x, }, +{6: , x, , x, , x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , x, , x, , , , x, , x, , x, , , , x, }, +{b: , , , , x, , , x, , x, , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 2 */ +{0010,0010,1,}, +{0011,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 9, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x03,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x03,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x04,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_132.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_132.txt new file mode 100644 index 0000000..d224c01 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_132.txt @@ -0,0 +1,422 @@ +132 Sbox: +LUT = { +0x08,0x00,0x0b,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x01,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{2: 0, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 4, 2, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 4, }, +{f: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:161, 2:71, 4:21, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 6, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{2: 16, 4, 8, 0, 6, 6, 4, 0, 4, 4, 6, 6, 4, 4, 4, 4, }, +{4: 16, 0, 4, 4, 0, 4, 4, 0, 0, 2, 0, 8, 2, 0, 2, 2, }, +{8: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{3: 16, 6, 4, 6, 0, 6, 4, 4, 0, 2, 0, 6, 2, 0, 0, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 16, 0, 4, 0, 4, 4, 16, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 2, 6, 0, 10, 0, 4, 0, 0, 4, 0, 0, 2, 4, 0, 0, }, +{c: 16, 0, 4, 2, 4, 0, 4, 2, 0, 0, 2, 0, 0, 8, 2, 4, }, +{7: 16, 2, 0, 6, 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 0, 6, 2, 0, 0, 4, 0, 8, 2, 6, 0, 4, 0, 0, 0, }, +{d: 16, 0, 4, 2, 0, 2, 4, 0, 4, 2, 8, 0, 0, 2, 4, 0, }, +{e: 16, 0, 6, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 2, 4, }, +{f: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:52, 4:49, 6:19, 8:5, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 8, 8, 0, 8, -8, 0, -16, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -8, -8, 8, 8, 8, -8, -8, -8, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 8, }, +{6: 16, 8, 0, -8, 0, 8, 0, 8, -8, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, -8, -8, 8, -8, 0, 0, 0, 0, 0, -8, 8, -8, }, +{c: 16, 0, 8, -16, 0, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 0, -8, -8, 8, 0, -8, -8, 0, 8, 0, 0, }, +{d: 16, 0, 8, -8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, 0, 0, 0, 8, 8, 0, 0, -8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , , x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , x, , x, , , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,1100,1,}, +{0110,1101,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x09,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +132 Inverse Sbox: +LUT = { +0x01,0x0b,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x02,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{3: 0, 2, 2, 0, 2, 6, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 2, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 4, 0, 2, 0, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 4, 0, 0, }, +{7: 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 0, 2, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, }, +{f: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:161, 2:71, 4:21, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 6, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 16, 4, 8, 4, 4, 4, 0, 4, 4, 6, 4, 0, 6, 4, 6, 6, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 0, 0, 2, 6, 2, 2, 2, 0, }, +{8: 16, 2, 6, 0, 4, 0, 0, 4, 2, 10, 4, 0, 0, 0, 0, 0, }, +{3: 16, 6, 6, 4, 2, 6, 6, 4, 0, 0, 0, 4, 0, 2, 0, 0, }, +{5: 16, 0, 4, 4, 0, 4, 4, 16, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 6, 4, 2, 0, 2, 0, 0, 0, 2, 2, }, +{9: 16, 2, 4, 0, 2, 0, 0, 4, 4, 0, 0, 2, 8, 4, 2, 0, }, +{a: 16, 0, 4, 2, 6, 2, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 0, 6, 0, 0, 0, 2, 4, 0, 0, 2, 0, 6, 8, 0, 4, }, +{7: 16, 0, 6, 8, 0, 6, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 2, 4, 2, 0, 2, 2, 0, 6, 2, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 0, 2, 4, 0, 4, 8, 2, 0, 2, 4, 2, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 4, }, +{f: 16, 2, 4, 2, 2, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:52, 4:49, 6:19, 8:5, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 0, 4, 4, 4, 0, 12, 0, 4, 0, 0, 0, 4, 0, 4, }, +{9: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 0, -8, 8, -8, 8, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{8: 16, 8, 0, 8, 0, -8, 0, 8, 0, -8, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 0, 0, -8, -8, -8, 8, 8, 0, -8, -8, 0, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, -8, 0, 0, 8, 0, -8, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, 0, }, +{c: 16, 0, 0, -8, 0, -8, 0, -8, 8, -8, 0, 8, -8, 0, 8, 0, }, +{7: 16, 0, -16, -8, 8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, 0, 0, -8, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 8, -8, -8, 0, 0, -8, 0, 0, 8, 8, }, +{e: 16, 0, 0, -8, -8, 8, 0, 8, 0, 0, 0, -8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, -8, 8, 0, 0, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , x, x, , x, x, , , x, }, +{5: , x, , , x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , , , x, , , x, x, , x, x, , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , , , x, , x, x, x, , , x, x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0c,}, {0x0e,}}, +{{0x03,0x0c,}, {0x07,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x0c,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_133.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_133.txt new file mode 100644 index 0000000..7e72113 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_133.txt @@ -0,0 +1,422 @@ +133 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x0b,0x07,0x06,0x09,0x0a,0x04,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 2, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 2, 0, 2, 2, 4, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 4, 2, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 4, }, +{f: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:161, 2:71, 4:21, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 6, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +{2: 16, 4, 8, 0, 6, 4, 4, 0, 6, 4, 6, 4, 4, 6, 4, 4, }, +{4: 16, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 16, 4, 4, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, 0, 2, 0, 2, 2, }, +{3: 16, 6, 6, 6, 0, 6, 4, 4, 0, 2, 0, 4, 0, 0, 2, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 0, 6, 0, 2, 6, 8, 4, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 16, 2, 4, 2, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 6, 2, 4, 0, 0, 0, 0, 8, 0, 4, 2, 6, 0, 0, }, +{c: 16, 2, 4, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 0, 6, }, +{7: 16, 2, 0, 6, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 2, 2, 0, 0, 2, 4, 2, 4, 4, 8, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 4, 0, 4, 0, 8, 2, 4, }, +{f: 16, 2, 6, 0, 0, 0, 0, 0, 0, 0, 10, 4, 4, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:52, 4:49, 6:19, 8:5, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 8, 0, 8, 0, -8, 8, -8, 8, -16, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, -16, 0, 16, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, -8, 0, }, +{3: 16, 0, -8, 8, 8, 0, -8, -8, -8, 0, 8, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 8, 0, 0, 8, 0, -16, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 8, -8, 0, 0, -8, -8, 8, 0, 8, -8, }, +{c: 16, -8, 8, -8, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, -8, 0, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 8, -8, 0, 8, -8, 0, 8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, x, x, x, , , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , , , x, , x, x, x, , x, x, , , x, }, +{b: , , x, , x, , , x, x, x, , , , , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , x, x, x, x, , , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,0100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +133 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x0b,0x05,0x08,0x07,0x00,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 0, 0, 8, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 4, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, 0, }, +{e: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:161, 2:71, 4:21, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 6, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 16, 4, 8, 4, 4, 6, 0, 6, 4, 6, 4, 0, 4, 4, 4, 6, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 2, 2, 2, 6, 2, 0, 0, 0, }, +{8: 16, 2, 6, 0, 4, 0, 0, 2, 2, 4, 0, 2, 2, 0, 0, 0, }, +{3: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 2, 4, 0, 2, 0, 0, }, +{5: 16, 0, 4, 4, 2, 4, 4, 8, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 2, 4, 6, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, 2, 4, 0, 2, 0, }, +{a: 16, 0, 4, 4, 4, 2, 2, 0, 0, 8, 0, 0, 2, 2, 4, 0, }, +{c: 16, 2, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, 4, 4, 0, 10, }, +{7: 16, 0, 4, 16, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 16, 0, 4, 4, 2, 0, 2, 0, 4, 2, 0, 2, 8, 0, 0, 4, }, +{d: 16, 0, 6, 4, 0, 0, 2, 0, 0, 6, 4, 0, 0, 2, 8, 0, }, +{e: 16, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 6, 2, 4, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:52, 4:49, 6:19, 8:5, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{4: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +{2: 16, 8, -16, 8, 8, -8, 8, -8, 8, -8, 8, -8, -8, 0, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, -8, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -16, 0, 8, -8, 0, 8, -8, 0, 0, }, +{c: 16, -8, 0, 0, -8, 0, 0, -8, 8, 0, 8, 0, -8, 0, 8, -8, }, +{7: 16, 0, -16, -8, 0, 0, 8, 8, 0, 0, -8, -8, 0, -8, 8, 8, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 8, 0, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, }, +{e: 16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 8, 0, 0, -8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{5: , x, , x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, , , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , , , x, , x, x, x, , , , , , x, }, +{d: , x, , x, , x, , , x, x, , , x, x, , x, }, +{e: , x, , , x, , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0110,1010,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,}}, +{{0x03,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x0a,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_134.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_134.txt new file mode 100644 index 0000000..96e33b1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_134.txt @@ -0,0 +1,422 @@ +134 Sbox: +LUT = { +0x08,0x00,0x0c,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x01,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +{2: 0, 0, 8, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{4: 0, 0, 0, 6, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{9: 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 4, 2, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 2, 4, 2, 0, 0, 2, 0, 0, 0, 2, 2, }, +{2: 16, 0, 8, 6, 4, 0, 4, 4, 4, 4, 6, 6, 4, 4, 4, 6, }, +{4: 16, 4, 8, 6, 2, 4, 8, 4, 0, 0, 0, 10, 2, 0, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 2, 4, 6, 0, 0, 4, 0, 2, 0, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, }, +{5: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{6: 16, 0, 8, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{9: 16, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, }, +{a: 16, 4, 10, 0, 4, 4, 2, 0, 8, 6, 0, 0, 8, 2, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 4, 6, 4, }, +{7: 16, 2, 0, 6, 0, 8, 0, 0, 4, 6, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 4, 2, 0, 4, 6, 2, 0, 0, 2, 0, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:58, 4:43, 6:13, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{5: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 0, 8, 0, 8, -8, 8, -8, 8, -16, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -16, 0, 0, 0, -8, -8, }, +{8: 16, 8, 0, 8, -8, -8, 0, 8, 0, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 0, -8, -8, -8, 0, 8, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 0, -8, -8, 0, 8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{a: 16, 0, -8, 8, -8, -8, 8, -16, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, -8, 0, -8, 0, -8, 8, 0, 0, 8, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, , , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , , , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, , , , , x, , , x, x, , , , x, }, +{b: , , , , x, x, , x, , , x, , x, , , x, }, +{d: , x, , x, x, x, , x, , , x, , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,1010,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x07,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0f,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +134 Inverse Sbox: +LUT = { +0x01,0x0c,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x02,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 4, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 6, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 0, 2, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 2, 2, 0, 0, 0, 6, 0, 2, 2, 2, 0, 0, }, +{c: 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, }, +{7: 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, }, +{f: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 8, 0, 2, 4, 0, 2, 0, 2, 0, 4, }, +{2: 16, 0, 8, 8, 10, 0, 0, 8, 0, 10, 10, 0, 0, 0, 10, 0, }, +{4: 16, 4, 6, 6, 0, 6, 4, 4, 2, 0, 0, 6, 2, 0, 0, 0, }, +{8: 16, 2, 4, 2, 4, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 4, 0, 8, 2, 4, 0, 2, }, +{5: 16, 4, 4, 8, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 2, 4, 4, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 16, 0, 4, 0, 4, 0, 0, 0, 2, 8, 2, 4, 2, 4, 2, 0, }, +{a: 16, 0, 4, 0, 6, 2, 4, 0, 0, 6, 0, 6, 2, 6, 0, 4, }, +{c: 16, 2, 6, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, }, +{7: 16, 0, 6, 10, 0, 4, 0, 4, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 4, 0, 2, 2, 0, 0, 2, 0, 6, 0, 0, 0, 4, 2, }, +{f: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:58, 4:43, 6:13, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 16, -8, 8, 0, -8, 8, -8, 0, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 8, 8, -8, -8, 8, 0, -8, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -16, 0, 0, 0, 0, 0, -8, 0, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, 8, 0, 8, -8, -8, -8, 0, 0, 8, 0, -8, }, +{a: 16, 0, -8, 8, -8, 0, 8, -8, -8, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, 0, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, 8, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , , , x, x, x, , , x, }, +{5: , , x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , x, , x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , , , , x, x, , , , x, }, +{b: , , x, , , , , , , , x, , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x0f,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_135.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_135.txt new file mode 100644 index 0000000..030a0a7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_135.txt @@ -0,0 +1,422 @@ +135 Sbox: +LUT = { +0x08,0x00,0x0d,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, }, +{2: 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:4, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 4, }, +{2: 16, 0, 8, 0, 0, 0, 10, 0, 8, 0, 10, 10, 8, 0, 10, 0, }, +{4: 16, 4, 4, 4, 2, 0, 8, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{8: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 2, 2, }, +{3: 16, 2, 0, 2, 0, 4, 4, 8, 0, 2, 0, 0, 4, 4, 0, 2, }, +{5: 16, 4, 4, 4, 0, 6, 6, 6, 0, 2, 0, 6, 0, 2, 0, 0, }, +{6: 16, 0, 4, 0, 2, 4, 8, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{9: 16, 2, 6, 0, 2, 0, 0, 4, 4, 0, 0, 0, 10, 4, 0, 0, }, +{a: 16, 0, 6, 4, 2, 0, 0, 6, 4, 2, 0, 0, 6, 6, 0, 4, }, +{c: 16, 2, 4, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{7: 16, 2, 4, 2, 2, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 4, 0, 2, 2, 0, 4, 2, 2, 0, 8, 0, 0, 4, }, +{d: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{e: 16, 2, 6, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:58, 4:43, 6:13, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{b: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, -8, -16, 0, 0, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 0, -8, 8, -8, -8, 16, -8, -8, }, +{4: 16, 0, 8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, -8, 8, -8, 8, -8, -8, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, 0, -8, -8, 8, 8, -8, -8, 0, -8, 0, 0, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -8, 8, 0, -8, 8, -8, 0, 8, -8, }, +{c: 16, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, 0, 8, -8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, 0, 0, 0, 8, }, +{e: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , x, , , , x, x, x, , x, x, , x, , x, }, +{b: , x, , , x, x, x, x, x, , x, , x, x, , x, }, +{d: , , , x, x, x, x, x, x, , x, , , , , x, }, +{e: , , , x, x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,1011,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x05,0x06,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x04,0x09,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +135 Inverse Sbox: +LUT = { +0x01,0x0d,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x02,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, }, +{8: 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 4, 2, 0, 0, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, }, +{a: 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 2, }, +{7: 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 2, 6, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, }, +{f: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:4, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 4, 6, 6, 4, 4, 4, 6, 6, 4, }, +{4: 16, 8, 0, 4, 2, 2, 4, 0, 0, 4, 2, 2, 4, 0, 0, 0, }, +{8: 16, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 4, 6, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 0, 2, 4, 2, 0, 0, 0, }, +{6: 16, 2, 0, 0, 0, 8, 6, 4, 4, 6, 0, 0, 0, 0, 2, 0, }, +{9: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 0, 2, 4, 2, 2, 0, }, +{a: 16, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 4, 6, }, +{7: 16, 0, 10, 4, 2, 0, 6, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 4, 8, 2, 4, 4, 0, 0, 10, 6, 0, 2, 8, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 4, 2, 0, 4, 6, 2, 0, 0, 2, 0, 2, }, +{e: 16, 0, 10, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 4, 4, 4, }, +{f: 16, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:58, 4:43, 6:13, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:7, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +{2: 16, 8, -8, 8, 0, -16, 8, -8, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 16, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, -8, 0, 0, }, +{3: 16, -8, 0, 0, 0, 0, -8, -8, -8, 0, 8, 8, 0, 0, 0, 0, }, +{5: 16, 0, 8, -8, 8, 0, 0, -16, 0, 8, -8, 0, -8, 8, -8, 0, }, +{6: 16, 0, 0, 0, 0, -16, -8, 8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, -8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 8, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 0, 8, -16, -8, 8, 0, 8, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{e: 16, 8, -8, -8, -8, 0, 0, 8, 0, 0, 8, 0, -8, 0, -8, 0, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , , x, , x, , x, x, , x, , x, }, +{b: , x, x, , , , x, , x, , x, , x, x, , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x03,0x05,0x06,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x0d,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_136.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_136.txt new file mode 100644 index 0000000..21a3c31 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_136.txt @@ -0,0 +1,422 @@ +136 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x0e,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x03,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{5: 0, 0, 0, 0, 2, 0, 4, 4, 0, 0, 0, 0, 2, 2, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 2, 4, 0, 0, 0, 2, }, +{9: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{c: 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 4, }, +{f: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 4, 4, 8, 0, 0, 2, 4, 2, 0, 0, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 4, 6, 6, 6, 4, 4, 4, 4, 6, }, +{4: 16, 4, 8, 8, 0, 4, 6, 10, 2, 2, 0, 4, 0, 0, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 0, 4, 4, 0, 2, 6, 0, 2, 0, }, +{3: 16, 4, 0, 4, 0, 4, 8, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{5: 16, 0, 0, 0, 2, 8, 8, 8, 0, 0, 0, 0, 2, 2, 2, 0, }, +{6: 16, 4, 8, 4, 0, 4, 10, 6, 0, 0, 2, 8, 0, 0, 0, 2, }, +{9: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 16, 0, 10, 0, 6, 0, 0, 0, 4, 4, 0, 2, 4, 2, 0, 0, }, +{c: 16, 0, 10, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 4, 6, 4, }, +{7: 16, 8, 0, 4, 0, 0, 4, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 16, 0, 10, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 6, 4, 4, }, +{f: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:38, 6:10, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 8, -8, 0, -8, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 8, 0, -8, 8, -8, 8, -8, 8, -16, -8, 8, -8, 0, }, +{4: 16, 0, 8, -8, 8, -8, 0, -8, 0, 8, -16, 0, 0, 0, -8, 8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, -8, }, +{3: 16, -8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, 8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 0, -8, -16, 8, 0, 0, 8, 0, -8, -8, 0, -8, 0, 8, 8, }, +{9: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{a: 16, 0, -8, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{c: 16, 8, 8, -8, -8, 0, 0, -8, 0, -8, 8, 0, 0, 0, 0, -8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, -16, 8, 0, 0, 0, }, +{b: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, 8, 8, 8, 0, 0, 0, -8, -8, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, , , x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, x, , , x, , , , x, x, x, , , x, x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, , , , , x, x, , , x, x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0110,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,}}, +{{0x09,0x02,}, {0x07,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +136 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x0e,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x04,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 0, }, +{8: 0, 2, 0, 0, 4, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 6, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{6: 0, 0, 0, 2, 0, 0, 4, 6, 2, 0, 0, 0, 2, 0, 0, 0, }, +{9: 0, 0, 2, 2, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{a: 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{c: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, }, +{b: 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 0, 4, 2, 0, 0, 8, 2, 2, 0, 2, }, +{2: 16, 0, 8, 8, 10, 0, 0, 8, 0, 10, 10, 0, 0, 0, 10, 0, }, +{4: 16, 0, 4, 8, 0, 4, 0, 4, 2, 0, 2, 4, 2, 0, 2, 0, }, +{8: 16, 2, 4, 0, 4, 0, 2, 0, 2, 6, 2, 0, 2, 0, 0, 0, }, +{3: 16, 4, 0, 4, 0, 4, 8, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 16, 4, 4, 6, 0, 8, 8, 10, 0, 0, 0, 4, 0, 2, 0, 2, }, +{6: 16, 8, 4, 10, 0, 4, 8, 6, 2, 0, 0, 4, 2, 0, 0, 0, }, +{9: 16, 0, 6, 2, 4, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{a: 16, 0, 6, 2, 4, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{c: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 4, 4, 4, 2, 0, 0, 8, 0, 2, 0, 4, 0, 2, 0, 2, }, +{b: 16, 2, 4, 0, 6, 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 4, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:38, 6:10, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 16, -8, 8, 0, -8, 8, -8, 0, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, 0, 0, 0, -8, -8, 8, 8, 0, -8, }, +{8: 16, 0, 8, 8, -8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, }, +{3: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -16, 8, 0, 0, -8, 8, 8, -8, 0, 0, -8, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, -8, 0, 8, 0, -16, 8, -8, 0, 0, 8, }, +{9: 16, 0, 0, 8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, -8, -8, }, +{a: 16, 0, -8, 8, 0, 0, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 8, 8, 0, -8, -8, 0, 0, -8, 8, 0, }, +{b: 16, 0, 0, 8, -8, -8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , x, , x, , x, x, , x, x, x, , x, x, x, }, +{6: , , x, x, x, x, , x, , x, x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , , x, x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, , x, }, +{7: , , x, , , , , x, , x, x, x, , , x, x, }, +{b: , , x, x, , , , x, , x, x, , x, , x, x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , x, x, x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,0101,1,}, +{1100,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,}}, +{{0x06,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_137.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_137.txt new file mode 100644 index 0000000..15b08ce --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_137.txt @@ -0,0 +1,422 @@ +137 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x0f,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 6, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 2, 0, 0, 4, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{6: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 0, }, +{a: 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 0, }, +{c: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 4, 0, 0, 2, 0, 0, 0, 0, 6, 0, 2, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{e: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:4, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 4, 4, 8, 0, 2, 0, 4, 0, 2, 0, 2, }, +{2: 16, 0, 8, 0, 0, 0, 8, 0, 10, 0, 10, 8, 10, 0, 10, 0, }, +{4: 16, 4, 4, 8, 2, 8, 6, 4, 0, 2, 0, 10, 0, 0, 0, 0, }, +{8: 16, 0, 4, 2, 2, 2, 0, 0, 4, 2, 0, 0, 6, 0, 2, 0, }, +{3: 16, 4, 0, 8, 2, 4, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{5: 16, 0, 4, 0, 0, 4, 8, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{6: 16, 4, 4, 0, 2, 0, 4, 4, 0, 2, 2, 8, 0, 0, 2, 0, }, +{9: 16, 2, 6, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 0, 0, 0, }, +{a: 16, 2, 6, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 0, 0, 0, }, +{c: 16, 2, 4, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 6, 2, }, +{7: 16, 8, 4, 8, 0, 4, 10, 4, 0, 0, 0, 6, 0, 2, 0, 2, }, +{b: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{e: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 2, 4, 2, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:38, 6:10, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 0, -8, 0, 8, 0, 0, -16, 0, 0, }, +{2: 16, 8, -8, 8, 0, -8, 0, -8, 8, -8, 8, -8, -8, 16, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, 8, -8, -8, 8, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, 0, 0, -8, 0, 8, 0, 0, -16, 0, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, 0, -8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 8, -8, }, +{c: 16, 0, 8, -8, -8, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, 0, }, +{7: 16, -8, 0, -16, 8, 8, 8, 0, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 0, 8, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, , , , x, , x, x, x, , x, x, x, x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , x, x, x, x, , x, x, x, x, x, , x, x, }, +{e: , , , x, x, x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,0111,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +137 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x0f,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{8: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{5: 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 2, 2, 0, 0, 0, 2, 2, 0, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, }, +{a: 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:4, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 0, 4, 2, 2, 2, 8, 0, 0, 0, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 4, 6, 6, 4, 4, 4, 6, 6, 4, }, +{4: 16, 0, 0, 8, 2, 8, 0, 0, 0, 0, 2, 8, 2, 0, 0, 2, }, +{8: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 4, 0, 8, 2, 4, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{5: 16, 4, 8, 6, 0, 4, 8, 4, 0, 0, 0, 10, 0, 2, 2, 0, }, +{6: 16, 8, 0, 4, 0, 0, 4, 4, 2, 2, 0, 4, 0, 2, 2, 0, }, +{9: 16, 0, 10, 0, 4, 0, 2, 0, 4, 4, 2, 0, 6, 0, 0, 0, }, +{a: 16, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 4, 6, }, +{7: 16, 4, 8, 10, 0, 4, 4, 8, 2, 2, 0, 6, 0, 0, 0, 0, }, +{b: 16, 0, 10, 0, 6, 0, 2, 0, 4, 4, 0, 0, 4, 0, 0, 2, }, +{d: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +{e: 16, 0, 10, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 4, 4, 4, }, +{f: 16, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:60, 4:38, 6:10, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{9: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, 8, }, +{2: 16, 8, -8, 8, 0, -16, 8, -8, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 16, 0, 0, 0, 0, -8, -8, 0, 0, 0, -8, }, +{8: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, -8, 0, 8, 8, 0, -8, 0, -8, }, +{5: 16, 0, 8, -16, 8, 0, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, }, +{6: 16, 0, 0, -8, 0, -16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, }, +{9: 16, 0, 8, 8, -8, 0, 0, 0, 0, -8, -8, 0, -8, 8, -8, 0, }, +{a: 16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, 0, -8, -16, -8, 8, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 8, -8, 0, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, -8, -8, -8, 0, 0, 8, 0, 0, 8, 0, -8, 0, -8, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, , x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, , , x, x, x, x, x, x, , x, x, x, x, }, +{b: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_138.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_138.txt new file mode 100644 index 0000000..2e53c70 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_138.txt @@ -0,0 +1,422 @@ +138 Sbox: +LUT = { +0x06,0x00,0x08,0x02,0x03,0x05,0x0b,0x07,0x01,0x09,0x0a,0x04,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 4, 2, 6, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 2, 2, 0, 0, }, +{c: 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, 0, 0, }, +{7: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{e: 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, }, +{f: 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 8, 4, 4, 0, 2, 2, 0, 0, 0, 2, 0, }, +{2: 16, 4, 8, 0, 6, 4, 4, 0, 4, 4, 4, 4, 6, 6, 6, 4, }, +{4: 16, 4, 4, 8, 0, 10, 6, 4, 0, 0, 0, 8, 2, 2, 0, 0, }, +{8: 16, 0, 6, 0, 4, 0, 2, 2, 2, 4, 0, 2, 0, 0, 0, 2, }, +{3: 16, 8, 4, 8, 2, 6, 10, 4, 0, 0, 0, 4, 0, 0, 2, 0, }, +{5: 16, 0, 0, 0, 0, 8, 8, 8, 2, 2, 2, 0, 0, 0, 0, 2, }, +{6: 16, 0, 4, 0, 0, 4, 8, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{9: 16, 2, 4, 2, 2, 0, 0, 0, 4, 0, 2, 0, 4, 0, 2, 2, }, +{a: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 2, 2, 2, 2, 0, 0, }, +{c: 16, 2, 6, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, 0, 4, }, +{7: 16, 4, 0, 8, 2, 4, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 16, 2, 6, 0, 0, 2, 0, 2, 4, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{e: 16, 2, 4, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 4, }, +{f: 16, 0, 6, 0, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:64, 4:46, 6:10, 8:11, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{4: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{3: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 4, 0, 0, 0, 4, 12, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{c: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 0, 0, -8, -8, 8, -8, 0, 0, 0, -8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 0, -8, 8, -8, 8, -8, 8, 0, -8, 8, -8, -16, }, +{4: 16, -8, 8, -8, 8, 0, 0, -16, 0, 8, -8, 8, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 0, 8, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, 0, 0, 8, 8, -8, -8, -8, 0, 0, 8, 8, -8, -16, 0, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, -8, 16, }, +{6: 16, -8, -8, -8, 0, 0, 0, 8, 8, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, -8, 8, 0, 8, 0, }, +{c: 16, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, 0, 0, -8, 8, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 8, -16, }, +{b: 16, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, 0, 0, -8, 0, 0, 8, 0, 8, 0, -8, 0, -8, -8, 0, }, +{f: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, x, x, x, , , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , x, x, , x, , , x, x, , x, x, , , x, }, +{b: , , x, , x, , , x, x, x, , , , , , x, }, +{d: , x, , , x, x, , x, , , , , , x, , x, }, +{e: , x, x, x, x, , , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,0100,1,}, +{1110,0011,1,}, +{1111,0010,1,}, +{1111,0101,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0f,}}, +{{0x01,0x02,0x04,}, {0x0f,}}, +{{0x09,0x02,0x0c,}, {0x0f,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x06,0x09,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x0f,}}, +{{0x09,0x02,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x0f,}}, +{{0x09,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +138 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x0b,0x05,0x00,0x07,0x02,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 0, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{8: 0, 2, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{3: 0, 0, 0, 2, 0, 6, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 6, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{6: 0, 4, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 0, 0, 2, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 2, 2, 0, }, +{c: 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 4, 0, 0, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, }, +{b: 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 0, 0, }, +{e: 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 0, 8, 0, 0, 2, 0, 2, 4, 2, 0, 2, 0, }, +{2: 16, 4, 8, 4, 6, 4, 0, 4, 4, 4, 6, 0, 6, 4, 4, 6, }, +{4: 16, 0, 0, 8, 0, 8, 0, 0, 2, 2, 0, 8, 0, 2, 2, 0, }, +{8: 16, 2, 6, 0, 4, 2, 0, 0, 2, 4, 0, 2, 0, 0, 2, 0, }, +{3: 16, 8, 4, 10, 0, 6, 8, 4, 0, 0, 2, 4, 2, 0, 0, 0, }, +{5: 16, 4, 4, 6, 2, 10, 8, 8, 0, 0, 0, 4, 0, 0, 0, 2, }, +{6: 16, 4, 0, 4, 2, 4, 8, 4, 0, 0, 2, 0, 2, 0, 0, 2, }, +{9: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 2, 2, }, +{a: 16, 2, 4, 0, 4, 0, 2, 0, 0, 4, 2, 0, 2, 2, 2, 0, }, +{c: 16, 2, 4, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 4, 0, 4, }, +{7: 16, 0, 4, 8, 2, 4, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, }, +{b: 16, 0, 6, 2, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, }, +{d: 16, 0, 6, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 4, 0, }, +{e: 16, 2, 6, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 4, }, +{f: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:64, 4:46, 6:10, 8:11, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +{5: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 8, -8, 0, 0, -8, 0, 8, 8, -8, }, +{2: 16, 8, -8, 8, 0, 0, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 16, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 8, 8, -8, -16, -8, 0, 0, 8, 0, 0, -8, 8, }, +{5: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -8, 0, 0, -8, -16, 0, }, +{6: 16, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, -16, -8, 8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, }, +{c: 16, -8, 8, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 8, 8, 0, -8, -8, 0, 0, -8, 8, 0, }, +{b: 16, 0, -8, 0, 0, 0, 0, -8, 8, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 8, 0, -8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 8, 0, }, +{e: 16, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, x, , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, x, x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , , x, x, , x, x, x, , , , , , x, }, +{d: , x, , x, x, x, , , x, x, , , x, x, , x, }, +{e: , x, x, , , , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0110,0011,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x07,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x0b,}}, +{{0x05,0x06,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_139.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_139.txt new file mode 100644 index 0000000..3d2ff70 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_139.txt @@ -0,0 +1,422 @@ +139 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x0c,0x07,0x04,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 8, 4, 6, 0, 4, 4, 6, 4, 4, 4, 4, 4, 6, 6, }, +{4: 16, 4, 10, 6, 0, 4, 8, 4, 0, 0, 0, 8, 2, 2, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 2, 0, 4, 4, 2, 0, 6, 0, 0, 0, }, +{3: 16, 2, 0, 6, 0, 8, 0, 0, 4, 6, 0, 4, 0, 0, 0, 2, }, +{5: 16, 4, 0, 4, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{6: 16, 0, 10, 6, 0, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{9: 16, 2, 0, 2, 2, 4, 0, 0, 6, 6, 0, 0, 0, 0, 2, 0, }, +{a: 16, 4, 10, 0, 4, 4, 2, 0, 8, 6, 0, 0, 8, 2, 0, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 6, 6, }, +{7: 16, 2, 0, 6, 0, 4, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 16, 4, 0, 0, 2, 2, 0, 2, 0, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 8, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:55, 4:39, 6:17, 8:9, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 8, -8, -8, 8, -8, }, +{2: 16, 8, -8, 8, 0, -8, 8, 0, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 8, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 8, -8, 0, 0, 0, 0, -8, -8, 0, -8, 8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, -8, 8, }, +{5: 16, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 0, 0, -8, -8, -8, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, 8, -8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 8, -16, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -16, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, -8, -8, 8, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , , x, x, , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, , , x, x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, x, , x, , , x, , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0100,1100,1,}, +{0110,0100,1,}, +{0110,1010,1,}, +{0110,1110,0,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +139 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x0c,0x07,0x00,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, }, +{2: 0, 0, 8, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{9: 0, 0, 2, 0, 4, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 0, 4, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 8, 10, 10, 0, 0, 10, 0, 10, 8, 0, 0, 0, 8, 0, }, +{4: 16, 4, 4, 6, 0, 6, 4, 6, 2, 0, 0, 6, 0, 0, 0, 2, }, +{8: 16, 2, 6, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, }, +{3: 16, 2, 0, 4, 0, 8, 2, 0, 4, 4, 0, 4, 2, 0, 0, 2, }, +{5: 16, 4, 4, 8, 2, 0, 4, 4, 0, 2, 0, 0, 0, 2, 0, 2, }, +{6: 16, 2, 4, 4, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{9: 16, 0, 6, 0, 4, 4, 2, 0, 6, 8, 0, 0, 0, 0, 2, 0, }, +{a: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{7: 16, 0, 4, 8, 0, 4, 0, 4, 0, 0, 2, 4, 0, 2, 2, 2, }, +{b: 16, 4, 4, 2, 6, 0, 0, 0, 0, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 2, 4, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 0, }, +{e: 16, 0, 6, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 6, 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:55, 4:39, 6:17, 8:9, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 8, 0, 0, }, +{9: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 0, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, 0, -8, -8, }, +{3: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 8, -8, 0, 8, -8, 0, 0, -8, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -16, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 0, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, 0, 0, 0, 0, -8, 8, -8, -8, 0, -8, 8, -8, }, +{d: 16, 0, 8, -8, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , , x, x, , x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , , , , x, , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , x, x, , , x, , , x, , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,0111,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x06,0x07,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_140.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_140.txt new file mode 100644 index 0000000..69fa543 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_140.txt @@ -0,0 +1,422 @@ +140 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x09,0x06,0x07,0x03,0x05,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 4, 0, }, +{6: 0, 2, 2, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 2, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 6, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 4, 2, 0, }, +{e: 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{f: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:5, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 6, 4, 4, 4, 6, 6, 4, 4, 4, 6, 4, 0, 0, }, +{2: 16, 4, 8, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, }, +{4: 16, 4, 0, 8, 2, 0, 4, 2, 2, 0, 0, 2, 4, 0, 0, 4, }, +{8: 16, 4, 0, 2, 4, 2, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{3: 16, 6, 4, 0, 2, 8, 2, 0, 0, 0, 6, 0, 0, 0, 0, 4, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 0, 0, 0, 4, 2, 4, 0, }, +{6: 16, 6, 2, 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{9: 16, 6, 2, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 16, 4, 2, 0, 0, 0, 0, 2, 0, 4, 2, 0, 6, 2, 2, 0, }, +{c: 16, 6, 4, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 6, 4, 6, }, +{7: 16, 4, 0, 0, 2, 2, 0, 6, 0, 2, 2, 4, 2, 0, 0, 0, }, +{b: 16, 4, 0, 6, 0, 0, 4, 0, 0, 6, 0, 2, 6, 2, 4, 6, }, +{d: 16, 4, 0, 0, 0, 0, 0, 2, 2, 2, 6, 2, 0, 4, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:96, 2:54, 4:46, 6:22, 8:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, }, +{6: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 8, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -16, 8, 0, 8, 0, -8, -8, -8, 8, -8, }, +{2: 16, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 8, 8, 0, -8, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 0, -8, 0, -8, 8, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 8, 0, 0, -8, 0, 8, 0, -8, -8, -8, 8, }, +{5: 16, 0, 0, -8, 0, -16, 0, 0, 0, 0, 0, 8, 0, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, 8, 0, }, +{9: 16, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, }, +{a: 16, 8, -8, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, -8, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, 0, 0, 8, 0, 0, -8, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, -8, -8, 0, -8, 8, 0, -8, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, -8, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 8, -16, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , , x, , , x, x, }, +{9: , , x, , x, x, x, , x, , , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, x, , x, , , x, , , , x, }, +{b: , , x, , x, , x, , x, , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0101,1,}, +{0101,0001,1,}, +{0101,1110,0,}, +{0101,1111,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x06,0x08,}, {0x05,}}, +{{0x01,0x0a,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x05,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,}}, +{{0x07,0x08,}, {0x05,0x09,0x0c,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +140 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x09,0x06,0x07,0x03,0x05,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 4, 0, }, +{4: 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, }, +{8: 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, }, +{5: 0, 0, 2, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 2, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 4, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{f: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:5, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 4, 6, 4, 6, 6, 4, 6, 4, 4, 4, 0, 0, }, +{2: 16, 4, 8, 0, 0, 4, 2, 2, 2, 2, 4, 0, 0, 0, 4, 0, }, +{4: 16, 6, 2, 8, 2, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 4, }, +{8: 16, 4, 2, 2, 4, 2, 0, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{3: 16, 4, 4, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 0, 0, 4, }, +{5: 16, 4, 2, 4, 2, 2, 8, 0, 2, 0, 0, 0, 4, 0, 4, 0, }, +{6: 16, 6, 0, 2, 0, 0, 2, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{9: 16, 6, 2, 2, 4, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, }, +{a: 16, 4, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 6, 2, 2, 0, }, +{c: 16, 4, 4, 0, 0, 6, 0, 0, 0, 2, 6, 2, 0, 6, 4, 6, }, +{7: 16, 4, 0, 2, 2, 0, 0, 6, 0, 0, 2, 4, 2, 2, 0, 0, }, +{b: 16, 6, 0, 4, 2, 0, 4, 0, 0, 6, 0, 2, 6, 0, 4, 6, }, +{d: 16, 4, 0, 0, 0, 0, 2, 2, 0, 2, 6, 0, 2, 4, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:96, 2:54, 4:46, 6:22, 8:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, }, +{6: 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 0, 0, 8, 8, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -16, 8, -8, 0, 8, -8, -8, -8, 8, 0, }, +{2: 16, 8, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 8, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, -8, -8, -8, -8, -8, }, +{8: 16, 8, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, -8, 0, 0, 8, 0, 8, 0, -8, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, }, +{9: 16, -8, 8, 0, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, }, +{7: 16, 0, 0, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 8, -8, 0, -8, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, -8, 0, 0, 0, 8, 0, 0, 8, 0, }, +{e: 16, 0, 0, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 8, -16, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , , x, , , x, x, }, +{9: , x, , x, x, x, x, , x, , , , x, x, , x, }, +{a: , , , x, x, x, x, , x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, x, , x, , , x, , , , x, }, +{b: , , , , x, , x, , x, , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0101,0001,1,}, +{0101,1110,0,}, +{0101,1111,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x06,0x08,}, {0x05,}}, +{{0x01,0x0a,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x05,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x07,0x09,0x0e,}}, +{{0x07,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_141.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_141.txt new file mode 100644 index 0000000..ba627d5 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_141.txt @@ -0,0 +1,422 @@ +141 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{4: 0, 4, 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 2, 0, 2, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 6, 0, 0, 2, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 8, 0, 0, 0, 10, 0, 10, 0, 8, 10, 10, 0, 8, 0, }, +{4: 16, 4, 4, 6, 2, 0, 8, 0, 0, 0, 0, 6, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 4, 0, 0, 4, 0, 2, 0, 8, 2, 2, 2, }, +{3: 16, 2, 0, 2, 4, 8, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 16, 4, 4, 6, 0, 6, 6, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{6: 16, 0, 6, 0, 0, 4, 8, 6, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 16, 2, 4, 2, 0, 0, 0, 0, 4, 2, 2, 0, 4, 2, 2, 0, }, +{a: 16, 4, 4, 0, 0, 0, 2, 0, 4, 4, 0, 2, 8, 2, 0, 2, }, +{c: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 6, 4, 0, 0, 6, 0, 0, 2, }, +{d: 16, 2, 4, 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 4, 0, }, +{e: 16, 0, 6, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 6, 0, 2, 2, 0, 0, 0, 2, 6, 0, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:55, 4:39, 6:17, 8:9, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{9: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -16, 0, -8, }, +{2: 16, 0, -8, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 16, -8, -8, }, +{4: 16, -8, 8, 0, 8, 0, 0, 0, -8, 8, -8, 0, -8, 0, 0, -8, }, +{8: 16, 0, 8, 0, -16, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{3: 16, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -16, 0, 8, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 0, -16, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, }, +{9: 16, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, }, +{a: 16, -8, -8, 0, -8, 0, 8, -8, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, -8, 0, 8, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 8, 0, -8, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, 0, }, +{e: 16, 8, -8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, , x, x, x, , x, x, , x, x, x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, , x, x, , x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , x, , , , x, x, x, , x, x, , x, x, x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, , , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0110,1,}, +{1000,1000,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +141 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{4: 0, 4, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 2, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 2, 2, }, +{7: 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:160, 2:74, 4:18, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 8, 4, 4, 0, 4, 6, 4, 4, 4, 6, 4, 4, 6, 6, }, +{4: 16, 4, 0, 6, 0, 2, 6, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 16, 2, 0, 2, 4, 4, 0, 0, 0, 0, 2, 0, 6, 2, 0, 2, }, +{3: 16, 2, 0, 0, 4, 8, 6, 4, 0, 0, 0, 0, 6, 0, 0, 2, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 6, 6, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 16, 0, 10, 0, 4, 0, 2, 0, 4, 4, 2, 0, 6, 0, 0, 0, }, +{a: 16, 4, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 4, 2, 2, 2, }, +{c: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 0, 10, 6, 0, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 16, 4, 10, 2, 8, 4, 0, 0, 4, 8, 0, 0, 6, 2, 0, 0, }, +{d: 16, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 8, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:55, 4:39, 6:17, 8:9, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:110, 8:28, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, 0, 0, 0, -8, 8, -8, 0, -8, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, -8, 8, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, 0, 0, 0, 8, -8, -8, 0, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 8, 8, -8, 0, 0, 0, 0, -8, -8, 0, -8, 8, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, -16, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , , x, x, x, , x, x, x, x, , x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , , x, x, x, x, x, , x, x, , x, x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0010,0010,1,}, +{0110,0101,1,}, +{0110,1011,1,}, +{0110,1110,0,}, +{1000,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x06,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_142.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_142.txt new file mode 100644 index 0000000..29f0ff4 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_142.txt @@ -0,0 +1,442 @@ +142 Sbox: +LUT = { +0x0c,0x00,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{5: 0, 2, 0, 0, 0, 2, 4, 4, 2, 0, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, 2, }, +{7: 0, 2, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 10, 6, 0, 0, 2, 0, 0, 0, 0, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 6, 4, 4, 6, 6, 4, 6, 4, 4, }, +{4: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 0, 8, 0, 0, 2, 2, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 4, 0, 10, 0, 4, 4, 0, 0, 0, 0, 6, 0, 2, 2, 0, }, +{5: 16, 6, 0, 4, 0, 6, 8, 4, 2, 0, 0, 0, 2, 0, 0, 0, }, +{6: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 16, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 0, }, +{a: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 2, 2, 4, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 6, 0, 8, 0, 6, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{b: 16, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, }, +{d: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 0, 4, 0, 12, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, -8, -8, 0, 8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, -16, 8, -8, -8, 8, 0, -8, }, +{4: 16, 0, 8, -16, 8, 0, 0, -8, 0, 16, -8, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, 8, -8, 0, -8, }, +{5: 16, -8, 0, 0, 8, -8, -8, 0, 0, 0, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, 0, 8, 0, 8, 8, 0, -16, -8, 0, -8, 0, 0, -8, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 16, 0, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 8, 8, -8, 0, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, 8, -16, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, , x, x, x, x, , , x, x, , x, , x, }, +{6: , , x, , x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, , , x, , x, x, , x, , x, x, , x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , x, , x, , , x, , , x, x, , , , x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1000,1000,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,1000,1,}, +{1110,0100,1,}, +{1110,1010,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 7, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x0a,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0e,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +142 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x0c,0x09,0x0a,0x0b,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 4, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, }, +{5: 0, 2, 0, 6, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, }, +{e: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 0, 4, 6, 0, 0, 0, 0, 6, 0, 2, 0, 2, }, +{2: 16, 0, 8, 8, 16, 0, 0, 16, 0, 8, 8, 0, 0, 0, 16, 0, }, +{4: 16, 4, 4, 10, 0, 10, 4, 4, 0, 0, 2, 8, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{3: 16, 4, 0, 8, 0, 4, 6, 0, 0, 0, 0, 6, 0, 2, 0, 2, }, +{5: 16, 10, 4, 10, 0, 4, 8, 4, 2, 0, 2, 4, 0, 0, 0, 0, }, +{6: 16, 6, 6, 8, 0, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{a: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 16, 2, 6, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 4, 2, }, +{7: 16, 0, 6, 8, 0, 6, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{d: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{e: 16, 0, 4, 2, 0, 2, 0, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 4, 2, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 12, 0, 4, 4, 4, 4, }, +{7: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 16, -16, 0, 8, -16, 0, 0, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 16, -8, -8, 0, 0, -8, -8, 8, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 8, -8, -8, 8, -8, -8, 0, 0, }, +{3: 16, -16, 0, 0, 8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 16, -8, 8, 0, -8, -8, 0, 8, -8, -8, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 8, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, 8, 0, 8, -8, -8, }, +{a: 16, 0, 0, 8, -16, 0, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 8, 0, -8, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 0, 8, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , x, x, x, , , x, }, +{5: , , , , x, , x, x, , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{1000,1010,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_143.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_143.txt new file mode 100644 index 0000000..83aed9d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_143.txt @@ -0,0 +1,442 @@ +143 Sbox: +LUT = { +0x0d,0x00,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{3: 0, 4, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 0, 2, 2, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 2, }, +{c: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 2, }, +{7: 0, 2, 2, 4, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:3, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 6, 0, 4, 8, 6, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 16, 0, 8, 0, 0, 0, 8, 0, 8, 0, 16, 16, 16, 0, 8, 0, }, +{4: 16, 10, 4, 8, 0, 4, 10, 4, 0, 2, 0, 4, 0, 0, 2, 0, }, +{8: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{3: 16, 4, 0, 6, 0, 4, 8, 6, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 16, 4, 4, 4, 2, 10, 10, 8, 0, 0, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 6, 0, 2, 6, 8, 4, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 16, 0, 4, 2, 2, 0, 0, 2, 4, 2, 4, 4, 8, 0, 0, 0, }, +{a: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{c: 16, 2, 4, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 2, }, +{7: 16, 6, 6, 4, 0, 0, 8, 0, 2, 2, 0, 4, 0, 0, 0, 0, }, +{b: 16, 0, 4, 2, 2, 0, 0, 2, 4, 2, 4, 4, 8, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{f: 16, 2, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 8, 0, 0, -16, 0, 0, }, +{2: 16, 8, -8, 0, 8, 0, 8, -8, 0, -16, 8, -16, -8, 16, 0, -8, }, +{4: 16, 0, 8, -8, 8, -8, 0, -8, -8, 16, -8, 0, 0, 0, -8, 0, }, +{8: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 8, 0, 0, -16, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, -8, 16, -8, 0, -8, 8, }, +{6: 16, 0, -8, 0, 8, 0, 0, 8, 0, -16, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, -8, 0, 8, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, -8, -8, 0, -8, 8, 8, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, }, +{7: 16, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, -16, 8, 0, 0, -8, }, +{b: 16, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , , x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, , x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , x, , x, x, x, x, , x, , , x, x, x, }, +{7: , x, x, , x, , x, x, x, , x, x, , x, , x, }, +{b: , , , , , x, x, x, x, , x, , x, x, , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , x, , x, , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,1000,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,1001,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +143 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x00,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{4: 0, 2, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{5: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 4, 4, 2, 0, 0, 0, 2, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 2, }, +{a: 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:3, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 10, 0, 4, 4, 0, 0, 0, 2, 6, 0, 0, 0, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 6, 4, 4, 4, 6, 4, 4, 6, 6, }, +{4: 16, 6, 0, 8, 0, 6, 4, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, }, +{3: 16, 4, 0, 4, 0, 4, 10, 6, 0, 0, 0, 0, 0, 2, 2, 0, }, +{5: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 6, 0, 4, 0, 6, 8, 4, 2, 0, 0, 0, 2, 0, 0, 0, }, +{9: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 0, 2, 4, 0, 2, 2, }, +{a: 16, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{b: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{d: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 8, 2, 0, 0, 2, 0, 0, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 8, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 8, -8, 0, -8, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, -8, 0, 0, 8, 8, -8, 0, 0, 0, -8, -8, 8, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, }, +{3: 16, -8, 0, 0, 8, -8, -8, 0, -8, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, 16, -16, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, -8, 0, 0, 8, -8, -8, 0, 0, 0, -8, 8, -8, 0, 0, 8, }, +{9: 16, 0, 0, 0, -8, 0, 0, 16, 0, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, }, +{c: 16, 0, 0, 0, -8, 0, 0, -16, 8, -8, 8, 0, -8, 8, 8, -8, }, +{7: 16, 8, -16, 0, 8, -8, 8, 0, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{e: 16, 0, 0, -16, -8, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , , , x, , x, x, , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , x, , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0100,1011,0,}, +{0100,1110,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,1011,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 7, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x05,0x06,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x01,0x0a,0x04,}, {0x04,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x06,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x04,0x09,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_144.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_144.txt new file mode 100644 index 0000000..d5411e0 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_144.txt @@ -0,0 +1,442 @@ +144 Sbox: +LUT = { +0x08,0x0e,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x00,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 8, 2, 0, 2, 2, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +{a: 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, }, +{d: 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{e: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 4, 4, 16, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 0, 10, 8, 8, 0, 0, 8, 2, 8, 10, 2, 0, 0, 8, 0, }, +{4: 16, 0, 4, 4, 0, 4, 4, 16, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{3: 16, 2, 0, 2, 0, 4, 4, 8, 0, 2, 0, 0, 4, 4, 0, 2, }, +{5: 16, 0, 0, 0, 0, 8, 8, 16, 0, 0, 0, 0, 8, 8, 0, 0, }, +{6: 16, 4, 6, 4, 0, 4, 4, 8, 6, 4, 6, 6, 4, 4, 0, 4, }, +{9: 16, 2, 0, 4, 4, 0, 0, 0, 2, 2, 4, 2, 2, 0, 2, 0, }, +{a: 16, 0, 6, 0, 6, 2, 2, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{c: 16, 2, 4, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{7: 16, 6, 0, 2, 0, 0, 0, 8, 4, 2, 0, 4, 0, 0, 0, 6, }, +{b: 16, 0, 0, 4, 6, 2, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:46, 6:14, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 0, 8, 0, -8, 8, 0, 0, 8, 0, -8, -16, 0, 8, }, +{2: 16, 8, 0, 0, 0, 0, 0, -8, 0, -16, 8, -16, -8, 16, 0, 0, }, +{4: 16, 0, 0, 0, 0, 0, 0, -16, 0, 16, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, -8, 8, 0, -8, 16, -8, 0, 8, 0, }, +{6: 16, 8, -8, -8, 8, -8, -8, 8, 8, -16, -8, 0, -8, 0, 8, 8, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, }, +{a: 16, 0, -8, 8, 0, 0, 8, -8, -8, 0, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{b: 16, 0, 8, 0, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{d: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , x, x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , x, x, x, , , x, x, }, +{b: , x, x, , x, x, , , , x, x, , x, , x, x, }, +{d: , , x, x, x, x, , , , x, x, , , x, x, x, }, +{e: , , x, x, x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x02,0x05,0x07,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +144 Inverse Sbox: +LUT = { +0x0e,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x01,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 4, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 2, 0, }, +{a: 0, 0, 0, 4, 0, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, }, +{c: 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 2, }, +{7: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 4, 2, 0, 2, 6, 0, 0, 2, 2, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 0, 6, 4, 0, 0, 4, 6, 4, }, +{4: 16, 0, 8, 4, 2, 2, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 4, 0, 4, 0, 4, 8, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{5: 16, 4, 0, 4, 0, 4, 8, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 4, 2, 0, 2, 0, 0, 6, 2, 0, 0, 4, 2, 0, 2, 0, }, +{a: 16, 0, 8, 4, 4, 2, 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, }, +{c: 16, 0, 10, 4, 0, 0, 0, 6, 4, 0, 4, 0, 6, 4, 4, 6, }, +{7: 16, 4, 2, 0, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, 2, }, +{b: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 0, 2, 2, 0, 4, 0, 0, 0, 6, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:46, 6:14, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{f: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:9, 8:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +{2: 16, 8, -8, 0, 0, -16, 8, -8, 8, -8, 8, 0, 0, 0, 0, -8, }, +{4: 16, 0, 0, 0, 0, 16, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 16, -16, -8, 8, 0, 0, -8, 8, -16, -8, 8, 8, }, +{9: 16, 0, -8, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, 8, 0, -8, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, -8, 16, -8, 0, 0, }, +{c: 16, 8, -8, 0, 0, 0, 0, -8, 8, -8, 8, -8, -16, 8, 0, 0, }, +{7: 16, 0, -8, 0, 0, 0, 8, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, -8, -8, 0, 8, 8, 0, 0, -8, 8, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, , x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, , , , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , x, x, , , x, x, x, }, +{7: , x, x, x, , , , x, , x, x, x, , , x, x, }, +{b: , x, x, , , , , x, , x, x, , x, , x, x, }, +{d: , x, x, x, , , , , , x, x, , , x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0110,0101,1,}, +{1000,0110,0,}, +{1000,1000,1,}, +{1000,1110,1,}, +{1011,0110,1,}, +{1011,1010,0,}, +{1011,1100,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x0a,0x0c,}, {0x0b,}}, +{{0x09,0x0a,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x0b,}}, +{{0x03,0x0c,}, {0x0b,}}, +{{0x09,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x0b,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x03,0x08,0x0b,}}, +{{0x05,0x06,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x0b,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_145.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_145.txt new file mode 100644 index 0000000..f21c22d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_145.txt @@ -0,0 +1,442 @@ +145 Sbox: +LUT = { +0x08,0x00,0x01,0x0f,0x02,0x05,0x06,0x07,0x04,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, }, +{4: 0, 2, 0, 2, 4, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 6, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 0, 2, 0, 0, 2, 2, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, 0, 4, 0, 0, 2, }, +{c: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 4, 2, }, +{b: 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 0, 0, }, +{e: 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:6, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 4, 0, 0, 0, 4, 0, 2, 8, 2, 2, 0, }, +{2: 16, 0, 6, 2, 0, 0, 4, 0, 10, 0, 4, 8, 4, 0, 8, 2, }, +{4: 16, 2, 0, 2, 4, 4, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, }, +{8: 16, 0, 2, 2, 4, 4, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, }, +{3: 16, 2, 0, 0, 4, 4, 2, 2, 0, 2, 0, 2, 4, 0, 0, 2, }, +{5: 16, 0, 10, 0, 0, 0, 8, 2, 6, 0, 4, 8, 4, 2, 4, 0, }, +{6: 16, 4, 0, 0, 4, 4, 0, 2, 0, 4, 0, 2, 8, 0, 2, 2, }, +{9: 16, 2, 4, 2, 0, 0, 4, 0, 8, 2, 4, 0, 4, 0, 0, 2, }, +{a: 16, 4, 0, 0, 4, 4, 2, 2, 0, 4, 2, 0, 8, 0, 0, 2, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{7: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 0, 8, 0, 2, 4, 2, }, +{b: 16, 8, 8, 0, 16, 16, 0, 0, 8, 8, 0, 0, 16, 0, 0, 0, }, +{d: 16, 4, 0, 2, 4, 4, 2, 0, 0, 4, 2, 0, 8, 2, 0, 0, }, +{e: 16, 2, 8, 0, 0, 0, 0, 2, 4, 2, 4, 0, 4, 2, 4, 0, }, +{f: 16, 0, 2, 0, 4, 4, 0, 2, 2, 0, 2, 0, 4, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:60, 4:50, 6:2, 8:16, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{9: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{c: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, -16, }, +{2: 16, 0, -8, 0, 8, 0, 8, 0, 8, -8, 0, -16, 0, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, -8, }, +{8: 16, 8, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, -8, -8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, -8, 8, 0, 0, -16, 0, 0, 8, -8, -8, 0, 0, 8, -8, 8, }, +{6: 16, 0, -16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, 8, }, +{9: 16, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, -16, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, 0, 8, 8, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, 0, -8, -16, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{b: 16, -8, -8, 16, -8, 16, -8, -8, 0, 0, -8, 16, -8, 0, 0, -8, }, +{d: 16, -8, 8, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, -8, }, +{e: 16, 8, -8, 0, 0, -16, 0, 0, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, , x, x, x, x, , x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, , x, x, , , , x, x, , , x, x, x, }, +{7: , , , , , , x, x, x, x, x, , x, x, x, x, }, +{b: , x, x, , , x, x, x, x, , x, x, , x, x, x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0110,1,}, +{0011,0101,1,}, +{0011,1011,0,}, +{0011,1110,1,}, +{0100,0111,1,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0111,0010,1,}, +{0111,1001,1,}, +{0111,1011,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x01,0x02,0x08,}, {0x07,}}, +{{0x05,0x06,0x08,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x07,}}, +{{0x01,0x0a,0x04,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x02,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,}}, +{{0x0d,0x0e,}, {0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +145 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0a,0x08,0x05,0x06,0x07,0x00,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 2, }, +{4: 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, }, +{8: 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 2, 0, 2, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 2, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, }, +{d: 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, }, +{f: 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:5, 2:6, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 2, 0, 4, 2, 4, 0, 0, 8, 4, 2, 0, }, +{2: 16, 0, 6, 0, 2, 0, 10, 0, 4, 0, 4, 4, 8, 0, 8, 2, }, +{4: 16, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, }, +{8: 16, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 16, 4, 0, 4, }, +{3: 16, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 16, 4, 0, 4, }, +{5: 16, 0, 4, 2, 0, 2, 8, 0, 4, 2, 4, 4, 0, 2, 0, 0, }, +{6: 16, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 2, }, +{9: 16, 0, 10, 0, 2, 0, 6, 0, 8, 0, 4, 4, 8, 0, 4, 2, }, +{a: 16, 4, 0, 2, 0, 2, 0, 4, 2, 4, 0, 0, 8, 4, 2, 0, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 4, 4, 4, 4, 4, 8, 4, 8, 0, 0, 16, 8, 4, 4, }, +{d: 16, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, }, +{e: 16, 2, 8, 0, 2, 0, 4, 2, 0, 0, 4, 4, 0, 0, 4, 2, }, +{f: 16, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:60, 4:50, 6:2, 8:16, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{5: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{b: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, -8, 0, 0, 0, 8, 0, 8, -8, 0, -8, }, +{2: 16, 8, -8, 0, 0, -8, 8, 0, 0, 0, 8, 0, -8, 8, -16, -8, }, +{4: 16, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{8: 16, 0, 8, 8, 0, 8, -8, 0, 0, 8, -8, 0, -8, -8, 0, -16, }, +{3: 16, -8, -16, 0, 0, 8, -8, 0, 8, 0, 0, 8, -8, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, }, +{9: 16, -8, 8, 0, 0, -8, 8, 0, 0, 0, -8, 0, -8, 8, -16, 8, }, +{a: 16, 8, -8, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, 0, -8, 0, 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, -16, 0, 0, -16, 8, 8, -8, 8, 0, 0, 16, -8, }, +{d: 16, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , , x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{7: , x, , , , x, , , , x, , x, , , , x, }, +{b: , , , , , , x, x, x, x, x, x, , x, x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, x, , x, x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0011,1,}, +{0110,0101,1,}, +{0110,1011,1,}, +{0110,1110,0,}, +{1000,0111,0,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1110,0010,1,}, +{1110,1001,1,}, +{1110,1011,0,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x05,0x06,0x08,}, {0x06,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x01,0x0a,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x06,0x09,0x0f,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x08,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_146.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_146.txt new file mode 100644 index 0000000..3770a0b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_146.txt @@ -0,0 +1,442 @@ +146 Sbox: +LUT = { +0x08,0x00,0x01,0x0b,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x02,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 4, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 6, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 0, 4, 6, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, }, +{2: 16, 4, 10, 0, 4, 4, 0, 0, 10, 4, 2, 2, 8, 0, 0, 0, }, +{4: 16, 4, 0, 8, 0, 4, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 0, 6, 4, 6, 0, 0, 2, 0, 2, 2, 0, 2, }, +{6: 16, 0, 2, 0, 2, 4, 4, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 16, 4, 8, 0, 0, 6, 0, 2, 4, 0, 0, 0, 6, 0, 2, 0, }, +{a: 16, 4, 10, 0, 10, 4, 0, 0, 4, 8, 0, 2, 4, 2, 0, 0, }, +{c: 16, 4, 0, 8, 0, 4, 4, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{7: 16, 4, 0, 8, 2, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 6, 4, 6, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 2, 0, 0, 4, 4, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 4, 0, 8, 0, 4, 4, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{a: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{c: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{e: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{f: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -16, 0, 0, }, +{2: 16, 0, -8, 8, 0, 0, 0, -8, 8, -8, 0, -8, -8, 16, 0, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 8, 16, 8, -16, -8, -8, 0, 8, 0, 8, -16, -8, 0, }, +{5: 16, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, -8, 0, 8, 0, -8, -16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 8, -8, 8, 0, -8, 16, -8, 0, -8, 0, -8, 0, 0, 0, -8, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, -8, 0, 8, -8, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0100,1100,1,}, +{0101,0011,1,}, +{0101,1001,1,}, +{0101,1010,0,}, +{0110,0100,1,}, +{1000,0011,0,}, +{1000,1000,1,}, +{1000,1011,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x09,0x0a,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x0a,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x0a,0x04,}, {0x03,0x05,0x06,}}, +{{0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0a,0x0c,}, {0x01,0x04,0x05,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x03,0x05,0x06,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x01,0x04,0x05,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x05,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +146 Inverse Sbox: +LUT = { +0x01,0x02,0x0b,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x03,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, }, +{8: 0, 4, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 8, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, 0, }, +{9: 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, }, +{b: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +{f: 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 0, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 16, 8, 10, 0, 8, 8, 0, 2, 8, 10, 0, 0, 8, 0, 2, 0, }, +{4: 16, 0, 0, 8, 0, 16, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, }, +{8: 16, 4, 4, 0, 4, 0, 0, 2, 0, 10, 0, 2, 6, 0, 0, 0, }, +{3: 16, 6, 4, 4, 0, 8, 6, 4, 6, 4, 4, 4, 0, 6, 4, 4, }, +{5: 16, 0, 0, 4, 0, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 16, 2, 0, 0, 0, 8, 6, 4, 2, 0, 0, 0, 0, 6, 4, 0, }, +{9: 16, 0, 10, 0, 4, 0, 0, 0, 4, 4, 0, 2, 6, 0, 2, 0, }, +{a: 16, 6, 4, 2, 6, 0, 0, 0, 0, 8, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{7: 16, 0, 2, 4, 0, 8, 0, 2, 0, 2, 4, 4, 0, 0, 2, 4, }, +{b: 16, 0, 8, 2, 6, 0, 2, 0, 6, 4, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +{f: 16, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, }, +{3: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{7: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 8, -8, 0, -8, -8, 8, }, +{2: 16, 16, -16, 8, 0, -16, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{4: 16, 0, 0, -8, 8, 16, -8, -8, -8, -8, 0, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, 0, -8, -8, 8, -8, }, +{3: 16, -16, 0, 8, 8, 0, -8, -8, -8, -8, 8, 8, 8, -8, -8, 8, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -16, -8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, -8, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, 0, 8, -8, 0, 0, -8, 8, -8, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, }, +{7: 16, 0, -16, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, -8, 8, -8, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , x, x, , x, x, , , x, }, +{5: , , , , x, , x, x, x, x, , x, x, x, , x, }, +{6: , , , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , , x, x, x, , , x, x, , , , x, x, , x, }, +{a: , , , x, x, x, , , x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , , , , , , , x, x, , x, x, , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, x, x, , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 7, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,0x09,0x0b,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_147.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_147.txt new file mode 100644 index 0000000..486f4af --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_147.txt @@ -0,0 +1,442 @@ +147 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x02,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +{3: 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 2, 0, 4, 0, 0, 4, 2, 0, 2, 2, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 0, 0, 0, }, +{d: 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 4, }, +{2: 16, 0, 10, 8, 8, 0, 0, 8, 2, 8, 10, 2, 0, 0, 8, 0, }, +{4: 16, 8, 4, 16, 4, 4, 8, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{8: 16, 2, 4, 0, 4, 0, 0, 0, 2, 6, 0, 2, 2, 0, 2, 0, }, +{3: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 4, 0, 8, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 4, }, +{6: 16, 0, 6, 8, 4, 0, 0, 4, 2, 0, 6, 2, 0, 0, 0, 0, }, +{9: 16, 2, 0, 0, 0, 0, 0, 4, 2, 6, 4, 2, 2, 0, 2, 0, }, +{a: 16, 0, 6, 0, 4, 0, 2, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 16, 0, 0, 0, 2, 2, 2, 4, 2, 4, 6, 0, 2, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 6, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:52, 4:50, 6:10, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 0, 8, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{e: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:9, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, -8, -16, 0, 0, }, +{2: 16, 8, 0, 0, 0, 0, 0, -8, 0, -16, 8, -16, -8, 16, 0, 0, }, +{4: 16, 0, 8, -8, 8, 8, -8, -16, 8, 16, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, }, +{3: 16, -8, 8, 0, 8, 0, -8, -8, 0, 0, 8, 0, 8, -16, 0, -8, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, 0, 0, 0, 0, 0, 8, 0, -16, -8, 0, -8, 0, 0, 0, }, +{9: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{a: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 8, 0, -8, -16, 8, 0, -8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, }, +{d: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{e: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , x, , , x, x, , , , x, }, +{b: , x, x, , x, x, , x, , , x, , x, , , x, }, +{d: , , x, x, x, x, , x, , , x, , , x, , x, }, +{e: , , x, x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x02,0x05,0x07,}}, +{{0x0d,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +147 Inverse Sbox: +LUT = { +0x01,0x02,0x0c,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, }, +{4: 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 4, 2, 0, 0, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{c: 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 2, }, +{7: 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 0, 6, 4, 0, 0, 4, 6, 4, }, +{4: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 2, 8, 4, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 0, 2, 4, 2, 2, 2, 0, }, +{5: 16, 4, 0, 8, 0, 4, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{6: 16, 2, 8, 4, 0, 0, 2, 4, 4, 2, 0, 0, 4, 0, 2, 0, }, +{9: 16, 0, 2, 4, 2, 4, 0, 2, 2, 0, 0, 4, 2, 0, 2, 0, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 10, 4, 0, 0, 0, 6, 4, 0, 4, 0, 6, 4, 4, 6, }, +{7: 16, 0, 2, 4, 2, 4, 0, 2, 2, 2, 0, 4, 0, 0, 0, 2, }, +{b: 16, 4, 0, 8, 2, 4, 4, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{d: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 8, 0, 4, 4, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:52, 4:50, 6:10, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{f: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:9, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{2: 16, 8, -8, 0, 0, -16, 8, -8, 8, -8, 8, 0, 0, 0, 0, -8, }, +{4: 16, 0, 0, -8, 16, 16, -8, -8, 0, 0, -8, -8, 16, -8, -8, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, 0, 0, -8, 8, -16, -8, 0, 0, }, +{3: 16, -8, 0, 0, 0, 0, -8, -8, -8, 0, 8, 8, 0, 0, 0, 0, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, -16, -8, 8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{9: 16, 0, -8, 0, 0, 0, 0, 8, 0, -8, -8, 0, 0, 8, 0, -8, }, +{a: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 8, -8, 0, 0, 0, 0, -8, 8, -8, 8, -8, -16, 8, 0, 0, }, +{7: 16, 0, -8, 0, 0, 0, 8, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, -8, 0, 8, -8, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, , x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , x, x, x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , x, , , , , x, x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , x, x, x, , x, , x, , , x, , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0110,0101,1,}, +{1000,0100,0,}, +{1000,1010,1,}, +{1000,1110,1,}, +{1011,0100,0,}, +{1011,1000,1,}, +{1011,1100,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x0b,}}, +{{0x03,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x03,0x04,}, {0x03,0x08,0x0b,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x0b,}}, +{{0x03,0x0c,}, {0x0b,}}, +{{0x09,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x0b,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x03,0x05,0x06,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_148.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_148.txt new file mode 100644 index 0000000..b07c60d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_148.txt @@ -0,0 +1,442 @@ +148 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x0b,0x05,0x04,0x07,0x00,0x09,0x0a,0x03,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{8: 0, 4, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 8, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 4, 2, }, +{9: 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, }, +{b: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 0, 16, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 16, 8, 10, 0, 8, 8, 0, 0, 8, 10, 0, 2, 8, 0, 0, 2, }, +{4: 16, 0, 0, 4, 0, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 16, 4, 4, 0, 4, 0, 0, 2, 0, 10, 0, 2, 6, 0, 0, 0, }, +{3: 16, 6, 4, 6, 0, 8, 4, 4, 6, 4, 6, 4, 0, 4, 4, 4, }, +{5: 16, 0, 0, 0, 0, 16, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{6: 16, 0, 2, 0, 0, 8, 4, 4, 0, 2, 0, 2, 0, 4, 4, 2, }, +{9: 16, 0, 10, 0, 4, 0, 0, 2, 4, 4, 0, 0, 6, 0, 0, 2, }, +{a: 16, 6, 4, 0, 6, 0, 2, 0, 0, 8, 2, 0, 4, 0, 0, 0, }, +{c: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{7: 16, 2, 0, 6, 0, 8, 0, 0, 2, 0, 6, 4, 0, 0, 0, 4, }, +{b: 16, 0, 8, 2, 6, 0, 2, 0, 6, 4, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{e: 16, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 0, 8, 0, -8, 0, }, +{2: 16, 8, -16, 8, 0, -8, 16, -8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{4: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, 0, -8, -8, 8, -8, }, +{3: 16, -8, 0, 8, 8, 8, -16, -8, -8, -8, 8, 0, 8, -8, -8, 8, }, +{5: 16, -8, 0, -8, 8, -8, 0, -8, 0, -8, 0, 16, 0, -8, 0, 8, }, +{6: 16, 8, -16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, 8, -8, -8, 0, -8, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 8, -8, 0, -8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 0, -8, 8, -8, -8, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, }, +{e: 16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, x, x, , x, x, , , x, }, +{5: , , , , x, x, x, x, x, x, , x, x, x, , x, }, +{6: , , , , x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, , x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, , , x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , , , , , , , x, x, , x, x, , , x, }, +{b: , x, , x, x, x, , x, x, x, , , , , , x, }, +{d: , , , , x, x, , x, x, x, , , x, x, , x, }, +{e: , , , , , x, , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 7, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +148 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x0b,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x04,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{a: 0, 0, 6, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 0, 4, 6, 0, 0, 0, 6, 0, 2, 0, 0, 2, 0, }, +{2: 16, 4, 10, 0, 4, 4, 0, 2, 10, 4, 0, 0, 8, 2, 0, 0, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 0, 0, 2, 6, 2, 2, 2, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 4, 0, 4, 0, 4, 8, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 4, 0, 4, 2, 4, 8, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 16, 4, 8, 0, 0, 6, 0, 0, 4, 0, 0, 2, 6, 0, 0, 2, }, +{a: 16, 4, 10, 0, 10, 4, 0, 2, 4, 8, 2, 0, 4, 0, 0, 0, }, +{c: 16, 0, 0, 4, 0, 6, 0, 0, 0, 2, 2, 6, 0, 2, 0, 2, }, +{7: 16, 0, 2, 4, 2, 4, 0, 2, 0, 0, 0, 4, 0, 2, 2, 2, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{f: 16, 0, 2, 4, 0, 4, 0, 2, 2, 0, 2, 4, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:48, 4:40, 6:12, 8:14, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{c: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{e: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{f: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 8, -16, 0, 0, 0, 0, -8, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 16, -8, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -16, 0, 8, 16, 0, -8, -8, -16, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, -8, 8, -8, 0, -8, 8, }, +{9: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{a: 16, 16, -8, 8, 0, -8, 8, -8, 0, -8, 0, -8, -8, 0, 0, 0, }, +{c: 16, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 0, }, +{7: 16, 0, -8, -8, 0, 0, 8, 8, 0, -8, 0, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{e: 16, 0, 0, -8, 0, -8, -8, 8, 0, 0, 8, 0, -8, -8, 8, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , , x, x, , , , x, x, , , , x, x, , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , x, , , x, x, , x, x, , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0001,0011,1,}, +{0001,1001,1,}, +{0001,1010,0,}, +{0100,1101,1,}, +{0110,0101,1,}, +{1000,0011,0,}, +{1000,1000,1,}, +{1000,1011,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x09,0x0a,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x09,0x0a,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x09,}}, +{{0x0a,0x04,}, {0x01,}}, +{{0x02,0x0c,}, {0x09,}}, +{{0x0a,0x0c,}, {0x01,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x01,0x06,0x07,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x06,0x09,0x0f,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x04,0x09,0x0d,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x01,0x04,0x05,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_149.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_149.txt new file mode 100644 index 0000000..ea1d2f9 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_149.txt @@ -0,0 +1,442 @@ +149 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x0d,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 13, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 13, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 0, 4, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, }, +{b: 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, }, +{d: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 4, 0, }, +{f: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 4, 8, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 16, 0, 10, 0, 4, 0, 4, 0, 6, 4, 6, 6, 4, 0, 4, 0, }, +{4: 16, 4, 0, 4, 0, 4, 8, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{8: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 2, 0, 2, 0, 4, 4, 4, 2, 2, 0, 0, 2, 2, 0, 0, }, +{5: 16, 8, 8, 8, 0, 16, 16, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 0, 2, 0, 2, 4, 4, 4, 0, 0, 2, 2, 0, 0, 2, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 0, 2, 2, 4, 4, 4, 0, 2, 2, 0, 2, 0, 0, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 6, 6, }, +{7: 16, 2, 8, 2, 0, 0, 4, 0, 2, 0, 2, 4, 0, 4, 0, 4, }, +{b: 16, 0, 10, 0, 6, 0, 4, 0, 4, 4, 0, 6, 4, 6, 0, 4, }, +{d: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 2, 8, 2, 2, 0, 4, 0, 0, 0, 4, 4, 0, 2, 4, 0, }, +{f: 16, 0, 2, 0, 0, 4, 4, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:52, 4:50, 6:10, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{5: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{7: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{2: 16, 8, -8, 8, 0, -8, 8, -8, 0, -8, 0, -16, 0, 8, 0, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 8, 0, -8, -8, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, -8, 0, -8, -8, 0, -8, 16, -8, 0, -8, 16, }, +{6: 16, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, 0, -8, 8, 0, 0, 8, -8, 8, -8, 0, 0, -8, 8, 0, -16, }, +{d: 16, 0, 8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{e: 16, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, 8, 0, 0, -16, }, +{f: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , x, x, , x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, , x, , , x, x, x, }, +{7: , , x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , x, x, , , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0100,1101,1,}, +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,0101,0,}, +{1000,1001,1,}, +{1000,1100,1,}, +{1111,0101,0,}, +{1111,1011,1,}, +{1111,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x05,0x06,0x08,}, {0x0f,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x01,0x0a,0x04,}, {0x0f,}}, +{{0x09,0x02,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x07,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x09,0x0f,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x0f,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x07,0x08,0x0f,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x04,0x07,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x07,0x08,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x04,0x0b,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +149 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x0d,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x04,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, }, +{9: 0, 2, 2, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, }, +{a: 0, 0, 4, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, }, +{c: 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 0, 0, }, +{7: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 4, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 0, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 4, 2, 8, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{2: 16, 0, 10, 0, 0, 0, 8, 2, 8, 0, 8, 8, 10, 0, 8, 2, }, +{4: 16, 4, 0, 4, 4, 2, 8, 0, 0, 2, 0, 2, 0, 4, 2, 0, }, +{8: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{3: 16, 4, 0, 4, 4, 4, 16, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{5: 16, 8, 4, 8, 8, 4, 16, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 16, 4, 0, 4, 4, 4, 16, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{9: 16, 2, 6, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, 0, 0, 2, }, +{a: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{c: 16, 0, 6, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 4, 0, }, +{7: 16, 0, 6, 0, 0, 0, 8, 2, 0, 0, 0, 4, 6, 0, 4, 2, }, +{b: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 4, 6, 2, 2, 2, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 0, 0, 0, 2, 2, 0, 6, 4, 4, 2, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:52, 4:50, 6:10, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{3: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 0, 0, 4, 0, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 8, -16, 0, 0, 0, 0, -8, 0, -8, }, +{2: 16, 0, -16, 8, 0, 0, 0, -8, 16, 0, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 16, -8, 0, -8, }, +{8: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 8, 8, -8, 0, -8, -16, 8, 0, 0, 0, -8, 0, 8, }, +{5: 16, -8, 16, -16, 8, -8, 8, -16, 0, 8, -8, 8, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, 0, 8, 8, 0, 0, -8, 8, -16, -8, -8, 8, }, +{9: 16, -8, 0, 8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 0, }, +{c: 16, 8, 0, -8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 8, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, , , x, , x, x, x, , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , , , , , , x, , x, , x, x, , x, , x, }, +{b: , x, , x, x, , x, , x, , x, , x, x, , x, }, +{d: , x, , , x, , x, x, x, , x, , , , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x05,0x09,0x0c,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x02,0x09,0x0b,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_150.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_150.txt new file mode 100644 index 0000000..d291958 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_150.txt @@ -0,0 +1,442 @@ +150 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x0f,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, 2, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 4, }, +{b: 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 4, 2, 0, 6, 0, 2, 0, 8, 0, 0, 0, 6, }, +{2: 16, 0, 8, 0, 0, 0, 16, 0, 16, 0, 16, 8, 8, 0, 8, 0, }, +{4: 16, 0, 4, 4, 0, 4, 4, 0, 0, 2, 0, 8, 2, 0, 2, 2, }, +{8: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{3: 16, 2, 0, 6, 2, 4, 0, 0, 0, 4, 0, 8, 0, 6, 0, 0, }, +{5: 16, 0, 4, 0, 0, 2, 4, 2, 0, 4, 0, 8, 2, 4, 2, 0, }, +{6: 16, 4, 6, 0, 6, 0, 4, 4, 0, 4, 0, 10, 0, 6, 0, 4, }, +{9: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 2, 6, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{7: 16, 6, 6, 6, 4, 4, 4, 4, 0, 0, 0, 10, 0, 0, 0, 4, }, +{b: 16, 0, 6, 2, 2, 2, 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, }, +{d: 16, 0, 4, 2, 0, 2, 4, 0, 4, 2, 8, 0, 0, 2, 4, 0, }, +{e: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 4, 2, 4, 0, 8, 0, 0, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:46, 6:14, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{c: 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -16, 0, 0, }, +{2: 16, 8, 0, 8, 0, -8, 0, -8, 8, -16, 8, -16, -8, 16, -8, 0, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, }, +{8: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 8, 0, 8, 8, 0, -16, -8, 0, 0, 0, 8, -8, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, -8, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, -8, -8, -8, 8, 8, 8, 8, 0, 0, 0, -16, 0, 0, 0, -8, }, +{b: 16, 0, -8, 8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 8, 0, -8, -8, 0, -8, 8, -8, 0, 8, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , x, , x, , x, x, , x, x, x, , x, x, x, x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , x, x, , x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0100,1100,1,}, +{0110,1101,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x01,0x06,0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +150 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x0f,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, }, +{8: 0, 4, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 2, 2, }, +{9: 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{a: 0, 2, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 6, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 2, 2, 0, 4, 2, 2, 0, 6, 0, 0, 0, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 6, 4, 6, 4, 6, 6, 4, 4, 4, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 0, 0, 2, 6, 2, 2, 2, 0, }, +{8: 16, 4, 0, 0, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, 2, }, +{3: 16, 2, 0, 4, 2, 4, 2, 0, 0, 2, 0, 4, 2, 2, 0, 0, }, +{5: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 16, 6, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 0, 0, 2, 2, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 2, 0, 2, 0, 4, 4, 4, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 16, 8, 8, 8, 0, 8, 8, 10, 0, 2, 0, 10, 2, 0, 0, 0, }, +{b: 16, 0, 8, 2, 6, 0, 2, 0, 6, 4, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, 6, 4, 6, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 8, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 4, 4, 4, }, +{f: 16, 6, 0, 2, 2, 0, 0, 4, 0, 0, 2, 4, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:46, 6:14, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 8, 0, 0, 4, 0, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 4, 4, 4, 0, 12, 0, 4, 0, 0, 0, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 8, 4, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, 0, -8, }, +{4: 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, }, +{8: 16, -8, 0, 8, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{9: 16, 8, 0, 8, -8, -8, 0, 8, 0, -8, 0, 0, 0, 8, -16, -8, }, +{a: 16, -8, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 8, -8, 8, -8, 16, -8, -8, 0, 0, 0, }, +{7: 16, 0, -16, -8, 8, 0, 0, 8, 0, -8, -16, 0, 0, 0, 16, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 0, 8, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 8, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{5: , x, , , x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, , x, x, x, x, , x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, , , , x, x, , x, x, x, , x, x, x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, , x, x, , x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1100,0111,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1110,0111,0,}, +{1110,1001,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0c,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_151.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_151.txt new file mode 100644 index 0000000..0ba9bff --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_151.txt @@ -0,0 +1,442 @@ +151 Sbox: +LUT = { +0x08,0x00,0x01,0x06,0x02,0x05,0x0f,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, }, +{4: 0, 2, 0, 4, 4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{8: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 0, 2, 4, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 6, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, }, +{b: 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, }, +{d: 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, }, +{e: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 2, 4, 0, }, +{f: 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 16, 0, 4, 0, 4, }, +{2: 16, 0, 6, 0, 0, 0, 4, 2, 10, 0, 4, 8, 4, 2, 8, 0, }, +{4: 16, 2, 0, 4, 4, 4, 2, 0, 0, 2, 0, 8, 0, 0, 2, 4, }, +{8: 16, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, }, +{3: 16, 2, 0, 4, 4, 4, 2, 0, 0, 2, 0, 8, 0, 0, 2, 4, }, +{5: 16, 0, 10, 0, 0, 0, 8, 2, 6, 0, 4, 8, 4, 2, 4, 0, }, +{6: 16, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 16, 0, 4, 0, 4, }, +{9: 16, 2, 4, 2, 0, 0, 4, 0, 8, 2, 4, 0, 4, 0, 0, 2, }, +{a: 16, 0, 2, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{7: 16, 4, 4, 8, 8, 8, 4, 4, 4, 4, 0, 16, 0, 4, 4, 8, }, +{b: 16, 2, 8, 0, 2, 2, 0, 0, 8, 2, 0, 0, 8, 0, 0, 0, }, +{d: 16, 2, 2, 2, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, }, +{e: 16, 0, 8, 0, 2, 2, 0, 2, 4, 0, 4, 0, 4, 2, 4, 0, }, +{f: 16, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:60, 4:50, 6:2, 8:16, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{9: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{7: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 8, 8, -8, -8, 0, 0, 0, -8, 8, -16, }, +{2: 16, 8, -8, 0, 0, -16, 0, 0, 8, -8, 8, 0, 0, 8, -8, -8, }, +{4: 16, 8, 8, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, -8, -8, -8, }, +{8: 16, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, }, +{3: 16, -8, -8, 0, 0, 0, 0, 0, -8, 8, 8, 0, 0, -8, -8, 8, }, +{5: 16, -8, 8, 0, 0, -16, 0, 0, 8, -8, -8, 0, 0, 8, -8, 8, }, +{6: 16, 0, -16, 0, 8, 0, 0, 0, -8, -8, -8, 0, 8, -8, 8, 8, }, +{9: 16, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, -16, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, -8, -8, -16, 8, 16, 8, 8, 0, 0, -8, -16, 8, 0, 0, -8, }, +{b: 16, 0, -8, 16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, }, +{d: 16, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, }, +{e: 16, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 16, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{6: , , , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, , x, x, x, , x, x, x, x, x, x, , x, }, +{7: , , , , , , x, x, x, x, x, , x, x, x, x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , x, x, x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0011,0101,1,}, +{0011,0111,0,}, +{0100,0111,1,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0111,0111,1,}, +{0111,1001,1,}, +{0111,1110,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x06,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x0a,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x02,0x05,0x07,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x04,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,}}, +{{0x01,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +151 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0f,0x08,0x05,0x03,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 0, }, +{8: 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 2, }, +{9: 0, 0, 2, 0, 2, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{d: 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 4, 0, 0, 0, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 2, 2, 0, 4, 2, 0, 0, 4, 2, 2, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 10, 0, 4, 2, 4, 4, 8, 2, 8, 0, }, +{4: 16, 4, 0, 4, 2, 4, 0, 4, 2, 0, 2, 8, 0, 2, 0, 0, }, +{8: 16, 4, 0, 4, 2, 4, 0, 4, 0, 0, 0, 8, 2, 2, 2, 0, }, +{3: 16, 4, 0, 4, 0, 4, 0, 4, 0, 2, 0, 8, 2, 0, 2, 2, }, +{5: 16, 0, 4, 2, 0, 2, 8, 0, 4, 2, 4, 4, 0, 2, 0, 0, }, +{6: 16, 4, 2, 0, 0, 0, 2, 4, 0, 2, 2, 4, 0, 0, 2, 2, }, +{9: 16, 0, 10, 0, 2, 0, 6, 0, 8, 0, 4, 4, 8, 0, 4, 2, }, +{a: 16, 4, 0, 2, 0, 2, 0, 4, 2, 2, 0, 4, 2, 0, 0, 2, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{7: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 4, 2, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 2, 2, 0, }, +{e: 16, 0, 8, 2, 2, 2, 4, 0, 0, 0, 4, 4, 0, 0, 4, 2, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 2, 2, 2, 8, 0, 0, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:60, 4:50, 6:2, 8:16, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{5: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{6: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, }, +{b: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, 8, -16, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 8, -8, 0, 8, 0, 0, 0, -8, -8, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, 0, -16, }, +{3: 16, 0, -16, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, 8, }, +{9: 16, -8, 8, 0, 0, -8, 8, 0, 0, 0, -8, 0, -8, 8, -16, 8, }, +{a: 16, 0, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, -8, 0, 8, }, +{c: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 16, 0, 0, 16, -8, -8, -8, -8, 0, 0, 16, -8, }, +{b: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 8, 0, 0, -8, 0, 0, -8, 0, 8, 0, -8, 0, 0, -8, }, +{e: 16, 8, -8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -16, -8, }, +{f: 16, -8, -8, 0, 0, 8, 0, 0, -8, -8, 0, -8, 8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, , , x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , , x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , x, , , , x, x, , x, x, x, , x, x, x, x, }, +{b: , , , , , , x, x, x, x, x, x, , x, x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0011,1,}, +{0110,0010,1,}, +{0110,0101,1,}, +{0110,0111,0,}, +{1000,0111,0,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1110,0111,0,}, +{1110,1001,1,}, +{1110,1110,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x08,}, {0x06,0x09,0x0f,}}, +{{0x06,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x06,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x06,0x08,0x0e,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_152.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_152.txt new file mode 100644 index 0000000..d8e81e7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_152.txt @@ -0,0 +1,442 @@ +152 Sbox: +LUT = { +0x04,0x00,0x08,0x02,0x03,0x05,0x06,0x0b,0x01,0x09,0x0a,0x07,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, }, +{8: 0, 0, 2, 2, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 0, 4, 8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 4, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{c: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, }, +{d: 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, }, +{e: 0, 0, 4, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, }, +{f: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 2, 4, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, }, +{2: 16, 4, 10, 0, 0, 4, 2, 0, 0, 0, 10, 0, 2, 4, 8, 4, }, +{4: 16, 0, 0, 4, 2, 4, 2, 0, 2, 0, 0, 6, 0, 2, 2, 0, }, +{8: 16, 0, 2, 2, 4, 8, 4, 4, 2, 0, 0, 0, 4, 0, 0, 2, }, +{3: 16, 4, 4, 4, 8, 16, 8, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 16, 2, 0, 2, 4, 8, 4, 4, 2, 0, 2, 0, 4, 0, 0, 0, }, +{6: 16, 0, 2, 0, 4, 8, 4, 4, 0, 2, 0, 2, 4, 0, 0, 2, }, +{9: 16, 2, 0, 0, 2, 4, 2, 0, 4, 4, 0, 0, 0, 2, 2, 2, }, +{a: 16, 0, 0, 0, 0, 4, 0, 2, 6, 4, 0, 2, 2, 2, 2, 0, }, +{c: 16, 4, 10, 0, 2, 4, 0, 2, 0, 0, 6, 0, 0, 8, 4, 8, }, +{7: 16, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 16, 2, 0, 0, 4, 8, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 2, 0, 4, 2, 0, 0, 2, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:88, 2:58, 4:57, 6:3, 8:15, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 12, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, 8, -8, }, +{2: 16, 8, -8, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 16, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, }, +{8: 16, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -16, 0, }, +{3: 16, 0, -8, 8, 8, 8, -8, 0, -8, -16, 0, 16, 0, -16, -8, 8, }, +{5: 16, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, 0, -8, 8, }, +{6: 16, 0, -16, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 8, 0, }, +{c: 16, 8, 8, -8, -8, 0, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -16, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, 0, 0, 8, 0, 8, 0, 0, -16, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , , x, x, , x, }, +{6: , x, , x, x, x, x, x, x, x, , , x, , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, , x, , x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, , x, , , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , x, , x, , , x, x, x, x, , , x, , , x, }, +{b: , x, x, , x, x, x, x, x, x, , x, , , , x, }, +{d: , x, x, , x, x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0110,1,}, +{0111,0011,0,}, +{0111,1101,1,}, +{0111,1110,1,}, +{1010,0011,1,}, +{1010,1100,1,}, +{1010,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x06,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x09,0x0a,0x04,}, {0x07,}}, +{{0x01,0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x0a,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x07,0x09,0x0e,}}, +{{0x07,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +152 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x00,0x05,0x06,0x0b,0x02,0x09,0x0a,0x07,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 4, 0, 0, }, +{2: 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, }, +{4: 0, 2, 0, 4, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{8: 0, 2, 0, 2, 4, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, }, +{5: 0, 0, 2, 2, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{6: 0, 2, 0, 0, 0, 4, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 2, 2, }, +{c: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 2, 4, 0, 0, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 0, 2, }, +{d: 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, }, +{e: 0, 0, 4, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 4, 2, 0, 2, 0, 4, 2, 2, 4, 0, 0, }, +{2: 16, 4, 10, 0, 2, 4, 0, 2, 0, 0, 10, 0, 0, 4, 8, 4, }, +{4: 16, 2, 0, 4, 2, 4, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, }, +{8: 16, 2, 0, 2, 4, 8, 4, 4, 2, 0, 2, 0, 4, 0, 0, 0, }, +{3: 16, 4, 4, 4, 8, 16, 8, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 16, 0, 2, 2, 4, 8, 4, 4, 2, 0, 0, 0, 4, 0, 0, 2, }, +{6: 16, 2, 0, 0, 4, 8, 4, 4, 0, 2, 2, 2, 4, 0, 0, 0, }, +{9: 16, 0, 0, 2, 2, 4, 2, 0, 4, 6, 0, 0, 0, 2, 2, 0, }, +{a: 16, 2, 0, 0, 0, 4, 0, 2, 4, 4, 0, 0, 2, 2, 2, 2, }, +{c: 16, 4, 10, 0, 0, 4, 2, 0, 0, 0, 6, 0, 2, 8, 4, 8, }, +{7: 16, 0, 0, 6, 0, 4, 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 16, 0, 2, 0, 4, 8, 4, 4, 0, 2, 0, 2, 4, 0, 0, 2, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 4, 0, 2, 2, 0, 8, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:88, 2:58, 4:57, 6:3, 8:15, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 0, 0, -8, 0, 0, 0, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, -8, -8, }, +{8: 16, 0, 8, 8, 0, 8, -8, 0, -8, -8, 0, 0, 0, -8, -8, 0, }, +{3: 16, -16, -8, 8, 8, 8, -8, -16, -8, 0, 0, 16, 0, 0, -8, 8, }, +{5: 16, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -16, 0, }, +{6: 16, 0, -8, 0, 8, 0, -8, 0, -8, -8, 0, 0, 0, -8, 8, 8, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -16, 0, -8, 8, 0, -8, 8, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, 8, -8, }, +{b: 16, 0, -16, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -16, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, 0, 0, 8, 0, 8, 0, 0, -16, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, , x, x, , , x, }, +{5: , , x, x, x, , x, x, x, x, , , x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , , x, , x, x, }, +{9: , , x, x, x, , x, x, x, x, , x, , x, , x, }, +{a: , , x, x, x, x, x, x, x, x, , x, , , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , , x, x, , , x, x, x, x, , , x, , , x, }, +{b: , , , , x, , x, x, x, x, , x, , , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,1011,1,}, +{0110,0011,1,}, +{0110,1100,1,}, +{0110,1111,0,}, +{0111,0011,0,}, +{0111,1101,1,}, +{0111,1110,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x06,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x09,0x0a,0x04,}, {0x07,}}, +{{0x01,0x02,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x05,0x08,}, {0x07,0x09,0x0e,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,}}, +{{0x05,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x06,0x07,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x06,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_153.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_153.txt new file mode 100644 index 0000000..30adbf2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_153.txt @@ -0,0 +1,442 @@ +153 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0e,0x0d,0x0c,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{3: 0, 4, 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 0, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 4, 4, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 6, 0, 2, 2, 0, 10, 0, 0, 8, 4, 4, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 0, 8, 4, 0, 0, 6, 6, 0, 0, 0, 4, 0, 2, 2, 0, }, +{8: 16, 2, 4, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 2, 0, 0, }, +{3: 16, 4, 4, 2, 0, 8, 0, 2, 2, 0, 4, 0, 2, 0, 0, 4, }, +{5: 16, 2, 4, 2, 0, 0, 6, 2, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 0, 8, 6, 0, 0, 4, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 6, 6, 0, 0, 4, 2, 2, 0, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, }, +{c: 16, 4, 4, 0, 0, 10, 2, 0, 0, 2, 6, 0, 0, 8, 8, 4, }, +{7: 16, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 4, 4, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 0, 0, 0, 4, 2, 2, 2, 2, 4, 0, 0, 8, 4, 0, }, +{e: 16, 0, 4, 0, 2, 4, 0, 2, 2, 0, 8, 2, 0, 0, 4, 4, }, +{f: 16, 0, 0, 2, 2, 8, 0, 0, 0, 0, 8, 2, 2, 0, 0, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:42, 6:14, 8:18, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{f: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -16, 0, -8, -8, 8, 0, 0, -8, 0, 8, }, +{2: 16, 8, -8, 8, 8, -16, 16, -16, 0, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -16, 8, 0, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, }, +{8: 16, 0, 8, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, -8, }, +{3: 16, -8, 0, 8, 8, 0, -16, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 0, 8, -8, 0, -8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, }, +{a: 16, 0, -8, 8, -8, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -16, -8, -8, 8, 0, 0, 0, 8, 8, }, +{7: 16, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, 0, 0, 0, -8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, 0, 8, -8, 0, -8, -8, 8, -8, 0, }, +{d: 16, 0, 0, -8, -8, -16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , , x, , x, x, x, x, , x, , x, , x, x, x, }, +{6: , , , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, , , x, x, x, x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , x, x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , , x, , x, , x, , , , x, x, x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0011,0010,1,}, +{0011,1101,1,}, +{0011,1111,0,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0110,1100,1,}, +{0110,1110,0,}, +{1000,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,}}, +{{0x01,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x09,0x0a,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x01,0x0e,}, {0x03,0x05,0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x03,0x05,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +153 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x01,0x09,0x0a,0x0b,0x0e,0x0d,0x0c,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, }, +{6: 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 0, 0, 0, 2, 2, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, }, +{a: 0, 0, 4, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 2, 0, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, }, +{d: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 4, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 4, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 2, 4, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 4, 16, 8, 4, 4, 4, 8, 8, 4, 4, 4, 8, 0, 4, 0, }, +{4: 16, 0, 4, 4, 2, 2, 2, 6, 0, 0, 0, 2, 0, 0, 0, 2, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 6, 4, 0, 0, 8, 0, 0, 0, 2, 10, 2, 0, 4, 4, 8, }, +{5: 16, 0, 8, 6, 0, 0, 6, 4, 0, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 2, 4, 6, 0, 2, 2, 4, 0, 0, 0, 0, 0, 2, 2, 0, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 4, 2, 2, 0, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 10, 4, 0, 0, 4, 0, 2, 0, 0, 6, 0, 2, 4, 8, 8, }, +{7: 16, 0, 8, 4, 0, 0, 4, 6, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 4, 2, 0, 0, 6, 0, 0, 2, }, +{d: 16, 8, 0, 2, 2, 0, 2, 0, 2, 0, 8, 0, 0, 8, 0, 0, }, +{e: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{f: 16, 4, 0, 0, 0, 4, 0, 2, 0, 2, 4, 2, 2, 0, 4, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:42, 6:14, 8:18, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, 0, 0, -16, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 8, -8, 0, -8, 16, -8, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 0, -8, 8, 8, 0, 0, 0, 0, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, 0, -16, 0, 8, -8, 0, -8, 8, 0, }, +{5: 16, 0, 0, -8, 8, 0, 8, -8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{6: 16, 0, 0, -8, 8, -8, -8, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, -8, 0, 0, 0, 8, -8, -16, 0, 8, 8, }, +{7: 16, 0, 0, -16, 8, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 8, }, +{d: 16, 0, 16, -8, -8, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 16, 0, 0, -8, }, +{f: 16, 0, -16, -8, -8, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, , x, x, , x, , x, , x, x, x, }, +{6: , x, , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, x, , , x, x, x, x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , x, x, , , x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, , , , x, , x, , , , x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0010,1,}, +{0010,1101,0,}, +{0010,1111,1,}, +{0100,0111,1,}, +{1000,1000,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +{1011,1100,1,}, +{1011,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x02,0x08,0x0a,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,0x05,0x07,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,}}, +{{0x01,0x0e,}, {0x02,0x09,0x0b,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0e,}, {0x02,0x09,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_154.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_154.txt new file mode 100644 index 0000000..f6bcc63 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_154.txt @@ -0,0 +1,442 @@ +154 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0f,0x0e,0x0d, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 2, 0, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{6: 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, }, +{a: 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 6, 2, 0, 0, 0, 4, }, +{7: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 4, 4, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:4, 4:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 6, 0, 2, 2, 0, 10, 0, 0, 8, 4, 4, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 0, 8, 6, 0, 0, 6, 4, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 16, 2, 4, 2, 6, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, }, +{3: 16, 4, 4, 2, 0, 8, 0, 2, 2, 0, 4, 0, 2, 0, 0, 4, }, +{5: 16, 2, 4, 2, 0, 0, 4, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{6: 16, 0, 8, 4, 0, 0, 4, 6, 0, 0, 0, 6, 0, 0, 2, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 2, 0, 6, 2, 0, 0, }, +{a: 16, 2, 4, 0, 4, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, }, +{c: 16, 4, 4, 0, 2, 10, 0, 0, 0, 0, 10, 2, 0, 4, 4, 8, }, +{7: 16, 2, 4, 2, 0, 2, 6, 0, 0, 0, 0, 4, 0, 2, 2, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 0, 0, 4, 0, 2, 2, }, +{d: 16, 4, 0, 2, 0, 4, 2, 0, 0, 2, 8, 0, 2, 4, 0, 4, }, +{e: 16, 0, 4, 0, 0, 4, 2, 2, 2, 2, 4, 0, 0, 4, 8, 0, }, +{f: 16, 0, 0, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:48, 4:47, 6:13, 8:15, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 4, 4, 4, 0, 0, 0, 8, 8, 0, 4, 4, 4, 4, 0, }, +{b: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{f: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -16, 0, -8, -8, 8, 0, 0, -8, 0, 8, }, +{2: 16, 8, -8, 8, 8, -16, 16, -16, 0, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -16, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 0, -16, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 8, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, }, +{6: 16, 8, -8, -8, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, -8, -8, }, +{9: 16, 0, 8, 8, -16, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, 8, 0, -8, 0, -8, }, +{c: 16, 0, 0, -8, -8, 16, 0, 0, -8, -8, 8, -8, -8, 0, 0, 8, }, +{7: 16, -8, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, -8, -8, }, +{d: 16, 0, 8, -8, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , , x, , x, x, x, x, , x, , x, x, x, x, x, }, +{6: , , , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, , x, x, x, x, x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, , x, x, x, x, x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , , , , x, , x, , x, x, x, x, x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0011,0010,1,}, +{0011,1100,0,}, +{0011,1110,1,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0110,1101,1,}, +{0110,1111,0,}, +{1000,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x09,0x02,0x04,}, {0x06,}}, +{{0x01,0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x03,0x04,0x07,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x05,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x06,0x09,0x0f,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x01,0x0e,}, {0x03,0x05,0x06,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x03,0x05,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +154 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0f,0x0e,0x0d, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 4, 4, 2, 0, 2, 0, 0, 2, }, +{3: 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{6: 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 4, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{c: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 6, 0, 0, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 4, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:4, 4:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 2, 4, 2, 0, 0, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 4, 16, 8, 4, 4, 4, 8, 8, 4, 4, 4, 8, 0, 4, 0, }, +{4: 16, 0, 4, 6, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 16, 0, 8, 0, 6, 0, 0, 0, 4, 4, 2, 0, 6, 0, 0, 2, }, +{3: 16, 6, 4, 0, 0, 8, 0, 0, 0, 2, 10, 2, 0, 4, 4, 8, }, +{5: 16, 0, 8, 6, 0, 0, 4, 4, 0, 0, 0, 6, 0, 2, 2, 0, }, +{6: 16, 2, 4, 4, 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, 2, 2, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 0, 8, 0, 4, 0, 0, 0, 6, 6, 0, 0, 4, 2, 2, 0, }, +{c: 16, 10, 4, 2, 0, 4, 0, 0, 2, 0, 10, 0, 0, 8, 4, 4, }, +{7: 16, 0, 8, 4, 0, 0, 6, 6, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 8, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{e: 16, 4, 4, 0, 0, 0, 0, 2, 0, 2, 4, 2, 2, 0, 8, 4, }, +{f: 16, 4, 0, 0, 2, 4, 2, 2, 0, 0, 8, 0, 2, 4, 0, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:48, 4:47, 6:13, 8:15, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{f: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, 0, 0, -16, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 8, -8, 0, -8, 16, -8, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 8, -16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, }, +{3: 16, -8, 0, 8, 8, 0, -8, 0, -16, 0, 8, -8, 0, -8, 8, 0, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, 0, 0, 0, 0, 0, 8, -8, -8, }, +{6: 16, 0, 0, -8, 8, 0, -8, 0, 0, 8, 0, 0, 0, -8, -8, 0, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, -8, -8, }, +{c: 16, 0, 16, -8, -8, 0, -8, -8, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, 0, 0, -16, 8, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 16, 0, 0, -8, }, +{e: 16, 0, -16, -8, -8, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, -16, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, x, x, x, x, }, +{6: , x, , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , x, , x, x, x, , x, x, x, x, x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, , x, , x, , x, , x, x, x, x, x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, , x, , x, , x, , x, x, x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0010,1,}, +{0010,1100,0,}, +{0010,1110,1,}, +{0100,0111,1,}, +{1000,1000,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +{1011,1101,0,}, +{1011,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0e,}, {0x02,0x09,0x0b,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x02,0x09,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_155.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_155.txt new file mode 100644 index 0000000..db38c84 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_155.txt @@ -0,0 +1,442 @@ +155 Sbox: +LUT = { +0x08,0x00,0x0f,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x01, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 2, 0, 2, 2, 4, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 8, 0, 0, 0, 2, }, +{b: 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:165, 2:64, 4:24, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:2, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 6, 2, 0, 6, 0, 0, 0, 8, 0, 2, 0, 4, }, +{2: 16, 0, 8, 0, 0, 0, 8, 0, 8, 0, 16, 16, 16, 0, 8, 0, }, +{4: 16, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 16, 4, 4, 0, 0, }, +{8: 16, 0, 4, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 2, 2, }, +{3: 16, 2, 0, 6, 0, 4, 0, 0, 0, 6, 0, 8, 0, 4, 0, 2, }, +{5: 16, 0, 4, 0, 2, 2, 4, 2, 0, 0, 4, 8, 4, 2, 0, 0, }, +{6: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 16, 4, 0, 0, 4, }, +{9: 16, 2, 4, 2, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 6, 2, 2, 0, 0, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{c: 16, 2, 4, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{7: 16, 6, 4, 6, 4, 4, 4, 4, 0, 6, 4, 8, 4, 4, 0, 6, }, +{b: 16, 0, 6, 2, 0, 2, 0, 2, 6, 2, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 2, 6, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, }, +{f: 16, 2, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:48, 6:16, 8:8, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, -8, -16, 0, 0, }, +{2: 16, 8, -8, 0, 8, 0, 8, -8, 0, -16, 8, -16, -8, 16, 0, -8, }, +{4: 16, 0, 0, 0, 0, 0, 0, -16, 0, 16, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, }, +{3: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, 8, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{6: 16, 8, 0, -8, 0, 8, 0, 8, -8, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, -8, }, +{c: 16, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, -8, -8, 8, 8, 8, 8, -8, 0, -8, -16, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{7: , , , , , x, x, , x, x, x, , x, x, x, x, }, +{b: , x, x, , x, , x, , x, x, x, x, , x, x, x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , x, x, x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0e,}, {0x02,0x05,0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +155 Inverse Sbox: +LUT = { +0x01,0x0f,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x02, +}; + +ANF of coordinates: +y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, }, +{7: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 4, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:165, 2:64, 4:24, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:2, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 2, 0, 4, 2, 0, 2, 6, 0, 0, 2, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 4, 4, 6, 4, 4, 6, 4, 6, 6, }, +{4: 16, 0, 0, 4, 0, 6, 0, 0, 2, 2, 2, 6, 2, 0, 0, 0, }, +{8: 16, 6, 0, 0, 2, 0, 2, 4, 2, 2, 0, 4, 0, 0, 0, 2, }, +{3: 16, 2, 0, 4, 0, 4, 2, 0, 0, 0, 2, 4, 2, 2, 2, 0, }, +{5: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 6, 0, 0, 2, 0, 2, 4, 2, 0, 0, 4, 2, 0, 2, 0, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 0, 0, 4, 2, 6, 0, 0, 0, 2, 0, 6, 2, 2, 0, 0, }, +{c: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 16, 2, 0, 4, 0, 4, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 0, 2, 2, 0, 4, 0, 0, 0, 6, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:48, 4:48, 6:16, 8:8, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{3: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{5: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 0, 0, -8, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +{2: 16, 8, -16, 8, 0, -8, 8, -8, 8, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, 0, -8, -8, 0, 8, }, +{3: 16, -8, 0, 0, 0, 0, -8, -8, -8, 0, 8, 8, 0, 0, 0, 0, }, +{5: 16, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, }, +{c: 16, 8, 0, -8, 0, -8, 0, -8, 8, -16, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -16, -8, 16, 0, 8, 8, 0, -16, -8, -8, 0, 8, 8, -8, }, +{b: 16, 0, 0, 0, 0, 0, 0, -16, 0, 16, -16, 0, 0, 0, 0, 0, }, +{d: 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, 0, 0, 0, 0, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , x, , x, , x, x, x, x, x, x, , x, x, x, x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, , x, x, , x, x, x, x, x, , x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0110,1011,1,}, +{1000,0111,0,}, +{1000,1001,1,}, +{1000,1110,1,}, +{1010,0111,1,}, +{1010,1011,0,}, +{1010,1100,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0a,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x0a,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_156.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_156.txt new file mode 100644 index 0000000..19681ff --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_156.txt @@ -0,0 +1,412 @@ +156 Sbox: +LUT = { +0x08,0x00,0x01,0x09,0x02,0x05,0x06,0x07,0x04,0x0f,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 2, 2, 4, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{8: 0, 0, 2, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 2, 0, 2, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 4, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 2, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 2, 2, 0, }, +{d: 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 6, 0, 0, }, +{e: 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{f: 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:164, 2:66, 4:21, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:4, 4:5, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 0, 4, 0, 0, 4, 4, 4, 4, 6, 6, 6, 0, 0, }, +{2: 16, 4, 4, 4, 4, 0, 0, 0, 16, 0, 0, 4, 4, 4, 4, 0, }, +{4: 16, 0, 2, 2, 4, 0, 2, 0, 0, 2, 0, 6, 0, 0, 2, 4, }, +{8: 16, 0, 2, 2, 4, 4, 0, 0, 0, 0, 2, 0, 6, 0, 2, 2, }, +{3: 16, 4, 0, 0, 16, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 0, 2, 0, 0, 2, 2, 2, 4, 0, 0, 4, 0, 2, 4, 2, }, +{6: 16, 4, 0, 0, 0, 2, 0, 8, 0, 6, 4, 6, 0, 0, 2, 0, }, +{9: 16, 0, 4, 2, 0, 2, 2, 0, 4, 2, 0, 2, 4, 0, 0, 2, }, +{a: 16, 4, 2, 0, 0, 0, 2, 4, 0, 8, 6, 0, 6, 0, 0, 0, }, +{c: 16, 4, 0, 2, 0, 0, 0, 6, 0, 4, 8, 0, 0, 6, 0, 2, }, +{7: 16, 6, 0, 2, 4, 0, 0, 6, 4, 0, 0, 6, 2, 0, 4, 6, }, +{b: 16, 6, 4, 0, 4, 6, 0, 0, 4, 6, 0, 0, 6, 2, 2, 0, }, +{d: 16, 6, 2, 4, 4, 0, 6, 0, 4, 0, 6, 2, 0, 6, 0, 0, }, +{e: 16, 0, 2, 2, 4, 2, 4, 2, 0, 0, 0, 0, 0, 6, 2, 0, }, +{f: 16, 0, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, 2, 4, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:45, 4:51, 6:24, 8:3, 10:1, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{a: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{c: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, 8, -16, }, +{2: 16, 8, 0, 0, 0, -8, -8, 0, 8, 0, 0, -8, 8, 8, -16, -8, }, +{4: 16, 8, 0, 0, 0, 0, 8, 0, -8, 0, -8, 0, 0, 0, -8, -8, }, +{8: 16, 8, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, -8, -8, }, +{3: 16, -16, 0, 0, 8, 0, 0, 0, -8, 8, 8, 0, -8, -8, -8, 8, }, +{5: 16, -8, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 8, }, +{9: 16, -8, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, 0, -8, 8, }, +{a: 16, 8, -8, 0, 0, -8, 0, -8, 0, 0, -8, 0, -8, 0, 8, 8, }, +{c: 16, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, -8, 0, -8, -8, 0, 8, 0, 8, 0, 0, 8, -8, }, +{d: 16, -8, 8, -8, 0, -8, 8, -8, 0, -8, 8, 0, 0, 0, 8, -8, }, +{e: 16, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, -8, }, +{f: 16, -8, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, , x, x, x, , x, x, x, x, , x, x, }, +{7: , , x, x, , x, , , x, , , x, , , , x, }, +{b: , , x, , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, , x, x, x, , x, x, x, x, , x, x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0001,0011,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x0a,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x07,0x09,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x06,0x09,0x0f,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +156 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0f,0x08,0x05,0x06,0x07,0x00,0x03,0x0a,0x0b,0x0c,0x0d,0x0e,0x09, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, }, +{8: 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, }, +{5: 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 0, 4, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 4, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 6, 0, 2, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 6, 2, 0, }, +{e: 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, }, +{f: 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:164, 2:66, 4:21, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:4, 4:5, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 0, 4, 0, 4, 0, 4, 4, 6, 6, 6, 0, 0, }, +{2: 16, 0, 4, 2, 2, 0, 2, 0, 4, 2, 0, 0, 4, 2, 2, 0, }, +{4: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 2, 0, 4, 2, 4, }, +{8: 16, 4, 4, 4, 4, 16, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{3: 16, 0, 0, 0, 4, 4, 2, 2, 2, 0, 0, 0, 6, 0, 2, 2, }, +{5: 16, 0, 0, 2, 0, 4, 2, 0, 2, 2, 0, 0, 0, 6, 4, 2, }, +{6: 16, 4, 0, 0, 0, 0, 2, 8, 0, 4, 6, 6, 0, 0, 2, 0, }, +{9: 16, 4, 16, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 16, 4, 0, 2, 0, 0, 0, 6, 2, 8, 4, 0, 6, 0, 0, 0, }, +{c: 16, 4, 0, 0, 2, 0, 0, 4, 0, 6, 8, 0, 0, 6, 0, 2, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 2, 0, 0, 6, 0, 2, 0, 0, }, +{b: 16, 6, 4, 0, 6, 4, 0, 0, 4, 6, 0, 2, 6, 0, 0, 2, }, +{d: 16, 6, 4, 0, 0, 4, 2, 0, 0, 0, 6, 0, 2, 6, 6, 4, }, +{e: 16, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{f: 16, 0, 0, 4, 2, 4, 2, 0, 2, 0, 2, 6, 0, 0, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:45, 4:51, 6:24, 8:3, 10:1, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{6: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 0, 8, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 8, 0, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, }, +{4: 16, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 8, -8, -8, }, +{8: 16, 8, 8, 0, 0, 0, -8, 8, -8, 8, 0, 0, 0, -8, -8, -16, }, +{3: 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, }, +{5: 16, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 8, -8, -8, 8, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, -8, 0, -8, 0, 0, 0, 8, 8, }, +{9: 16, -8, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, -8, 8, -16, 8, }, +{a: 16, 8, 0, 0, -8, 0, -8, -8, 0, 0, -8, -8, 0, 0, 8, 8, }, +{c: 16, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, -8, -8, 8, 8, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, 0, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 8, -8, 0, -8, 0, 8, -8, }, +{d: 16, -8, 8, -8, -8, -8, 0, -8, 0, 0, 8, 8, 0, 0, 8, -8, }, +{e: 16, 8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, -8, }, +{f: 16, -8, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{9: , , x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, , , x, , x, , , x, x, x, }, +{7: , , , x, , , x, x, x, x, x, , x, x, x, x, }, +{b: , , x, , x, x, x, x, , x, x, x, , x, x, x, }, +{d: , , , x, x, x, , , x, , , , , x, , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0001,0001,1,}, +{1110,1001,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x0a,}}, +{{0x09,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x0b,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_157.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_157.txt new file mode 100644 index 0000000..3354c48 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_157.txt @@ -0,0 +1,412 @@ +157 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x06,0x07,0x03,0x09,0x0d,0x0b,0x0c,0x0a,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{3: 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 4, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 0, 0, 0, 2, 2, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, }, +{a: 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 6, 4, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, 0, 2, 2, 4, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:164, 2:66, 4:21, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 2, 4, 0, 0, 4, 6, 2, 0, 6, 0, 0, 0, 0, }, +{2: 16, 0, 6, 2, 2, 0, 8, 0, 4, 0, 4, 4, 8, 0, 10, 0, }, +{4: 16, 0, 0, 10, 0, 4, 2, 2, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 4, 0, 0, 4, 2, 0, 0, 6, 0, 2, 2, 0, 0, 2, 2, }, +{3: 16, 2, 0, 4, 2, 8, 2, 0, 4, 4, 2, 4, 0, 0, 0, 0, }, +{5: 16, 2, 8, 0, 0, 0, 4, 2, 2, 0, 0, 4, 0, 4, 2, 4, }, +{6: 16, 4, 2, 0, 0, 2, 0, 10, 0, 0, 0, 6, 4, 4, 0, 0, }, +{9: 16, 4, 4, 0, 6, 6, 2, 0, 6, 6, 0, 0, 4, 2, 0, 0, }, +{a: 16, 2, 2, 0, 0, 4, 0, 0, 6, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 2, 4, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 2, }, +{7: 16, 4, 4, 6, 0, 6, 4, 6, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 8, 4, 2, 0, 0, 4, 4, 0, 2, 0, 6, 8, 0, 10, }, +{d: 16, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 10, 6, 4, 0, }, +{e: 16, 0, 10, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 6, 4, 4, }, +{f: 16, 0, 0, 4, 2, 0, 4, 0, 2, 0, 0, 0, 8, 0, 6, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:44, 4:43, 6:20, 8:8, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{4: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -8, -8, 8, 0, 0, -8, -8, 0, -8, 8, 0, }, +{2: 16, 8, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, -8, 8, -16, -8, }, +{4: 16, -8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, }, +{3: 16, 0, 8, 0, 8, 8, -8, -8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, 0, 0, 0, 8, -16, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, -8, 0, 0, 8, -8, 0, 0, 0, -8, 8, 0, 0, -8, 8, -8, }, +{9: 16, -8, 8, 8, -8, -8, 0, 0, 0, -8, -8, 0, 8, 0, -8, 8, }, +{a: 16, 0, 0, 8, -8, -8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 0, 0, -8, 8, 0, 0, -8, 0, 0, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, 0, 0, -8, -8, -8, -8, 8, 0, 8, 0, }, +{b: 16, -8, 0, 0, -16, 8, 0, -8, 8, 0, 0, 8, -8, 0, 8, -8, }, +{d: 16, 8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 0, 8, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, -8, 0, 8, 8, -8, 0, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, x, x, x, , , , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, x, x, , x, x, , x, }, +{d: , x, x, x, x, x, x, , x, x, x, , , , , x, }, +{e: , x, , x, x, x, x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0101,1,}, +{1000,1011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x01,0x08,0x09,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +157 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x03,0x09,0x0d,0x0b,0x0c,0x0a,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 4, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 4, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 6, 2, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 0, 0, 4, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, 4, 2, }, +{f: 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:164, 2:66, 4:21, 6:4, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 0, 4, 2, 2, 4, 4, 2, 2, 4, 0, 0, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 8, 2, 4, 2, 4, 4, 8, 0, 10, 0, }, +{4: 16, 2, 2, 10, 0, 4, 0, 0, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 4, 2, 0, 4, 2, 0, 0, 6, 0, 2, 0, 2, 0, 0, 2, }, +{3: 16, 0, 0, 4, 2, 8, 0, 2, 6, 4, 0, 6, 0, 0, 0, 0, }, +{5: 16, 0, 8, 2, 0, 2, 4, 0, 2, 0, 0, 4, 0, 4, 2, 4, }, +{6: 16, 4, 0, 2, 0, 0, 2, 10, 0, 0, 0, 6, 4, 4, 0, 0, }, +{9: 16, 6, 4, 0, 6, 4, 2, 0, 6, 6, 0, 0, 4, 0, 0, 2, }, +{a: 16, 2, 0, 0, 0, 4, 0, 0, 6, 4, 2, 2, 0, 2, 2, 0, }, +{c: 16, 0, 4, 0, 2, 2, 0, 0, 0, 2, 4, 2, 2, 2, 4, 0, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 8, 4, 0, 0, 0, 4, 4, 2, 2, 0, 6, 10, 0, 8, }, +{d: 16, 0, 0, 0, 0, 0, 4, 4, 2, 2, 0, 0, 8, 6, 6, 0, }, +{e: 16, 0, 10, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 4, 4, 6, }, +{f: 16, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, 0, 10, 0, 4, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:44, 4:43, 6:20, 8:8, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{2: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{c: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -8, -8, 0, -8, 0, 0, 0, -8, -8, 8, 8, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 0, 0, 0, 0, -8, 8, -8, 0, }, +{4: 16, -8, -8, 0, 8, 8, 0, 0, 0, 0, 8, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, -8, 0, }, +{3: 16, 0, 0, 0, 8, 8, -8, 0, 0, -8, -8, 0, 8, -8, -8, 0, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{6: 16, -8, 8, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, }, +{9: 16, -8, 8, 8, -8, -8, 0, 8, 0, 0, -8, -8, 0, 0, -8, 8, }, +{a: 16, 0, 0, 0, -8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 8, 0, }, +{c: 16, 0, 0, 0, -8, 8, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 0, -16, 8, 0, -8, 8, 8, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, -8, 0, -8, -8, -8, 0, 8, 0, -8, 8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, 8, 0, -8, -8, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, x, x, x, , , , x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{9: , x, x, , x, x, x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, x, , , , x, , x, x, x, , x, x, , x, }, +{d: , , x, , x, x, x, , x, x, x, , , , , x, }, +{e: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{1000,1011,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x09,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_158.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_158.txt new file mode 100644 index 0000000..0b148f6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_158.txt @@ -0,0 +1,412 @@ +158 Sbox: +LUT = { +0x0b,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0d,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{4: 0, 2, 2, 2, 4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 6, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 4, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{9: 0, 0, 2, 2, 2, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, }, +{a: 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 0, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 4, 0, 2, 0, 2, }, +{7: 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 6, 4, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, 0, }, +{2: 16, 0, 6, 2, 0, 0, 6, 0, 4, 2, 4, 6, 4, 0, 6, 0, }, +{4: 16, 2, 6, 2, 4, 0, 4, 0, 0, 0, 0, 10, 0, 0, 0, 4, }, +{8: 16, 8, 0, 0, 8, 0, 0, 4, 10, 0, 0, 4, 2, 2, 4, 6, }, +{3: 16, 2, 0, 2, 0, 6, 4, 10, 8, 4, 4, 0, 0, 0, 0, 8, }, +{5: 16, 0, 0, 2, 0, 8, 4, 6, 0, 0, 2, 0, 0, 4, 6, 0, }, +{6: 16, 0, 6, 0, 0, 4, 10, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{9: 16, 4, 6, 2, 6, 4, 0, 0, 6, 4, 2, 0, 6, 0, 0, 0, }, +{a: 16, 2, 0, 0, 0, 8, 2, 0, 4, 4, 0, 0, 2, 4, 4, 2, }, +{c: 16, 0, 0, 0, 6, 4, 0, 0, 0, 2, 4, 4, 0, 2, 0, 10, }, +{7: 16, 4, 2, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 4, 4, }, +{b: 16, 0, 4, 0, 2, 0, 0, 4, 8, 2, 2, 0, 4, 0, 2, 4, }, +{d: 16, 2, 4, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 6, 0, }, +{e: 16, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, }, +{f: 16, 4, 4, 2, 0, 10, 0, 0, 2, 0, 8, 0, 0, 4, 6, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:51, 4:42, 6:17, 8:9, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 4, 12, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 0, 0, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 8, 0, 8, 0, 8, 0, -8, 0, -8, 0, -8, 0, -8, -8, }, +{8: 16, -8, 0, 0, -16, 8, 8, 8, 8, 0, 0, 0, -8, -8, -8, 0, }, +{3: 16, -8, 0, 8, 8, 0, -16, 0, 0, -8, 0, 0, 8, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, 0, -8, -8, -8, 0, 0, 8, 0, 0, -8, 8, }, +{6: 16, 0, -8, -8, 8, -8, 8, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, 0, -8, 0, 8, -8, -8, -8, 0, 8, -8, 0, }, +{a: 16, -8, 0, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 8, 0, -8, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, -8, 0, 8, -8, }, +{b: 16, 8, -8, 0, -8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, -8, 8, 0, 8, 8, 0, 8, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, x, x, x, x, , , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , , x, x, , x, x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, , x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , , x, , x, x, x, , x, , x, x, }, +{7: , x, x, x, x, x, , , x, x, , x, x, , , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , , x, , , x, , , x, x, , x, , , x, }, +{e: , x, x, , , , , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0101,0011,1,}, +{1000,1000,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x08,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x07,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x05,}}, +{{0x05,0x02,}, {0x06,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +158 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x0d,0x09,0x0a,0x00,0x0c,0x0b,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, }, +{4: 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 4, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 4, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 4, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 4, 0, 0, }, +{7: 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 6, }, +{f: 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:3, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 8, 2, 0, 0, 4, 2, 0, 4, 0, 2, 0, 4, }, +{2: 16, 0, 6, 6, 0, 0, 0, 6, 6, 0, 0, 2, 4, 4, 2, 4, }, +{4: 16, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 16, 4, 0, 4, 8, 0, 0, 0, 6, 0, 6, 0, 2, 0, 2, 0, }, +{3: 16, 2, 0, 0, 0, 6, 8, 4, 4, 8, 4, 0, 0, 2, 0, 10, }, +{5: 16, 0, 6, 4, 0, 4, 4, 10, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 16, 2, 0, 0, 4, 10, 6, 4, 0, 0, 0, 2, 4, 0, 0, 0, }, +{9: 16, 4, 4, 0, 10, 8, 0, 0, 6, 4, 0, 0, 8, 0, 2, 2, }, +{a: 16, 0, 2, 0, 0, 4, 0, 2, 4, 4, 2, 0, 2, 2, 2, 0, }, +{c: 16, 0, 4, 0, 0, 4, 2, 0, 2, 0, 4, 2, 2, 4, 0, 8, }, +{7: 16, 2, 6, 10, 4, 0, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, }, +{b: 16, 2, 4, 0, 2, 0, 0, 0, 6, 2, 0, 2, 4, 2, 0, 0, }, +{d: 16, 2, 0, 0, 2, 0, 4, 2, 0, 4, 2, 0, 0, 2, 2, 4, }, +{e: 16, 0, 6, 0, 4, 0, 6, 0, 0, 4, 0, 4, 2, 6, 2, 6, }, +{f: 16, 0, 0, 4, 6, 8, 0, 0, 0, 2, 10, 4, 4, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:51, 4:42, 6:17, 8:9, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 12, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 0, -8, 0, 0, -8, 8, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, 8, -8, -8, }, +{4: 16, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, 0, -8, 0, }, +{8: 16, 8, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, -16, 0, 0, 8, 0, 0, -8, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 8, 0, -8, 8, -8, 0, -8, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, -8, 0, 0, 8, 0, -16, 8, }, +{a: 16, 8, -8, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, -8, 8, -8, -8, 0, 0, -8, 0, -8, 0, 0, 0, 8, 8, 0, }, +{7: 16, 8, 0, -8, 8, 0, -8, 0, 0, -8, 0, -8, -8, 0, 8, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 8, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, 0, }, +{e: 16, -8, -8, -8, -8, 0, 8, 0, 8, 8, 8, 0, -8, 0, -8, 0, }, +{f: 16, 8, 0, 0, -16, 8, 8, 8, -8, 0, 0, 0, -8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, , , x, x, x, , x, , x, }, +{5: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , , x, x, x, }, +{c: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , x, , x, x, x, , , x, x, , , x, , x, }, +{d: , x, , x, x, x, , , x, x, , , x, x, , x, }, +{e: , x, , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0001,0011,1,}, +{1000,1111,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_159.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_159.txt new file mode 100644 index 0000000..fa80a42 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_159.txt @@ -0,0 +1,412 @@ +159 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, }, +{4: 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{8: 0, 2, 0, 0, 4, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, 0, 0, 0, 4, 0, }, +{6: 0, 0, 2, 4, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, }, +{9: 0, 0, 2, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 6, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 4, 2, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 2, 2, }, +{e: 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 2, 4, 6, 0, 4, 0, 6, 0, 4, 0, 0, 6, 0, 2, }, +{2: 16, 0, 8, 4, 2, 2, 2, 4, 4, 0, 0, 0, 4, 0, 2, 0, }, +{4: 16, 8, 4, 6, 0, 4, 4, 8, 0, 0, 2, 10, 0, 0, 0, 2, }, +{8: 16, 10, 0, 0, 4, 2, 0, 4, 6, 0, 0, 4, 2, 0, 0, 0, }, +{3: 16, 2, 0, 10, 0, 8, 0, 0, 4, 6, 0, 8, 0, 4, 4, 2, }, +{5: 16, 4, 0, 8, 0, 2, 4, 2, 2, 4, 2, 0, 0, 0, 4, 0, }, +{6: 16, 0, 6, 8, 0, 0, 0, 4, 0, 6, 0, 2, 0, 0, 4, 2, }, +{9: 16, 4, 6, 2, 4, 4, 0, 0, 6, 6, 0, 0, 6, 0, 2, 0, }, +{a: 16, 2, 0, 0, 2, 4, 2, 0, 4, 6, 0, 0, 2, 2, 0, 0, }, +{c: 16, 8, 0, 0, 0, 0, 2, 4, 0, 4, 8, 6, 4, 10, 0, 2, }, +{7: 16, 0, 0, 4, 0, 4, 2, 2, 0, 0, 4, 8, 4, 2, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 6, 2, 4, 4, 10, 0, 0, 0, }, +{d: 16, 4, 0, 0, 2, 0, 2, 2, 0, 2, 4, 0, 0, 4, 2, 2, }, +{e: 16, 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{f: 16, 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 4, 0, 4, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:53, 4:43, 6:16, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{c: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 8, 0, 0, 8, -8, -8, -8, 0, -8, }, +{2: 16, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, 0, 0, 8, 0, -16, 0, -8, 0, -8, }, +{8: 16, 0, 0, 8, 0, 0, -8, 8, 0, -8, -8, 8, -8, -8, 0, 0, }, +{3: 16, 0, -8, 8, 0, 0, 0, -8, -8, 8, 0, -8, 8, -16, 0, 8, }, +{5: 16, 0, 0, -8, 0, -8, -8, 0, -8, 0, 0, 8, 0, 8, -8, 8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, -8, 8, 8, -8, 0, }, +{a: 16, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, }, +{c: 16, -8, 0, -16, 0, 8, 8, 0, -8, -8, 0, -8, 0, 8, 8, 0, }, +{7: 16, -8, -8, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, 8, 8, -8, }, +{b: 16, 8, 0, 8, -8, 0, 0, -8, 0, -8, 0, -8, -8, 8, 0, 0, }, +{d: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{e: 16, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 8, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, , x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, , x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, , x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, , , x, , , , x, x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , x, x, , , x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0100,1100,1,}, +{0111,0100,1,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x04,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x01,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +159 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x0c,0x06,0x07,0x03,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, }, +{2: 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 2, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, }, +{3: 0, 0, 2, 0, 2, 4, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{6: 0, 0, 0, 0, 4, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 6, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 6, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 4, 0, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 4, 0, 0, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 4, }, +{e: 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:4, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 10, 2, 4, 0, 4, 2, 8, 0, 0, 4, 0, 0, }, +{2: 16, 2, 8, 4, 0, 0, 0, 6, 6, 0, 0, 0, 4, 0, 2, 0, }, +{4: 16, 4, 4, 6, 0, 10, 8, 8, 2, 0, 0, 4, 0, 0, 2, 0, }, +{8: 16, 6, 2, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 2, }, +{3: 16, 0, 2, 4, 2, 8, 2, 0, 4, 4, 0, 4, 0, 0, 0, 2, }, +{5: 16, 4, 2, 4, 0, 0, 4, 0, 0, 2, 2, 2, 0, 2, 2, 0, }, +{6: 16, 0, 4, 8, 4, 0, 2, 4, 0, 0, 4, 2, 0, 2, 0, 2, }, +{9: 16, 6, 4, 0, 6, 4, 2, 0, 6, 4, 0, 0, 6, 0, 2, 0, }, +{a: 16, 0, 0, 0, 0, 6, 4, 6, 6, 6, 4, 0, 2, 2, 0, 4, }, +{c: 16, 4, 0, 2, 0, 0, 2, 0, 0, 0, 8, 4, 4, 4, 2, 2, }, +{7: 16, 0, 0, 10, 4, 8, 0, 2, 0, 0, 6, 8, 4, 0, 2, 4, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 6, 2, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 4, 0, 4, }, +{e: 16, 0, 2, 0, 0, 4, 4, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:53, 4:43, 6:16, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 8, 0, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 0, 4, 0, 0, 12, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 8, 0, -8, 0, -8, 8, 0, -8, 0, -16, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, -8, 0, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 8, 0, -8, 8, 0, -16, 0, 8, 0, -8, 0, 8, -8, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, -8, 0, -8, }, +{3: 16, 0, -8, 8, 0, 0, 8, -8, -8, 0, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, -8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 16, 0, 0, -8, 0, 0, 8, 8, 0, -8, -8, 8, -8, -8, 0, 0, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 8, -8, 0, }, +{a: 16, -8, -8, 8, 0, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 8, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, 0, 8, 0, 0, -8, 8, 0, 0, }, +{7: 16, 8, 0, -16, 0, 8, -8, 0, -8, -8, 0, -8, 0, 8, 8, 0, }, +{b: 16, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, -8, }, +{d: 16, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, -8, 0, -8, 8, 0, }, +{e: 16, -8, 0, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, , x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , x, x, , , x, x, }, +{9: , x, , x, x, x, , , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, x, , , , x, , , x, x, x, }, +{7: , , x, , , x, x, , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , x, , x, x, x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0100,0111,1,}, +{0101,0100,1,}, +{1101,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x06,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x04,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_160.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_160.txt new file mode 100644 index 0000000..03717a5 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_160.txt @@ -0,0 +1,412 @@ +160 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x0a,0x06,0x07,0x03,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 4, }, +{8: 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 6, 0, }, +{6: 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 2, }, +{a: 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 0, 2, 0, }, +{2: 16, 4, 6, 6, 2, 4, 6, 6, 0, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 0, 4, 8, 0, 0, 0, 6, 0, 2, 0, 2, 6, 0, 0, 4, }, +{8: 16, 4, 0, 2, 4, 2, 0, 0, 10, 0, 0, 4, 0, 0, 6, 0, }, +{3: 16, 10, 8, 0, 2, 8, 2, 0, 0, 0, 6, 0, 0, 4, 4, 4, }, +{5: 16, 0, 10, 0, 0, 0, 8, 2, 4, 2, 4, 8, 4, 0, 6, 0, }, +{6: 16, 0, 8, 4, 0, 2, 0, 4, 2, 0, 4, 2, 0, 2, 4, 0, }, +{9: 16, 8, 0, 0, 4, 2, 0, 2, 4, 2, 4, 0, 0, 4, 0, 2, }, +{a: 16, 8, 2, 0, 0, 0, 2, 0, 0, 4, 6, 0, 6, 4, 0, 0, }, +{c: 16, 2, 0, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 2, 0, 6, }, +{7: 16, 0, 4, 0, 2, 2, 4, 2, 0, 2, 2, 4, 2, 0, 0, 0, }, +{b: 16, 4, 0, 6, 2, 0, 6, 0, 0, 4, 0, 0, 6, 2, 4, 6, }, +{d: 16, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 6, 0, }, +{e: 16, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 4, 2, 6, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:46, 4:40, 6:25, 8:9, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{b: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, -8, -8, 8, -8, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, 0, 0, 8, -8, 8, -8, 8, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, -8, -8, 0, 8, 0, 0, 8, 8, -8, -8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, -8, -8, -8, 0, 8, 0, -8, -8, }, +{3: 16, 0, 8, 0, 0, 8, -8, -8, -16, -8, 8, 0, -8, 0, 0, 8, }, +{5: 16, 8, -8, -8, 0, -16, 0, 0, -8, 8, 0, 8, 0, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 8, -16, 0, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 8, -8, 0, 8, }, +{a: 16, 0, 0, 8, 0, -8, 0, -8, -8, 8, 0, -8, -8, 0, 8, 0, }, +{c: 16, -8, 0, 0, 0, 8, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, }, +{7: 16, 0, -8, 0, 0, 8, 0, 0, -8, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, -8, 0, 0, -8, 8, 0, -8, 8, 8, -8, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, -8, -8, 0, 8, -8, 0, 0, 0, 8, 0, 0, }, +{e: 16, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, , x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, , , x, , x, , , x, , , x, , , x, }, +{d: , x, x, x, , x, x, , , x, , , , x, , x, }, +{e: , x, , x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0101,1,}, +{1001,0011,1,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +160 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x0a,0x06,0x07,0x03,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, }, +{8: 0, 2, 2, 0, 4, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 4, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 4, 0, }, +{6: 0, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 4, 0, 2, }, +{a: 0, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 2, 0, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 6, 2, 0, 2, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:7, 2:5, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 4, 10, 0, 0, 8, 8, 2, 0, 4, 0, 2, 0, }, +{2: 16, 4, 6, 4, 0, 8, 10, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{4: 16, 2, 6, 8, 2, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 4, }, +{8: 16, 6, 2, 0, 4, 2, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, }, +{3: 16, 4, 4, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 0, 0, 4, }, +{5: 16, 0, 6, 0, 0, 2, 8, 0, 0, 2, 0, 4, 6, 0, 4, 0, }, +{6: 16, 0, 6, 6, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 6, 0, 0, 10, 0, 4, 2, 4, 0, 0, 0, 0, 4, 0, 2, }, +{a: 16, 6, 0, 2, 0, 0, 2, 0, 2, 4, 0, 2, 4, 0, 2, 0, }, +{c: 16, 0, 0, 0, 0, 6, 4, 4, 4, 6, 6, 2, 0, 2, 0, 6, }, +{7: 16, 0, 4, 2, 4, 0, 8, 2, 0, 0, 2, 4, 0, 4, 2, 0, }, +{b: 16, 4, 0, 6, 0, 0, 4, 0, 0, 6, 0, 2, 6, 2, 4, 6, }, +{d: 16, 0, 2, 0, 0, 4, 0, 2, 4, 4, 2, 0, 2, 2, 2, 0, }, +{e: 16, 2, 0, 0, 6, 4, 6, 4, 0, 0, 0, 0, 4, 6, 6, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:46, 4:40, 6:25, 8:9, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{b: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:3, 4:8, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, -8, 0, -16, 8, 8, -8, 0, -8, 8, 0, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, -8, -8, -8, -8, -8, }, +{8: 16, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, 0, -8, 0, 0, -8, }, +{3: 16, 0, 0, 0, 0, 8, -8, 0, -8, -16, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, -8, 0, 0, -8, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 8, -8, 0, 0, 0, -8, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, 0, -8, 8, -8, -8, 8, 0, 0, 0, }, +{c: 16, -8, -8, 0, 0, 8, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, }, +{7: 16, 8, 0, -8, 0, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, -8, 8, 0, -8, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, -8, -8, 0, 8, -8, 0, 0, 0, 8, 0, 0, }, +{e: 16, -8, 8, -8, 0, -8, 8, 0, -8, 8, 0, 8, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, x, , x, , x, , , x, , , x, , , x, }, +{d: , , x, , , x, x, , , x, , , , x, , x, }, +{e: , x, x, x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{1001,0001,1,}, +{1010,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x0a,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0e,}, {0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_161.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_161.txt new file mode 100644 index 0000000..bb111bf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_161.txt @@ -0,0 +1,412 @@ +161 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x05,0x06,0x07,0x04,0x0d,0x0a,0x0b,0x0c,0x09,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 6, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, }, +{5: 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{6: 0, 0, 6, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 2, 0, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 2, 0, 4, 0, 0, 4, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 4, 0, 0, 2, 2, }, +{7: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6, 0, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 4, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 2, 4, 4, 0, 10, 2, 8, 0, 8, 0, 0, 4, 0, 0, }, +{2: 16, 0, 8, 4, 2, 2, 2, 4, 4, 0, 0, 0, 4, 0, 2, 0, }, +{4: 16, 6, 4, 6, 2, 4, 6, 4, 0, 0, 0, 6, 0, 0, 0, 2, }, +{8: 16, 4, 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 2, 2, 0, 2, }, +{3: 16, 2, 0, 6, 0, 8, 0, 0, 4, 6, 0, 4, 0, 0, 0, 2, }, +{5: 16, 6, 0, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{6: 16, 0, 6, 6, 4, 0, 0, 6, 0, 6, 4, 2, 0, 2, 4, 0, }, +{9: 16, 4, 10, 2, 8, 4, 0, 0, 6, 8, 0, 0, 4, 0, 0, 2, }, +{a: 16, 0, 0, 0, 2, 4, 4, 0, 8, 4, 4, 0, 2, 2, 2, 0, }, +{c: 16, 4, 0, 0, 2, 0, 0, 0, 2, 0, 8, 4, 4, 4, 2, 2, }, +{7: 16, 0, 0, 6, 0, 4, 2, 2, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 0, 8, 0, 0, 0, 4, 0, 10, 2, 6, 4, 8, 0, 4, 2, }, +{d: 16, 6, 4, 0, 0, 0, 0, 2, 0, 0, 10, 0, 2, 4, 4, 0, }, +{e: 16, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, }, +{f: 16, 0, 4, 2, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:53, 4:43, 6:16, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 12, 0, 0, 4, 0, }, +{6: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -16, -8, 8, 0, 0, 0, -8, -8, 0, 0, 0, }, +{2: 16, 8, -8, 0, 8, -8, 0, 0, 0, -8, 0, 8, -8, 0, -8, 0, }, +{4: 16, 0, 8, -8, 8, 8, 0, 0, 0, 8, -8, -8, 0, -8, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 0, 0, -8, 0, 8, -8, -8, 0, 0, }, +{3: 16, -8, -8, 0, 8, 8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 0, }, +{5: 16, -8, 0, -8, 8, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, -8, 0, 8, -8, 8, -8, 8, -8, 0, -8, 0, 0, 0, -8, }, +{9: 16, 0, 0, 8, -8, -8, 0, 0, 8, 0, -8, -16, 8, 0, -8, 8, }, +{a: 16, 0, 0, 0, -8, -8, 8, -8, -8, 8, -8, 8, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, 8, -8, -8, 0, -8, 0, 8, 0, 0, }, +{7: 16, -8, -8, 0, 8, 8, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, -16, 8, -8, -8, 0, 0, 0, -8, -8, 8, 8, 8, }, +{d: 16, 0, 0, -8, -8, -8, -8, 0, 0, 0, 8, 8, 0, 0, 8, -8, }, +{e: 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 8, 0, -8, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, x, , x, }, +{5: , , , x, x, x, x, , , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, , x, x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, x, , x, x, x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, , , x, x, , , , x, , x, x, , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0001,1,}, +{0111,1001,1,}, +{1000,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x03,0x05,0x06,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x01,0x08,}, {0x03,0x04,0x07,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x03,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +161 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x05,0x06,0x07,0x03,0x0d,0x0a,0x0b,0x0c,0x09,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 2, 2, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, }, +{3: 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, }, +{5: 0, 2, 2, 2, 0, 0, 4, 0, 0, 4, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 6, 2, 2, 0, }, +{7: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 4, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 4, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 4, 2, 6, 0, 4, 0, 4, 0, 0, 6, 2, 0, }, +{2: 16, 2, 8, 4, 0, 0, 0, 6, 10, 0, 0, 0, 8, 4, 2, 4, }, +{4: 16, 4, 4, 6, 0, 6, 4, 6, 2, 0, 0, 6, 0, 0, 0, 2, }, +{8: 16, 4, 2, 2, 4, 0, 0, 4, 8, 2, 2, 0, 0, 0, 0, 4, }, +{3: 16, 0, 2, 4, 2, 8, 2, 0, 4, 4, 0, 4, 0, 0, 0, 2, }, +{5: 16, 10, 2, 6, 0, 0, 4, 0, 0, 4, 0, 2, 4, 0, 0, 0, }, +{6: 16, 2, 4, 4, 2, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 8, 4, 0, 4, 4, 0, 0, 6, 8, 2, 0, 10, 0, 2, 0, }, +{a: 16, 0, 0, 0, 0, 6, 0, 6, 8, 4, 0, 0, 2, 0, 2, 4, }, +{c: 16, 8, 0, 0, 2, 0, 0, 4, 0, 4, 8, 4, 6, 10, 2, 0, }, +{7: 16, 0, 0, 6, 0, 4, 2, 2, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{d: 16, 4, 0, 0, 2, 0, 2, 2, 0, 2, 4, 0, 0, 4, 2, 2, }, +{e: 16, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 0, 4, 4, 2, 2, }, +{f: 16, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:53, 4:43, 6:16, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{6: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{7: 0, 4, 0, 0, 4, 4, 12, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, -8, 8, 8, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 8, -16, -8, 8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 0, -8, 8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 0, }, +{8: 16, 8, 0, 0, -8, 8, 8, 0, 0, 0, 0, -8, -8, -8, -8, 0, }, +{3: 16, -8, -8, 0, 8, 8, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, }, +{5: 16, 0, 0, 0, 8, -8, 8, -8, -8, 8, -8, -8, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 8, -8, 8, 0, 0, -8, 0, 0, -8, 0, 0, -8, }, +{9: 16, -8, 8, 8, -8, -8, -16, 8, 0, 0, 0, -8, 0, 8, 0, 0, }, +{a: 16, 0, -8, 8, -8, -8, -8, 0, 0, 0, -8, 0, 8, 0, 0, 8, }, +{c: 16, 0, 0, 0, -16, 8, -8, -8, 0, 0, 0, 8, -8, 8, 8, -8, }, +{7: 16, 0, 0, -8, 8, 8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 8, }, +{b: 16, -8, -8, 0, -8, 8, 8, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, -8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, , x, x, x, x, , x, , x, , x, x, , x, }, +{a: , , , x, x, x, x, , , x, x, , x, x, x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , , x, , x, , , , x, , x, x, , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{0101,1001,1,}, +{1000,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_162.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_162.txt new file mode 100644 index 0000000..a4499b3 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_162.txt @@ -0,0 +1,412 @@ +162 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x09,0x07,0x03,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, }, +{8: 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, }, +{5: 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 6, 0, 0, }, +{9: 0, 0, 4, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 4, 0, }, +{c: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 6, 2, 0, 2, }, +{d: 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 6, 0, 4, 6, 4, 2, 0, 0, 6, 0, 0, 2, 0, }, +{2: 16, 4, 6, 0, 6, 4, 2, 0, 6, 4, 0, 0, 6, 2, 0, 0, }, +{4: 16, 4, 0, 8, 2, 0, 6, 2, 0, 0, 0, 0, 6, 0, 0, 4, }, +{8: 16, 0, 4, 0, 4, 2, 0, 2, 0, 8, 0, 4, 2, 4, 2, 0, }, +{3: 16, 10, 8, 0, 2, 8, 2, 0, 0, 0, 6, 0, 0, 4, 4, 4, }, +{5: 16, 8, 2, 4, 0, 0, 4, 2, 0, 2, 4, 0, 0, 4, 2, 0, }, +{6: 16, 8, 0, 0, 0, 2, 0, 8, 2, 4, 4, 10, 4, 6, 0, 0, }, +{9: 16, 0, 8, 0, 0, 2, 0, 2, 4, 2, 4, 0, 4, 0, 4, 2, }, +{a: 16, 0, 10, 0, 4, 0, 2, 0, 0, 4, 6, 0, 2, 0, 4, 0, }, +{c: 16, 2, 0, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 2, 0, 6, }, +{7: 16, 4, 0, 2, 2, 2, 0, 4, 2, 2, 2, 4, 0, 0, 0, 0, }, +{b: 16, 0, 4, 6, 0, 0, 0, 4, 4, 2, 0, 2, 6, 6, 0, 6, }, +{d: 16, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 4, 6, 2, 0, }, +{e: 16, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 4, 0, 6, 2, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:48, 4:42, 6:23, 8:9, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{2: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{8: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{b: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{d: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 8, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 8, -8, 8, 0, -8, 0, 0, 0, -8, }, +{2: 16, 0, 0, 8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 8, 8, -8, 0, -8, -8, -8, 0, }, +{8: 16, 0, -8, 0, 0, 8, 0, 8, -8, -8, -8, 8, 0, 0, 0, -8, }, +{3: 16, 0, 8, 0, 0, 8, -8, -8, -16, -8, 8, 0, -8, 0, 0, 8, }, +{5: 16, 0, 0, 0, 8, -16, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, }, +{6: 16, -8, 0, -8, 0, -8, 0, 0, 8, -16, 0, 8, 8, -8, 8, 0, }, +{9: 16, 0, -8, 8, 0, -8, 0, 0, 8, -8, 0, -8, 0, 0, -8, 8, }, +{a: 16, 8, -8, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 8, 0, 0, }, +{c: 16, -8, 0, 0, 0, 8, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, }, +{7: 16, 0, 0, 0, 0, 8, 0, 0, -8, -8, -8, -8, 8, 0, 0, 0, }, +{b: 16, -8, -8, 0, -8, 8, 0, -8, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 8, 0, -8, 0, -8, -8, 0, 8, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, 8, 0, -8, 8, 0, 0, 0, -8, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, x, , , x, x, , , x, }, +{5: , x, x, x, , x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, , x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , , x, , x, , x, x, , , x, , , , x, }, +{b: , x, , , x, , , x, x, , , , x, , , x, }, +{d: , x, x, x, , x, , x, x, , , , , x, , x, }, +{e: , x, , x, , x, , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0101,1,}, +{1001,0011,1,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,0x08,0x0b,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +162 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x09,0x07,0x03,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, }, +{8: 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 4, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 2, 0, 2, 4, 2, 0, 0, 0, 0, 4, 0, 0, }, +{9: 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, 0, 4, 0, }, +{c: 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 2, }, +{d: 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:163, 2:69, 4:18, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 10, 8, 8, 0, 0, 2, 4, 0, 0, 2, 0, }, +{2: 16, 4, 6, 0, 4, 8, 2, 0, 8, 10, 0, 0, 4, 2, 0, 0, }, +{4: 16, 6, 0, 8, 0, 0, 4, 0, 0, 0, 0, 2, 6, 2, 0, 4, }, +{8: 16, 0, 6, 2, 4, 2, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, }, +{3: 16, 4, 4, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 0, 0, 4, }, +{5: 16, 6, 2, 6, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 16, 4, 0, 2, 2, 0, 2, 8, 2, 0, 0, 4, 4, 4, 0, 0, }, +{9: 16, 2, 6, 0, 0, 0, 0, 2, 4, 0, 0, 2, 4, 2, 0, 2, }, +{a: 16, 0, 4, 0, 8, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{c: 16, 0, 0, 0, 0, 6, 4, 4, 4, 6, 6, 2, 0, 2, 0, 6, }, +{7: 16, 6, 0, 0, 4, 0, 0, 10, 0, 0, 2, 4, 2, 0, 4, 0, }, +{b: 16, 0, 6, 6, 2, 0, 0, 4, 4, 2, 0, 0, 6, 4, 0, 6, }, +{d: 16, 0, 2, 0, 4, 4, 4, 6, 0, 0, 2, 0, 6, 6, 6, 0, }, +{e: 16, 2, 0, 0, 2, 4, 2, 0, 4, 4, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:48, 4:42, 6:23, 8:9, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{2: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{8: 0, 0, 8, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, -16, 8, 8, 0, -8, 0, 0, 0, }, +{2: 16, 0, 0, 8, 0, -16, 8, -8, 8, -8, 0, -8, 0, 8, -8, 0, }, +{4: 16, -8, 0, -8, 0, 8, 0, 0, 8, 8, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, 0, 0, 0, 0, 8, -8, 0, -8, -16, 0, 0, 0, 0, 0, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 8, -8, 0, -8, 0, 0, 8, -8, -8, 8, 0, -8, 0, 0, }, +{9: 16, -8, 0, 0, 0, -8, 0, 8, 8, -8, 0, -8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 8, 0, 0, }, +{c: 16, -8, -8, 0, 0, 8, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, }, +{7: 16, 0, 0, 0, 0, 8, 0, 8, -8, -8, -8, 0, -8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 8, 8, -8, 0, -8, 0, 0, -8, }, +{d: 16, 8, -8, -8, 0, -8, -8, 0, 8, -8, 0, 8, -8, 0, 8, 0, }, +{e: 16, 0, 0, 0, -8, -8, 8, 0, -8, 8, 0, 0, 0, -8, 0, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , , x, x, , , x, }, +{5: , , x, x, , x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , , , x, , x, , x, x, , , x, , , , x, }, +{b: , x, x, , x, , , x, x, , , , x, , , x, }, +{d: , , x, , , x, , x, x, , , , , x, , x, }, +{e: , x, x, x, , x, , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{1001,0001,1,}, +{1010,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x0a,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x01,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x02,0x09,0x0b,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_163.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_163.txt new file mode 100644 index 0000000..6d28942 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_163.txt @@ -0,0 +1,424 @@ +163 Sbox: +LUT = { +0x04,0x00,0x08,0x02,0x03,0x0b,0x06,0x07,0x01,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y3 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 6, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, }, +{8: 0, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 4, 2, 6, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 4, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, }, +{b: 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 4, 2, 0, 2, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 4, }, +{f: 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 8, 2, 8, 4, 0, 0, 4, 10, 0, 0, 4, 0, 0, 2, }, +{2: 16, 8, 10, 0, 0, 8, 2, 0, 0, 0, 10, 0, 2, 8, 8, 8, }, +{4: 16, 0, 0, 4, 0, 4, 2, 0, 0, 2, 0, 6, 2, 2, 2, 0, }, +{8: 16, 4, 2, 0, 4, 0, 2, 2, 6, 0, 0, 2, 0, 0, 0, 2, }, +{3: 16, 4, 8, 8, 2, 6, 4, 10, 0, 0, 0, 4, 0, 2, 0, 0, }, +{5: 16, 0, 0, 2, 0, 10, 4, 4, 0, 0, 6, 0, 2, 0, 0, 4, }, +{6: 16, 0, 2, 0, 2, 4, 4, 4, 2, 0, 0, 2, 2, 0, 0, 2, }, +{9: 16, 10, 0, 0, 6, 0, 0, 0, 4, 0, 4, 2, 0, 4, 2, 0, }, +{a: 16, 4, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 6, 2, 2, 0, }, +{c: 16, 0, 10, 4, 6, 0, 0, 6, 0, 4, 6, 0, 0, 4, 4, 4, }, +{7: 16, 2, 0, 4, 0, 8, 0, 2, 2, 0, 4, 4, 0, 0, 2, 4, }, +{b: 16, 8, 0, 0, 0, 2, 2, 0, 0, 6, 6, 0, 4, 4, 0, 0, }, +{d: 16, 0, 8, 0, 4, 2, 0, 0, 2, 4, 4, 2, 0, 2, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{f: 16, 2, 8, 4, 0, 0, 2, 4, 0, 0, 4, 0, 2, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:49, 4:44, 6:12, 8:14, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +{6: 0, 0, 0, 4, 4, 0, 4, 12, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{e: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, 0, 8, -8, 8, 0, -8, -8, -16, 0, -8, }, +{2: 16, 8, 0, 0, 0, 0, 0, -16, 0, -8, 8, -8, -16, 16, 0, 0, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 8, -8, 0, 8, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 0, 8, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, 0, 0, 8, 8, -8, -8, 0, -8, 0, 8, 8, -16, -8, 0, }, +{5: 16, -8, 0, -8, 0, 8, 0, -8, 0, 8, 0, 0, -8, 0, -8, 8, }, +{6: 16, 0, -8, 0, 0, 0, 0, 8, 8, -8, -8, 0, -8, 0, 0, 0, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 0, -8, 0, 0, 8, 0, 0, -8, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 8, -8, 0, 8, 0, 0, 0, }, +{c: 16, 8, 0, 0, 0, -8, 8, -8, 8, -16, 8, 0, -8, 0, 0, -8, }, +{7: 16, -8, -8, 0, 8, 0, -8, 8, -8, -8, 0, 0, 8, 0, 0, 0, }, +{b: 16, -8, 0, 8, 0, 0, -8, -8, -8, 8, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, 0, 0, -8, -8, -8, 0, -8, 8, 0, 8, 8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 8, 0, -8, 8, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , x, , x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , x, x, x, , x, x, , x, x, , x, x, , , x, }, +{b: , x, , , x, , x, , x, x, , , , , , x, }, +{d: , x, , x, , , x, , x, x, , , x, x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0110,0010,1,}, +{1010,1100,1,}, +{1011,0010,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +163 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x00,0x0b,0x06,0x07,0x02,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, }, +{2: 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 4, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{8: 0, 4, 0, 0, 4, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, }, +{5: 0, 0, 2, 2, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 2, }, +{6: 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 0, 4, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 2, 2, 0, }, +{a: 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 2, 4, 2, 0, }, +{c: 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, }, +{b: 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 2, 0, 0, 4, 2, 4, 0, 0, 2, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 4, }, +{f: 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 8, 0, 4, 4, 0, 0, 10, 4, 0, 2, 8, 0, 0, 2, }, +{2: 16, 8, 10, 0, 2, 8, 0, 2, 0, 0, 10, 0, 0, 8, 8, 8, }, +{4: 16, 2, 0, 4, 0, 8, 2, 0, 0, 2, 4, 4, 0, 0, 2, 4, }, +{8: 16, 8, 0, 0, 4, 2, 0, 2, 6, 0, 6, 0, 0, 4, 0, 0, }, +{3: 16, 4, 8, 4, 0, 6, 10, 4, 0, 0, 0, 8, 2, 2, 0, 0, }, +{5: 16, 0, 2, 2, 2, 4, 4, 4, 0, 2, 0, 0, 2, 0, 0, 2, }, +{6: 16, 0, 0, 0, 2, 10, 4, 4, 0, 0, 6, 2, 0, 0, 0, 4, }, +{9: 16, 4, 0, 0, 6, 0, 0, 2, 4, 2, 0, 2, 0, 2, 2, 0, }, +{a: 16, 10, 0, 2, 0, 0, 0, 0, 0, 4, 4, 0, 6, 4, 2, 0, }, +{c: 16, 0, 10, 0, 0, 0, 6, 0, 4, 0, 6, 4, 6, 4, 4, 4, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 2, 0, 0, 4, 0, 2, 2, 0, }, +{b: 16, 4, 2, 2, 0, 0, 2, 2, 0, 6, 0, 0, 4, 0, 0, 2, }, +{d: 16, 0, 8, 2, 0, 2, 0, 0, 4, 2, 4, 0, 4, 2, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{f: 16, 2, 8, 0, 2, 0, 4, 2, 0, 0, 4, 4, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:99, 2:49, 4:44, 6:12, 8:14, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{8: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{5: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{a: 0, 0, 0, 4, 4, 0, 4, 4, 4, 12, 0, 4, 4, 0, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, 8, -8, }, +{2: 16, 16, 0, 0, 0, 0, 0, -8, 0, -16, 8, -8, -16, 8, 0, 0, }, +{4: 16, 0, 0, 0, 8, 0, -8, -8, -8, 8, 0, 0, 8, -8, -8, 0, }, +{8: 16, 0, 8, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, -8, 0, 0, }, +{3: 16, -16, -8, 0, 8, 8, 0, -8, -8, -8, 0, 8, 8, 0, 0, 0, }, +{5: 16, 0, 0, 0, 0, 0, 8, -8, 0, 8, -8, 0, -8, 0, -8, 0, }, +{6: 16, 0, -8, -8, 0, 8, 0, 8, 0, -8, 0, 0, -8, -8, 0, 8, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 0, -8, -8, 0, 8, 0, 0, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, -8, 8, -8, }, +{c: 16, 0, 0, 0, 0, -8, 8, -16, 8, -8, 8, 0, -8, 8, 0, -8, }, +{7: 16, 0, 0, -8, 0, 0, 0, 8, 0, -8, -8, 0, 8, 0, 0, -8, }, +{b: 16, 0, -8, 0, 0, 0, 0, -8, 8, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 8, 0, -8, 0, -8, -8, 0, -8, 0, -8, 8, 0, 0, 8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 8, 0, -8, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, -8, 0, 8, -8, 8, 0, 8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , , x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , , x, , x, x, , x, x, , x, x, , , x, }, +{b: , , x, , x, x, x, , x, x, , , , , , x, }, +{d: , , , , x, x, x, , x, x, , , x, x, , x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,1100,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0b,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_164.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_164.txt new file mode 100644 index 0000000..6ee9896 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_164.txt @@ -0,0 +1,424 @@ +164 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x0e,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, }, +{8: 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 4, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 2, 2, 0, 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 2, 0, }, +{9: 0, 2, 4, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 2, 2, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 4, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 4, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:1, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 2, 2, 0, 4, 0, 10, 4, 8, 4, 8, 0, 0, }, +{2: 16, 0, 10, 8, 0, 0, 2, 8, 10, 0, 0, 0, 8, 8, 2, 8, }, +{4: 16, 0, 4, 4, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 2, }, +{8: 16, 0, 4, 0, 6, 4, 0, 0, 4, 0, 2, 0, 10, 0, 0, 2, }, +{3: 16, 2, 0, 2, 4, 8, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 16, 0, 0, 2, 0, 6, 4, 8, 6, 0, 0, 0, 0, 0, 2, 4, }, +{6: 16, 6, 6, 4, 0, 4, 4, 6, 0, 0, 2, 6, 0, 0, 2, 0, }, +{9: 16, 2, 4, 2, 2, 0, 0, 0, 6, 2, 0, 0, 4, 0, 2, 0, }, +{a: 16, 6, 6, 0, 0, 0, 2, 2, 4, 4, 0, 0, 8, 0, 0, 0, }, +{c: 16, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 16, 0, 4, }, +{7: 16, 6, 0, 0, 0, 0, 0, 10, 4, 0, 2, 4, 2, 0, 0, 4, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 4, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 4, 0, 0, 0, 0, 2, 0, 0, 4, 6, 6, 0, 8, 2, 0, }, +{e: 16, 0, 6, 4, 0, 0, 2, 0, 6, 0, 0, 0, 0, 8, 2, 4, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:40, 6:20, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 8, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 0, -8, 0, 8, 0, 0, -16, 8, -8, }, +{2: 16, 0, 0, 8, 0, -16, 0, 0, 8, -8, 0, -8, 0, 16, -16, 0, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, -8, 0, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, }, +{3: 16, 0, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -16, -8, 0, }, +{5: 16, 0, 0, -8, 8, -8, -8, 0, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, -8, 8, 0, -8, 0, 0, -8, 0, 8, 0, }, +{9: 16, 8, 0, 8, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, -8, }, +{a: 16, 0, -8, 8, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, }, +{c: 16, 0, 8, -16, 0, 8, 0, -8, 0, -8, 0, -8, 8, 0, 8, -8, }, +{7: 16, -8, -8, -8, 0, 8, 0, 8, 0, 0, 0, -8, -8, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, -8, 8, -8, -8, 0, 0, 0, 8, 0, 8, 0, }, +{e: 16, -8, 0, -8, -8, -8, 8, 0, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, , x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, x, x, , , x, x, , x, x, x, , , x, x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, , , x, x, x, x, , x, x, , , x, x, x, }, +{e: , x, x, , x, x, x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,1100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +164 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x0e,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, }, +{8: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 0, 0, 0, 0, 4, 6, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 6, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, }, +{e: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:1, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 6, 2, 6, 4, 6, 4, 4, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 0, 8, 4, 0, 2, 2, 4, 2, 0, 4, 0, 0, 0, 4, 2, }, +{8: 16, 2, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 0, 4, 8, 6, 4, 0, 0, 0, 0, 6, 0, 0, 2, }, +{5: 16, 0, 2, 2, 0, 4, 4, 4, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 2, 0, 10, 2, 0, 0, 0, }, +{9: 16, 0, 10, 0, 4, 0, 6, 0, 6, 4, 4, 4, 4, 0, 6, 0, }, +{a: 16, 10, 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 6, 4, 0, 0, }, +{c: 16, 4, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 6, 0, 2, }, +{7: 16, 8, 0, 2, 0, 0, 0, 6, 0, 0, 4, 4, 0, 6, 0, 2, }, +{b: 16, 4, 8, 2, 10, 4, 0, 0, 4, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 8, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 8, 8, 0, }, +{e: 16, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 8, 2, 2, 2, 4, 0, 0, 0, 4, 4, 0, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:40, 6:20, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{6: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 8, -8, 0, 0, -8, 0, -8, 8, 0, }, +{2: 16, 8, -8, 8, 0, -16, 0, 0, 8, -8, 0, -8, 0, 8, -8, 0, }, +{4: 16, 0, 8, -8, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, -8, 8, }, +{8: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 8, -8, -8, -8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 0, 0, 0, -16, 8, -8, 0, 8, 8, }, +{9: 16, 8, 0, 8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 8, -16, -8, }, +{a: 16, -8, 0, 8, -8, -8, 0, -8, 0, 0, 0, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, -8, 0, -8, 0, 16, 0, 0, 0, 8, -8, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 8, 0, 8, -8, 0, 0, 0, 8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, x, x, , x, x, , x, , , x, }, +{c: , x, x, x, x, x, x, x, , x, x, , , x, x, x, }, +{7: , x, x, , , , x, x, , x, x, x, , , x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , x, x, , x, x, , x, x, , , x, x, x, }, +{e: , x, x, x, x, x, x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,0111,1,}, +{1100,0110,1,}, +{1100,1011,1,}, +{1100,1101,0,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_165.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_165.txt new file mode 100644 index 0000000..828f952 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_165.txt @@ -0,0 +1,424 @@ +165 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x04,0x06,0x0e,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x07,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 0, 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, }, +{8: 0, 4, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 0, 4, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 0, 0, 2, 0, 4, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, }, +{c: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 6, 2, 0, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 2, 0, 2, 0, }, +{b: 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:2, 4:5, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 16, 4, 8, 4, 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 16, 0, 4, 10, 0, 0, 0, 4, 10, 2, 0, 2, 4, 8, 0, 4, }, +{8: 16, 4, 0, 6, 6, 0, 0, 0, 8, 0, 0, 2, 2, 4, 0, 0, }, +{3: 16, 4, 6, 0, 0, 8, 4, 6, 0, 2, 0, 0, 0, 0, 2, 0, }, +{5: 16, 0, 0, 0, 4, 4, 10, 6, 4, 4, 6, 0, 0, 4, 0, 6, }, +{6: 16, 4, 6, 6, 0, 4, 4, 6, 2, 0, 0, 6, 0, 0, 2, 0, }, +{9: 16, 4, 0, 4, 10, 0, 8, 0, 6, 2, 4, 0, 2, 8, 0, 0, }, +{a: 16, 0, 0, 6, 2, 2, 4, 0, 0, 4, 0, 0, 4, 0, 0, 10, }, +{c: 16, 4, 0, 4, 4, 0, 10, 2, 8, 0, 8, 0, 0, 6, 2, 0, }, +{7: 16, 4, 0, 0, 0, 0, 2, 6, 0, 2, 2, 4, 2, 0, 2, 0, }, +{b: 16, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 16, 4, 0, 4, 0, 0, 0, 0, 4, 0, 6, 0, 0, 10, 2, 2, }, +{e: 16, 0, 2, 4, 0, 2, 2, 0, 0, 0, 0, 2, 4, 2, 2, 4, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 0, 4, 2, 2, 2, 2, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:45, 4:48, 6:16, 8:8, 10:7, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 8, 0, 4, 0, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 8, 0, }, +{5: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 0, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{e: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 8, 0, 0, 0, 0, -8, -8, 8, -8, -16, 0, 0, -8, }, +{2: 16, 0, -16, 8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{4: 16, 0, 8, -8, 0, 0, 0, -8, 8, 0, -8, -8, 16, -8, 0, -8, }, +{8: 16, -8, 8, 8, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{3: 16, 0, -8, 8, 8, -8, -8, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 0, 0, 8, 0, -8, 0, -8, 8, -16, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, -8, 8, 8, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 0, 0, 0, -16, 0, 0, 8, -8, 8, }, +{a: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, 8, -16, -8, -8, 0, -8, 0, -8, 8, 8, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 8, 8, 0, }, +{b: 16, 0, -8, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 8, -8, 0, 0, -8, 0, 0, 8, 8, -8, 0, -8, 0, -8, }, +{e: 16, -8, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{5: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{6: , x, , x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , x, , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, x, x, x, , , x, }, +{c: , x, x, , x, x, x, , , x, x, x, , x, , x, }, +{7: , , , x, , x, , , , x, x, , , , x, x, }, +{b: , x, , x, x, , x, , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , x, , , x, x, , , , x, x, x, , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0010,1,}, +{0100,1100,1,}, +{1011,0001,1,}, +{1011,0100,0,}, +{1011,0101,1,}, +{1100,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x01,0x0a,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0b,}}, +{{0x03,0x04,}, {0x0b,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x03,0x08,0x0b,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +165 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x08,0x06,0x0e,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x07,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 4, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, }, +{8: 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{5: 0, 0, 0, 0, 0, 0, 6, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 2, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 2, 4, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{c: 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 0, 0, 2, }, +{d: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{f: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:2, 4:5, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 16, 4, 8, 4, 0, 6, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, }, +{4: 16, 0, 4, 10, 6, 0, 0, 6, 4, 6, 4, 0, 0, 4, 4, 0, }, +{8: 16, 4, 0, 0, 6, 0, 4, 0, 10, 2, 4, 0, 2, 0, 0, 0, }, +{3: 16, 4, 4, 0, 0, 8, 4, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{5: 16, 0, 0, 0, 0, 4, 10, 4, 8, 4, 10, 2, 0, 0, 2, 4, }, +{6: 16, 4, 4, 4, 0, 6, 6, 6, 0, 0, 2, 6, 2, 0, 0, 0, }, +{9: 16, 4, 0, 10, 8, 0, 4, 2, 6, 0, 8, 0, 2, 4, 0, 0, }, +{a: 16, 0, 2, 2, 0, 2, 4, 0, 2, 4, 0, 2, 2, 0, 0, 4, }, +{c: 16, 4, 0, 0, 0, 0, 6, 0, 4, 0, 8, 2, 0, 6, 0, 2, }, +{7: 16, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 2, 4, 2, 0, 0, 0, 2, 4, 0, 2, 2, 0, 4, 2, }, +{d: 16, 4, 0, 8, 4, 0, 4, 0, 8, 0, 6, 0, 0, 10, 2, 2, }, +{e: 16, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{f: 16, 0, 2, 4, 0, 0, 6, 0, 0, 10, 0, 0, 0, 2, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:45, 4:48, 6:16, 8:8, 10:7, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{3: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 8, 0, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +{b: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, 0, 0, -8, -8, 8, 8, 0, -16, 0, -8, }, +{2: 16, 0, -8, 8, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, }, +{4: 16, 8, 8, -8, 0, 0, 0, -8, 8, 0, -8, 0, 8, -16, 0, -8, }, +{8: 16, -8, 8, 8, 0, -8, 0, 0, -8, 8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, -16, 8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{5: 16, -8, 8, -8, 0, -8, 0, 0, -8, 0, -8, 0, 0, 16, -8, 8, }, +{6: 16, 0, -8, -8, 8, 0, -8, 0, 0, -8, -8, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 8, -8, 0, -8, 8, 8, -8, -16, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, 0, 0, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{c: 16, -8, 8, -8, 0, 0, 0, 0, -8, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 0, }, +{d: 16, 8, 8, -16, -8, 8, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, -8, 8, 0, 0, 8, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{5: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{6: , x, x, x, , x, x, x, , x, x, x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, x, x, , , x, }, +{c: , x, x, x, x, x, x, , , x, x, x, , x, , x, }, +{7: , x, , x, , x, x, , , x, x, , , , x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , x, x, x, , x, , , , x, x, x, , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0011,1,}, +{0100,1101,1,}, +{1100,1001,1,}, +{1101,0001,1,}, +{1101,0100,1,}, +{1101,0101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x0a,0x04,}, {0x0d,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x04,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x04,0x09,0x0d,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_166.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_166.txt new file mode 100644 index 0000000..0e8bcc9 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_166.txt @@ -0,0 +1,424 @@ +166 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x0c,0x04,0x09,0x0a,0x0b,0x07,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, }, +{8: 0, 0, 0, 2, 4, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 4, 2, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 2, 2, 0, }, +{9: 0, 2, 4, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 4, }, +{7: 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 2, 4, }, +{f: 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 10, 8, 0, 0, 2, 8, 10, 0, 0, 0, 8, 8, 2, 8, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 0, 0, 0, 6, 2, 0, 2, 0, }, +{8: 16, 0, 4, 2, 4, 6, 0, 0, 4, 0, 2, 0, 10, 0, 0, 0, }, +{3: 16, 2, 0, 4, 10, 6, 0, 0, 0, 2, 4, 8, 4, 0, 0, 8, }, +{5: 16, 4, 0, 10, 0, 2, 4, 0, 6, 0, 0, 0, 0, 4, 2, 0, }, +{6: 16, 0, 6, 4, 0, 0, 0, 4, 0, 2, 2, 2, 0, 2, 2, 0, }, +{9: 16, 2, 4, 2, 2, 0, 0, 0, 6, 2, 0, 0, 4, 0, 2, 0, }, +{a: 16, 4, 6, 0, 0, 0, 2, 0, 4, 6, 0, 0, 8, 2, 0, 0, }, +{c: 16, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 16, }, +{7: 16, 2, 0, 8, 0, 4, 0, 2, 4, 0, 2, 4, 2, 4, 0, 0, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 4, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 6, 0, 0, 0, 2, 4, 6, 0, 0, 0, 0, 4, 2, 8, }, +{f: 16, 0, 0, 0, 4, 4, 2, 0, 0, 0, 6, 6, 0, 0, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:44, 4:41, 6:19, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 8, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, 8, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -16, 8, 0, }, +{2: 16, 0, 0, 8, 0, -16, 0, 0, 8, -8, 0, -8, 0, 16, -16, 0, }, +{4: 16, 0, 0, -8, 8, 8, -8, -8, 0, 8, -8, 0, 8, 0, -8, -8, }, +{8: 16, 0, 8, 8, -8, 8, -8, 0, 0, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, -8, 8, 0, 8, 0, 0, -8, 0, 8, 0, 0, -16, -8, 8, }, +{5: 16, -8, 8, -8, 0, -8, 0, -8, 0, 0, 0, 8, 8, 0, -8, 0, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, }, +{9: 16, 8, 0, 8, 0, -8, 0, 0, 0, 0, 0, -8, 0, 0, -8, -8, }, +{a: 16, -8, 0, 8, 0, -8, 0, -8, 0, 8, 0, 0, -8, 0, 8, -8, }, +{c: 16, -8, 0, -16, -8, 8, 8, 0, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, -8, 0, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 8, 0, 0, 0, -8, 0, -8, 8, }, +{f: 16, 0, 0, -8, -8, 8, 8, 8, -8, 0, 0, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, , x, , , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, , x, , x, x, , , x, x, , x, x, x, }, +{7: , x, x, x, , x, x, x, , , x, , , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, , , x, , x, x, , , x, x, , x, , x, }, +{e: , x, x, , x, , x, x, , , x, x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,1100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x01,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +166 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x0c,0x00,0x09,0x0a,0x0b,0x07,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, }, +{3: 0, 2, 0, 2, 2, 6, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 4, 0, }, +{9: 0, 0, 6, 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 4, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 4, 0, 0, 2, 0, 0, }, +{e: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 4, 8, 6, 2, 4, 10, 4, 2, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 2, 0, 0, 4, 10, 0, 0, 2, 0, 4, 0, 6, 0, 0, 4, }, +{3: 16, 2, 0, 6, 6, 6, 2, 0, 0, 0, 4, 4, 6, 0, 0, 4, }, +{5: 16, 4, 2, 6, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 16, 2, 8, 4, 0, 0, 0, 4, 0, 0, 4, 2, 2, 2, 4, 0, }, +{9: 16, 0, 10, 0, 4, 0, 6, 0, 6, 4, 4, 4, 4, 0, 6, 0, }, +{a: 16, 4, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 4, 2, 2, 2, 0, 6, }, +{7: 16, 0, 0, 6, 0, 8, 0, 2, 0, 0, 4, 4, 0, 2, 0, 6, }, +{b: 16, 4, 8, 2, 10, 4, 0, 0, 4, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 2, 8, 0, 0, 0, 4, 2, 0, 2, 4, 4, 0, 2, 4, 0, }, +{e: 16, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, }, +{f: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:44, 4:41, 6:19, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, -8, 8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 0, -16, 0, 0, 8, -8, 0, -8, 0, 8, -8, 0, }, +{4: 16, 0, 8, -8, 8, 8, 0, 0, 0, 0, -16, -8, 8, 0, -8, -8, }, +{8: 16, -8, 0, 8, -8, 8, 0, 8, 0, 0, 0, 0, -8, -8, -8, 0, }, +{3: 16, -8, 0, 8, 8, 8, -8, -8, -8, 0, 0, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 8, 0, 0, 8, -8, }, +{9: 16, 8, 0, 8, 0, -8, 8, 0, 0, -8, 0, 0, -8, 8, -16, -8, }, +{a: 16, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, -8, 0, -8, 0, -8, -8, 0, 0, 0, -8, 0, 8, 8, }, +{e: 16, 0, 0, -8, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, -8, 0, 16, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, , x, , , x, }, +{5: , x, x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{c: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{7: , x, x, , , x, x, x, , , x, , , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , x, x, x, x, x, , , x, x, , x, , x, }, +{e: , x, x, x, x, , x, x, , , x, x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,0111,1,}, +{1100,0100,1,}, +{1100,1011,1,}, +{1100,1111,0,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_167.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_167.txt new file mode 100644 index 0000000..08dc1e9 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_167.txt @@ -0,0 +1,424 @@ +167 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x06,0x07,0x03,0x0c,0x0a,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 2, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 2, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 4, 0, 2, }, +{7: 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 4, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 0, }, +{e: 0, 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 4, 0, 4, 0, 10, 0, 4, 2, 0, 8, 0, 2, }, +{2: 16, 0, 8, 2, 6, 0, 6, 0, 2, 4, 0, 4, 0, 0, 0, 0, }, +{4: 16, 6, 0, 4, 0, 0, 6, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 16, 4, 4, 0, 10, 10, 0, 0, 4, 4, 2, 2, 8, 0, 0, 0, }, +{3: 16, 2, 0, 0, 6, 8, 6, 4, 0, 0, 2, 0, 4, 0, 0, 0, }, +{5: 16, 6, 6, 4, 0, 4, 10, 6, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 2, 0, 4, 6, 4, 10, 0, 0, 0, 2, 8, 8, 4, 0, }, +{9: 16, 4, 2, 0, 6, 2, 0, 0, 4, 2, 2, 0, 0, 0, 0, 2, }, +{a: 16, 0, 6, 2, 4, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 2, }, +{c: 16, 6, 0, 4, 0, 0, 0, 0, 6, 0, 4, 2, 0, 8, 0, 2, }, +{7: 16, 0, 4, 2, 0, 2, 4, 2, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 4, 8, 4, 4, 0, 2, 0, 0, 6, 8, 10, 2, }, +{d: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 16, 4, 0, }, +{e: 16, 0, 0, 0, 4, 4, 4, 0, 0, 2, 0, 0, 10, 0, 6, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:42, 6:18, 8:10, 10:7, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 8, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:9, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 8, 0, 8, 0, -16, 0, -8, 0, -8, }, +{2: 16, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 8, -8, 16, 0, 0, -8, -8, -8, 8, -8, 0, 0, -8, }, +{3: 16, 0, 0, 0, 8, 0, -8, 0, -8, -8, 0, 8, -8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -16, 0, 0, -8, 8, 0, 8, -8, 8, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, 0, -8, 0, -16, 8, 8, 8, -8, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, }, +{a: 16, 8, -8, 0, -8, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, }, +{c: 16, -8, 8, -8, -8, 0, 0, 0, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, 8, -8, 0, 8, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, -8, -8, 0, -16, 0, 0, -8, 8, 8, 0, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -16, -8, 8, 8, -8, 0, 8, 8, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, 0, 8, 0, -8, 8, -8, 8, -8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, , , x, }, +{5: , x, x, , x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{9: , x, x, , x, x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , x, , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, x, , , , , , x, , x, , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , x, x, x, x, x, , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0101,1,}, +{0011,1000,0,}, +{0011,1101,1,}, +{0111,0001,1,}, +{1000,1011,1,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x03,}}, +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x05,0x06,0x08,}, {0x03,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x03,0x09,0x0a,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x03,0x04,0x07,}}, +{{0x03,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x01,0x02,0x03,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +167 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x03,0x0c,0x0a,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 4, 0, 0, 0, 2, 2, 2, 2, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 2, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 4, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{c: 0, 0, 0, 0, 2, 2, 0, 0, 2, 2, 4, 2, 0, 0, 0, 2, }, +{7: 0, 2, 4, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 6, 0, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 4, 2, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 4, 2, 6, 0, 4, 0, 6, 0, 0, 4, 0, 2, }, +{2: 16, 0, 8, 0, 4, 0, 6, 2, 2, 6, 0, 4, 0, 0, 0, 0, }, +{4: 16, 8, 2, 4, 0, 0, 4, 0, 0, 2, 4, 2, 0, 4, 0, 2, }, +{8: 16, 4, 6, 0, 10, 6, 0, 4, 6, 4, 0, 0, 4, 0, 4, 0, }, +{3: 16, 0, 0, 0, 10, 8, 4, 6, 2, 0, 0, 2, 8, 4, 4, 0, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 0, 2, 0, 4, 6, 10, 0, 0, 0, 2, 4, 4, 0, 0, }, +{9: 16, 10, 2, 0, 4, 0, 0, 0, 4, 0, 6, 0, 0, 4, 0, 2, }, +{a: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{c: 16, 4, 0, 0, 2, 2, 0, 0, 2, 2, 4, 2, 0, 4, 0, 2, }, +{7: 16, 2, 4, 2, 2, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 8, 4, 4, 8, 0, 2, 0, 0, 6, 4, 10, 2, }, +{d: 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 16, 0, 0, }, +{e: 16, 0, 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 10, 4, 6, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:42, 6:18, 8:10, 10:7, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 8, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:9, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, -8, 8, 8, -8, -8, -8, 0, 0, }, +{2: 16, 0, -8, 0, 8, -8, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, }, +{4: 16, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, -16, 0, -8, 0, -8, }, +{8: 16, 8, 0, 8, -8, 0, 0, 8, -8, -8, 0, 8, 0, 0, -16, -8, }, +{3: 16, 0, -8, 0, 8, 0, -8, 8, 0, -16, -8, 8, 0, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -16, 0, }, +{6: 16, -8, 0, -8, 8, 0, 0, -8, 0, -8, 0, 8, 8, -8, 0, 0, }, +{9: 16, -8, 8, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, }, +{c: 16, 0, 0, 0, -8, 8, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, 8, 0, 0, 8, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -16, 8, 0, 0, 0, 8, -8, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, -8, 8, -8, 0, 8, -8, 0, 16, 0, }, +{e: 16, -8, 0, -8, -8, -8, 8, -8, 0, 8, 0, 8, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , x, , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{9: , x, , x, x, x, , , x, , x, , x, x, , x, }, +{a: , x, , x, x, x, , , x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , x, , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, , , , , , , x, , x, , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, , x, x, x, , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0111,0100,1,}, +{1000,1011,1,}, +{1010,0011,1,}, +{1110,0101,1,}, +{1110,1000,1,}, +{1110,1101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x05,0x06,0x08,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,0x09,0x0e,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_168.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_168.txt new file mode 100644 index 0000000..2653580 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_168.txt @@ -0,0 +1,424 @@ +168 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x0d,0x0a,0x0b,0x0c,0x09,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, }, +{5: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 6, 4, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 0, 4, 0, 0, 2, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:1, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 6, 2, 6, 2, 6, 0, 4, 0, 0, 4, 0, 0, }, +{2: 16, 0, 10, 4, 0, 0, 6, 4, 6, 0, 4, 4, 4, 0, 6, 0, }, +{4: 16, 4, 8, 6, 2, 4, 8, 4, 0, 0, 0, 10, 2, 0, 0, 0, }, +{8: 16, 8, 0, 0, 4, 0, 0, 0, 6, 0, 4, 0, 2, 6, 0, 2, }, +{3: 16, 2, 0, 6, 0, 8, 0, 0, 4, 6, 0, 4, 0, 0, 0, 2, }, +{5: 16, 10, 0, 6, 0, 2, 4, 2, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 16, 0, 10, 4, 4, 0, 4, 6, 0, 6, 4, 4, 0, 0, 6, 0, }, +{9: 16, 4, 8, 2, 10, 4, 2, 0, 6, 8, 0, 0, 4, 0, 0, 0, }, +{a: 16, 0, 2, 0, 0, 4, 2, 0, 4, 4, 0, 0, 2, 2, 2, 2, }, +{c: 16, 4, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 6, 0, 2, }, +{7: 16, 2, 0, 6, 0, 4, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 0, 8, 0, 0, 2, 0, 2, 4, 2, 4, 0, 4, 0, 4, 2, }, +{d: 16, 8, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 8, 8, 0, }, +{e: 16, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 0, 8, 0, 4, 2, 0, 0, 0, 4, 4, 2, 2, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:40, 6:20, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 0, 4, 4, 4, 4, 8, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 8, -8, 0, 0, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 0, 8, -16, 0, 0, 8, -8, 0, 0, -8, 8, -8, 0, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, -8, -8, 0, 8, 8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 0, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 0, }, +{6: 16, 8, -16, 0, 8, -8, 8, 0, 0, -8, 0, -8, 0, 8, 0, -8, }, +{9: 16, 0, 8, 8, -8, -8, 0, 0, 0, 0, -16, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{b: 16, 0, -8, 0, -8, 8, -8, -8, 0, 0, 0, 0, -8, 0, 8, 8, }, +{d: 16, 0, 8, -8, -8, -8, -8, 0, -8, 0, 16, 0, 0, 0, 8, -8, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 8, -8, 0, 0, 8, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, , , x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, , x, x, , , x, x, , x, x, x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, , , x, x, , , , x, , x, x, , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0110,1,}, +{0011,0010,1,}, +{1000,1000,1,}, +{1100,0100,1,}, +{1100,1001,1,}, +{1100,1101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,0x05,0x07,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +168 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x0d,0x0a,0x0b,0x0c,0x09,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, }, +{5: 0, 2, 2, 4, 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 2, 0, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, }, +{d: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:1, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 8, 2, 10, 0, 4, 0, 4, 2, 0, 8, 0, 0, }, +{2: 16, 0, 10, 8, 0, 0, 0, 10, 8, 2, 0, 0, 8, 8, 2, 8, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 2, 0, 2, 6, 0, 0, 0, 0, }, +{8: 16, 6, 0, 2, 4, 0, 0, 4, 10, 0, 2, 0, 0, 0, 0, 4, }, +{3: 16, 2, 0, 4, 0, 8, 2, 0, 4, 4, 0, 4, 2, 0, 0, 2, }, +{5: 16, 6, 6, 8, 0, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 16, 2, 4, 4, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 16, 6, 6, 0, 6, 4, 0, 0, 6, 4, 2, 0, 4, 0, 2, 0, }, +{a: 16, 0, 0, 0, 0, 6, 0, 6, 8, 4, 0, 0, 2, 0, 2, 4, }, +{c: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 16, 0, 4, }, +{7: 16, 0, 4, 10, 0, 4, 0, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 2, 2, }, +{d: 16, 4, 0, 0, 6, 0, 4, 0, 0, 2, 6, 0, 0, 8, 2, 0, }, +{e: 16, 0, 6, 0, 0, 0, 0, 6, 0, 2, 0, 0, 4, 8, 2, 4, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:40, 6:20, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, }, +{7: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 8, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 16, -16, 0, 8, -16, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, 0, 0, 0, -8, -8, -8, -8, 0, }, +{3: 16, -16, -8, 0, 8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 8, 0, 8, -8, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, -8, }, +{9: 16, 0, 8, 8, -8, -8, -8, 8, 0, -8, 0, -8, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, -8, 0, 0, 0, -8, 0, 8, 0, 0, 8, }, +{c: 16, 0, 8, 0, -16, 8, 0, -8, 0, -8, 0, 8, -8, 0, 8, -8, }, +{7: 16, 0, -8, -8, 8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 0, 8, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, -8, -8, 8, -8, -8, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 8, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, x, , , , x, x, x, x, , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , x, , x, , x, , x, x, , x, }, +{a: , , , x, x, x, x, , , x, x, , x, x, x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , , x, , x, , , , x, , x, x, , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{1000,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_169.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_169.txt new file mode 100644 index 0000000..4ea5f55 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_169.txt @@ -0,0 +1,424 @@ +169 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0e,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 6, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 2, 0, 2, 4, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 2, 0, 4, }, +{a: 0, 2, 2, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 4, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, }, +{7: 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 6, 2, 2, 0, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 4, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 6, 0, 0, 4, 0, 2, 10, 0, 2, 8, 0, 4, 4, }, +{2: 16, 0, 8, 2, 6, 0, 6, 0, 2, 4, 0, 4, 0, 0, 0, 0, }, +{4: 16, 4, 0, 10, 0, 0, 6, 2, 0, 0, 0, 2, 4, 0, 0, 4, }, +{8: 16, 0, 4, 0, 4, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{3: 16, 2, 0, 0, 0, 6, 6, 6, 4, 4, 6, 0, 0, 2, 0, 4, }, +{5: 16, 6, 6, 4, 0, 4, 10, 6, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 2, 0, 2, 8, 4, 4, 0, 0, 4, 2, 0, 2, 0, 4, }, +{9: 16, 0, 2, 0, 0, 10, 0, 0, 4, 4, 6, 0, 0, 2, 0, 4, }, +{a: 16, 6, 6, 4, 4, 4, 0, 0, 6, 10, 0, 0, 4, 0, 4, 0, }, +{c: 16, 2, 0, 0, 2, 4, 0, 0, 2, 2, 4, 2, 0, 2, 0, 4, }, +{7: 16, 0, 4, 2, 0, 2, 4, 2, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 0, 8, 2, 0, 4, 0, 0, 8, 0, 0, 6, 2, 10, 4, }, +{d: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 0, 4, 2, 0, 4, 0, 0, 0, 0, 0, 10, 2, 6, 4, }, +{f: 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:42, 6:18, 8:10, 10:7, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 0, 0, 4, 0, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:9, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -8, 0, 0, 8, -8, -16, 8, -8, 0, -8, }, +{2: 16, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, -8, 0, 8, -8, -8, }, +{4: 16, -8, 0, -8, 8, 0, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, -8, -8, 8, 0, 0, 0, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, -8, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -16, 0, 0, -8, 8, 0, 8, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, 0, 0, 0, 0, -16, 0, 8, 0, -8, 0, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 0, 8, -8, 8, -8, 0, 0, -8, 8, }, +{a: 16, 8, -8, 8, -8, -16, 0, 0, -8, 8, 0, -8, 8, 0, 0, 0, }, +{c: 16, 0, 8, 0, -8, 0, 0, 0, -8, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, 8, -8, 0, 8, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, -8, 8, -16, 0, 0, -8, 0, 8, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{e: 16, -8, 0, -8, -8, 0, 8, 0, 0, 8, 0, 8, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 16, -8, -8, 8, 8, 0, -8, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{5: , x, x, , x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, x, , , x, }, +{9: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{a: , x, x, x, x, x, , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, x, , x, , , , x, x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , x, x, x, x, , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0101,1,}, +{0011,1010,1,}, +{0011,1111,0,}, +{0111,0001,1,}, +{1000,1011,1,}, +{1010,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x0a,0x04,}, {0x03,}}, +{{0x09,0x0a,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x0a,}, {0x01,0x02,0x03,}}, +{{0x01,0x0e,}, {0x03,0x04,0x07,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +169 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x03,0x09,0x0a,0x0e,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 2, 2, 2, 2, 0, 4, 0, 0, 0, 0, }, +{4: 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 2, 0, 4, }, +{7: 0, 2, 4, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 4, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 4, 0, 0, 2, 2, 2, 0, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 6, 0, 0, 6, 2, 0, 4, 0, 0, 0, }, +{2: 16, 0, 8, 0, 4, 0, 6, 2, 2, 6, 0, 4, 0, 0, 0, 0, }, +{4: 16, 6, 2, 10, 0, 0, 4, 0, 0, 4, 0, 2, 8, 0, 4, 8, }, +{8: 16, 0, 6, 0, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{3: 16, 0, 0, 0, 0, 6, 4, 8, 10, 4, 4, 2, 0, 2, 0, 8, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 0, 2, 2, 6, 6, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 2, 2, 0, 2, 4, 0, 0, 4, 6, 2, 0, 0, 2, 0, 0, }, +{a: 16, 10, 4, 0, 4, 4, 0, 0, 4, 10, 2, 2, 8, 0, 0, 0, }, +{c: 16, 0, 0, 0, 0, 6, 0, 4, 6, 0, 4, 2, 0, 2, 0, 8, }, +{7: 16, 2, 4, 2, 2, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 8, 0, 4, 2, 0, 4, 0, 0, 4, 0, 0, 6, 2, 10, 8, }, +{d: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 4, 0, 0, 2, 0, 4, 0, 0, 4, 0, 0, 10, 2, 6, 0, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:43, 4:42, 6:18, 8:10, 10:7, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:9, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -8, -8, -8, 8, 0, -8, 0, -8, 0, 0, }, +{2: 16, 0, -8, 0, 8, -8, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, }, +{4: 16, -8, 0, 0, 8, 0, 0, 8, 0, 8, 8, -16, -8, -8, 0, -8, }, +{8: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, 0, -16, 0, 8, 8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 8, 0, -8, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -8, -8, 8, -8, -8, 0, 0, 16, 0, }, +{c: 16, -8, 0, -8, -8, 8, 0, 0, 0, -8, 8, -8, 0, 0, 0, 8, }, +{7: 16, 8, 0, 0, 8, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, -8, }, +{b: 16, -8, -8, 0, -16, 8, 0, 0, 8, 8, 0, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -8, -8, 8, -8, -8, 8, -8, 8, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 8, 8, 8, 0, -8, 8, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, , x, x, , , x, x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , x, x, x, , , x, }, +{9: , x, , x, x, x, , x, x, , x, , , x, x, x, }, +{a: , x, , x, x, x, , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , x, x, , x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, , , , x, , x, x, , x, , , , x, x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, , x, x, , , x, x, , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0111,0100,1,}, +{1000,1011,1,}, +{1010,0011,1,}, +{1110,0101,1,}, +{1110,1010,0,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x07,0x09,0x0e,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x02,}}, +{{0x03,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_170.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_170.txt new file mode 100644 index 0000000..4bef381 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_170.txt @@ -0,0 +1,424 @@ +170 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0f,0x0c,0x0d,0x0e,0x0b, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{5: 0, 4, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 4, 0, 0, 2, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 10, 4, 0, 0, 6, 4, 6, 0, 4, 4, 4, 0, 6, 0, }, +{4: 16, 4, 8, 6, 2, 4, 8, 4, 0, 0, 0, 10, 2, 0, 0, 0, }, +{8: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 4, 0, 6, 2, 0, 6, }, +{3: 16, 2, 0, 6, 4, 6, 0, 0, 0, 2, 4, 6, 6, 0, 0, 4, }, +{5: 16, 4, 0, 6, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 16, 0, 10, 4, 4, 0, 4, 6, 0, 6, 4, 4, 0, 0, 6, 0, }, +{9: 16, 2, 8, 2, 2, 0, 0, 0, 4, 0, 4, 0, 4, 2, 4, 0, }, +{a: 16, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 6, 2, 2, 2, }, +{c: 16, 0, 0, 2, 2, 4, 0, 0, 2, 0, 4, 2, 0, 2, 0, 6, }, +{7: 16, 2, 0, 6, 0, 10, 0, 2, 0, 0, 4, 4, 0, 0, 0, 4, }, +{b: 16, 4, 8, 0, 8, 4, 0, 2, 4, 10, 0, 2, 6, 0, 0, 0, }, +{d: 16, 2, 8, 0, 4, 0, 2, 0, 2, 4, 4, 0, 0, 2, 4, 0, }, +{e: 16, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 2, }, +{f: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:44, 4:41, 6:19, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, 0, 0, -8, 0, 0, 8, -8, -8, 0, 0, }, +{2: 16, 8, -8, 0, 8, -16, 0, 0, 8, -8, 0, 0, -8, 8, -8, 0, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, -8, -8, 8, 8, 8, -8, -8, -8, 0, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 8, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{6: 16, 8, -16, 0, 8, -8, 8, 0, 0, -8, 0, -8, 0, 8, 0, -8, }, +{9: 16, 0, 8, 0, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, 0, 0, 0, -16, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, 0, -8, -8, 0, -8, -8, 0, 0, -8, 0, 0, 8, 8, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, -8, 0, 16, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, x, x, x, , x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, , x, x, x, x, x, x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, , , x, x, x, , , x, x, x, x, x, x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0110,1,}, +{0011,0010,1,}, +{1000,1000,1,}, +{1100,0100,1,}, +{1100,1011,1,}, +{1100,1111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,0x05,0x07,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x05,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +170 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0f,0x0c,0x0d,0x0e,0x0b, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 4, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{5: 0, 4, 2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, 2, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 6, 0, 2, 0, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:63, 4:21, 6:5, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 10, 8, 0, 0, 0, 10, 8, 2, 0, 0, 8, 8, 2, 8, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 2, 0, 2, 6, 0, 0, 0, 0, }, +{8: 16, 2, 0, 2, 4, 4, 0, 4, 2, 0, 2, 0, 8, 4, 0, 0, }, +{3: 16, 2, 0, 4, 8, 6, 2, 0, 0, 0, 4, 10, 4, 0, 0, 8, }, +{5: 16, 4, 6, 8, 0, 0, 6, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 16, 2, 4, 4, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 2, 2, 0, }, +{a: 16, 4, 0, 0, 0, 2, 0, 6, 0, 4, 0, 0, 10, 4, 2, 0, }, +{c: 16, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 16, }, +{7: 16, 0, 4, 10, 0, 6, 0, 4, 0, 0, 2, 4, 2, 0, 0, 0, }, +{b: 16, 4, 4, 2, 6, 6, 0, 0, 4, 6, 0, 0, 6, 0, 2, 0, }, +{d: 16, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 6, 0, 0, 0, 0, 6, 4, 2, 0, 0, 0, 4, 2, 8, }, +{f: 16, 0, 0, 0, 6, 4, 0, 0, 0, 2, 6, 4, 0, 0, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:103, 2:44, 4:41, 6:19, 8:12, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, 8, }, +{7: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -16, 0, 8, -16, 0, 0, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 8, -8, 8, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, }, +{3: 16, -16, -8, 0, 8, 8, 0, 0, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, 0, 8, 0, 8, -8, 0, -8, 0, 8, 0, -8, 0, -8, 0, -8, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, -8, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, -8, 0, 0, 0, 8, 8, -8, 8, 0, }, +{c: 16, 0, 8, -8, -16, 8, 8, 0, 0, -8, 8, 0, -8, -8, 0, 0, }, +{7: 16, 0, -8, -8, 8, 8, -8, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 8, -8, 8, 0, 0, 0, -8, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 8, 8, 0, 0, -8, 0, 0, -8, 8, }, +{f: 16, 0, -8, -8, -8, 8, 8, 8, -8, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, x, x, }, +{2: , , x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , , x, x, x, x, x, , , x, x, x, x, x, x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , x, x, x, , x, x, x, x, x, x, }, +{a: , , , x, x, x, x, x, , x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , , x, , x, x, , , x, x, x, x, x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{1000,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0d,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_171.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_171.txt new file mode 100644 index 0000000..f6ec75e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_171.txt @@ -0,0 +1,412 @@ +171 Sbox: +LUT = { +0x04,0x00,0x01,0x0f,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 2, 6, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 4, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 2, 2, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, 2, 2, 2, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 6, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 4, 0, 0, }, +{e: 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:72, 4:15, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 2, 0, 0, 0, 6, 0, 6, 4, 6, 4, 4, 2, 0, }, +{2: 16, 0, 6, 2, 0, 0, 8, 0, 10, 0, 8, 4, 4, 0, 4, 2, }, +{4: 16, 0, 0, 4, 2, 6, 2, 2, 0, 0, 0, 6, 0, 0, 0, 2, }, +{8: 16, 0, 0, 2, 4, 4, 0, 0, 2, 0, 0, 2, 6, 0, 2, 2, }, +{3: 16, 2, 0, 6, 6, 6, 2, 0, 0, 0, 4, 4, 6, 0, 0, 4, }, +{5: 16, 2, 8, 0, 4, 0, 4, 2, 2, 4, 0, 4, 0, 0, 2, 0, }, +{6: 16, 6, 2, 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{9: 16, 0, 4, 0, 0, 2, 2, 0, 4, 2, 0, 0, 4, 2, 2, 2, }, +{a: 16, 4, 2, 0, 0, 0, 0, 2, 0, 4, 2, 0, 6, 2, 2, 0, }, +{c: 16, 6, 4, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 6, 4, 6, }, +{7: 16, 4, 4, 6, 0, 6, 4, 6, 0, 0, 0, 6, 2, 2, 0, 0, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 6, 0, 0, 0, 0, 4, 2, 4, 0, 10, 0, 2, 4, 0, 0, }, +{e: 16, 0, 10, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 2, 4, 0, }, +{f: 16, 0, 0, 2, 0, 6, 4, 0, 6, 0, 8, 0, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:46, 4:39, 6:28, 8:6, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{a: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -8, -8, 8, -8, 8, 0, -8, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, 8, -8, 8, -8, 8, 0, 0, -8, -8, 8, -16, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, 0, 0, 0, -8, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 8, 8, 8, -8, -8, -8, 0, 0, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, 0, 8, -16, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, 8, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 8, }, +{a: 16, 8, -8, 0, -8, -8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, -8, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 0, 0, -8, -8, 0, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -16, 8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, -8, 8, 0, -8, -8, -8, 0, 8, -8, 0, 0, 0, 0, 8, 0, }, +{e: 16, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 8, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , x, x, x, x, x, , x, x, x, x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0101,1,}, +{1000,1011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x01,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x07,0x09,0x0e,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x0f,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +171 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 2, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, }, +{3: 0, 0, 0, 2, 0, 6, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 4, 0, 2, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 2, 0, 4, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 6, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 4, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, }, +}; +Diff: 6, DDT_spectrum: {0:162, 2:72, 4:15, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:4, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 2, 6, 0, 4, 6, 4, 4, 6, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 8, 2, 4, 2, 4, 4, 8, 0, 10, 0, }, +{4: 16, 2, 2, 4, 2, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, }, +{8: 16, 0, 0, 2, 4, 6, 4, 0, 0, 0, 2, 0, 10, 0, 4, 0, }, +{3: 16, 0, 0, 6, 4, 6, 0, 2, 2, 0, 4, 6, 4, 0, 0, 6, }, +{5: 16, 0, 8, 2, 0, 2, 4, 0, 2, 0, 0, 4, 0, 4, 2, 4, }, +{6: 16, 6, 0, 2, 0, 0, 2, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{9: 16, 0, 10, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 4, 0, 6, }, +{a: 16, 6, 0, 0, 0, 0, 4, 2, 2, 4, 0, 0, 8, 0, 6, 0, }, +{c: 16, 4, 8, 0, 0, 4, 0, 0, 0, 2, 6, 0, 2, 10, 4, 8, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 6, 0, 0, 4, 6, 0, 2, 6, 2, 0, 0, }, +{d: 16, 4, 0, 0, 0, 0, 0, 2, 2, 2, 6, 2, 0, 4, 2, 0, }, +{e: 16, 2, 4, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 2, }, +{f: 16, 0, 2, 2, 2, 4, 0, 0, 2, 0, 6, 0, 2, 0, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:46, 4:39, 6:28, 8:6, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 8, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, -8, 0, 8, 0, -8, -8, 8, 0, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 0, 0, 0, 0, -8, 8, -8, 0, }, +{4: 16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, -8, 0, -8, -8, -8, }, +{8: 16, 8, 0, 0, -8, 8, -8, 0, -8, 0, 0, 8, 0, 0, -8, -8, }, +{3: 16, -8, -8, 0, 8, 8, -8, 0, 0, -8, 0, 0, 8, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, }, +{9: 16, -8, 8, 0, -8, -8, 8, 0, 8, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, -8, 0, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -16, 8, 0, -8, 0, 0, 8, -8, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, -8, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, -8, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , , x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{1000,1100,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x09,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,}}, +{{0x03,0x08,}, {0x02,0x05,0x07,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_172.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_172.txt new file mode 100644 index 0000000..5e5347d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_172.txt @@ -0,0 +1,424 @@ +172 Sbox: +LUT = { +0x08,0x0e,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x00,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 0, 2, 4, 0, 0, }, +{6: 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 6, 2, 0, 2, 0, 0, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 4, 0, 0, 0, }, +{d: 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, }, +{e: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 8, 0, 4, 4, 4, 8, 10, 0, 2, }, +{2: 16, 0, 10, 4, 4, 0, 2, 4, 2, 4, 8, 0, 0, 0, 10, 0, }, +{4: 16, 0, 4, 4, 2, 0, 2, 8, 0, 2, 0, 2, 4, 4, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 0, 2, 2, 4, 2, 2, 2, 0, 0, 2, }, +{3: 16, 0, 0, 2, 0, 6, 8, 4, 4, 10, 4, 0, 0, 2, 0, 8, }, +{5: 16, 0, 0, 2, 0, 4, 4, 10, 2, 0, 0, 0, 6, 4, 0, 0, }, +{6: 16, 4, 6, 6, 0, 4, 4, 6, 2, 0, 0, 6, 0, 0, 2, 0, }, +{9: 16, 2, 0, 0, 2, 4, 4, 0, 4, 8, 0, 2, 0, 0, 2, 4, }, +{a: 16, 4, 6, 0, 4, 6, 4, 0, 4, 10, 0, 0, 6, 0, 0, 4, }, +{c: 16, 6, 4, 2, 0, 6, 0, 0, 0, 0, 6, 2, 0, 6, 4, 4, }, +{7: 16, 6, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 4, 0, 2, 2, 2, 2, 2, 0, 4, 2, 0, 4, 0, 0, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 2, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:46, 4:47, 6:19, 8:8, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, 0, 0, 8, 0, -8, -16, 8, 0, }, +{2: 16, 8, 0, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 16, -8, 0, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, -8, 0, 0, 8, 0, -8, 0, 0, 8, 0, 8, -16, -8, 8, }, +{5: 16, -8, 8, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, 0, 0, 0, }, +{6: 16, 8, -8, -8, 8, -8, -8, 8, 8, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, 0, 8, -8, 0, -8, -8, 8, 0, 0, 0, }, +{a: 16, 0, -8, 8, 0, -8, 8, -16, -8, 8, -8, 0, 0, 0, 0, 8, }, +{c: 16, 0, 8, -8, 0, 8, -8, -8, -8, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , x, x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , x, , , , , x, , x, x, x, , , x, x, }, +{b: , x, , , x, x, , x, , x, x, , x, , x, x, }, +{d: , , , x, x, x, , x, , x, x, , , x, x, x, }, +{e: , , x, x, x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,1101,1,}, +{0110,1010,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x0d,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x04,0x09,0x0d,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0d,0x0a,}, {0x03,0x05,0x06,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +172 Inverse Sbox: +LUT = { +0x0e,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x01,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 4, 0, 0, 2, 0, 2, 6, 0, 0, 0, 0, 2, 0, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 0, 4, 6, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 0, 0, 4, 2, 4, 6, 6, 4, 6, 2, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 0, 6, 4, 0, 0, 4, 6, 4, }, +{4: 16, 0, 4, 4, 0, 2, 2, 6, 0, 0, 2, 2, 2, 0, 0, 0, }, +{8: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{3: 16, 2, 0, 0, 0, 6, 4, 4, 4, 6, 6, 0, 2, 0, 0, 6, }, +{5: 16, 0, 2, 2, 0, 8, 4, 4, 4, 4, 0, 0, 2, 2, 0, 0, }, +{6: 16, 8, 4, 8, 2, 4, 10, 6, 0, 0, 0, 4, 2, 0, 0, 0, }, +{9: 16, 0, 2, 0, 2, 4, 2, 2, 4, 4, 0, 2, 0, 0, 2, 0, }, +{a: 16, 4, 4, 2, 4, 10, 0, 0, 8, 10, 0, 0, 4, 2, 0, 0, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 8, 4, 10, }, +{7: 16, 4, 0, 2, 2, 0, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{d: 16, 10, 0, 4, 0, 2, 4, 0, 0, 0, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 0, 0, 2, 8, 0, 0, 4, 4, 4, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:46, 4:47, 6:19, 8:8, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 4, 0, 4, 4, 12, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, -8, 8, -8, 0, 8, -8, 0, 0, 8, -8, }, +{2: 16, 8, -8, 0, 0, -16, 8, -8, 8, -8, 8, 0, 0, 0, 0, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, -8, 8, 0, 8, -8, -8, -8, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 8, -8, -8, 8, 0, 0, -8, 8, -16, -8, 8, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 0, -8, 0, 0, -8, -8, 16, -8, 0, 8, }, +{c: 16, 8, 0, 0, -8, 8, 0, -8, 0, -8, 8, -8, -16, 8, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, -8, 8, -8, 0, -8, 0, -8, -8, 0, 8, 8, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, -8, 0, 0, 8, 0, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, , x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , x, x, x, , , , x, , x, x, x, , , x, x, }, +{b: , x, x, , , , , x, , x, x, , x, , x, x, }, +{d: , x, , , x, , , x, , x, x, , , x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1011,0110,1,}, +{1011,1010,0,}, +{1011,1100,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x0b,}}, +{{0x09,0x0a,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x09,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x0b,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0a,}, {0x0b,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_173.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_173.txt new file mode 100644 index 0000000..a576c48 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_173.txt @@ -0,0 +1,424 @@ +173 Sbox: +LUT = { +0x08,0x0f,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x00, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 2, }, +{7: 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 6, 0, 4, 4, 6, 4, 6, 2, 0, }, +{2: 16, 0, 10, 0, 0, 0, 6, 0, 6, 0, 4, 4, 4, 4, 6, 4, }, +{4: 16, 0, 0, 4, 6, 8, 2, 0, 0, 2, 0, 6, 4, 0, 0, 0, }, +{8: 16, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 6, 0, 0, 2, }, +{3: 16, 0, 0, 6, 4, 6, 0, 0, 0, 2, 6, 4, 4, 0, 2, 6, }, +{5: 16, 0, 4, 2, 0, 0, 4, 2, 2, 2, 2, 4, 0, 2, 0, 0, }, +{6: 16, 4, 2, 0, 2, 0, 0, 4, 2, 2, 0, 6, 0, 0, 2, 0, }, +{9: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 8, 2, 6, 0, 0, 4, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{c: 16, 4, 8, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 8, 4, 10, }, +{7: 16, 10, 4, 8, 0, 4, 8, 4, 2, 0, 0, 6, 0, 0, 0, 2, }, +{b: 16, 4, 4, 0, 10, 8, 2, 2, 4, 4, 0, 0, 10, 0, 0, 0, }, +{d: 16, 8, 0, 4, 0, 2, 6, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 0, 0, 4, 10, 0, 0, 0, 0, 6, 0, 4, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:41, 4:42, 6:24, 8:8, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 4, 0, 4, 4, 12, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{5: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, 0, -16, 8, -8, 8, -8, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, -8, 0, 0, 8, -8, -8, -8, 0, 8, 0, 8, -8, -8, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, -8, 0, 8, 0, -8, 0, -8, 8, -16, -8, 8, 0, 0, }, +{7: 16, -8, 0, -8, 8, 8, 0, 8, 0, 0, -8, -16, 8, 0, 0, -8, }, +{b: 16, -8, -8, 8, 0, 8, -8, -8, 0, 0, -8, 16, -8, 0, 0, 0, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 8, -8, 0, 8, 0, -8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{7: , x, x, , , x, x, x, x, x, x, , x, x, x, x, }, +{b: , , , , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, x, , x, x, x, x, x, x, x, , x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0110,1010,1,}, +{0111,0111,1,}, +{0111,1011,0,}, +{0111,1100,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x01,0x0a,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x02,0x05,0x07,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +173 Inverse Sbox: +LUT = { +0x0f,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x01, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 2, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 0, }, +{d: 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:11, 2:1, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 0, 0, 4, 2, 8, 4, 10, 4, 8, 0, 2, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 4, 2, 8, 4, 4, 0, 10, 0, }, +{4: 16, 0, 0, 4, 0, 6, 2, 0, 0, 6, 2, 8, 0, 4, 0, 0, }, +{8: 16, 0, 0, 6, 4, 4, 0, 2, 2, 0, 0, 0, 10, 0, 0, 4, }, +{3: 16, 2, 0, 8, 4, 6, 0, 0, 0, 0, 4, 4, 8, 2, 0, 10, }, +{5: 16, 0, 6, 2, 0, 0, 4, 0, 0, 4, 0, 8, 2, 6, 0, 0, }, +{6: 16, 6, 0, 0, 2, 0, 2, 4, 2, 0, 0, 4, 2, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, 2, 4, 0, 2, 0, }, +{a: 16, 4, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 4, 4, 0, 2, 6, 2, 0, 0, 0, 6, 0, 0, 6, 4, 6, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 4, 4, 6, 4, 0, 0, 6, 6, 0, 0, 10, 0, 0, 4, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 2, 6, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:103, 2:41, 4:42, 6:24, 8:8, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{2: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:6, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 8, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -16, -8, 8, 0, 8, -8, -8, 0, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, -8, -8, 8, 0, -8, 0, 0, 8, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 8, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, x, , x, x, x, x, x, x, , x, x, x, x, }, +{b: , , x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , , x, x, x, x, x, x, x, x, x, , x, x, }, +{e: , , x, , x, , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0011,1101,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x03,0x05,0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x02,0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_174.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_174.txt new file mode 100644 index 0000000..7ab8173 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_174.txt @@ -0,0 +1,424 @@ +174 Sbox: +LUT = { +0x04,0x00,0x01,0x0d,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{4: 0, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 2, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 4, 0, 0, 0, }, +{6: 0, 0, 2, 0, 2, 4, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 0, 2, 0, 0, 6, 4, 0, 2, 0, 2, 0, 0, }, +{a: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 2, }, +{c: 0, 2, 2, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, }, +{7: 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{d: 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 8, 0, 4, 0, 4, 2, 10, 2, 0, 4, 0, 0, }, +{2: 16, 0, 6, 2, 0, 0, 6, 0, 6, 0, 4, 6, 4, 2, 4, 0, }, +{4: 16, 6, 0, 4, 0, 0, 6, 2, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 16, 4, 0, 0, 4, 0, 0, 2, 6, 0, 0, 2, 2, 2, 2, 0, }, +{3: 16, 2, 0, 0, 2, 6, 6, 6, 6, 4, 4, 0, 0, 0, 0, 4, }, +{5: 16, 6, 6, 4, 0, 4, 10, 6, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 2, 0, 2, 8, 4, 4, 4, 4, 0, 2, 0, 2, 0, 0, }, +{9: 16, 4, 4, 0, 4, 10, 0, 0, 10, 8, 0, 2, 4, 2, 0, 0, }, +{a: 16, 0, 2, 2, 0, 4, 0, 0, 4, 4, 2, 0, 2, 0, 2, 2, }, +{c: 16, 6, 6, 4, 4, 4, 0, 0, 0, 0, 10, 0, 0, 4, 4, 6, }, +{7: 16, 0, 6, 2, 0, 2, 4, 2, 0, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 4, 0, 4, 4, 2, 0, 2, 0, 0, 8, 0, 2, 4, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 2, 0, 2, 0, 8, 0, 0, 4, 4, 4, 0, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:48, 4:51, 6:19, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 0, 4, 4, 12, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, }, +{f: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:9, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, 0, -8, 0, -8, 8, 0, -16, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, 8, -8, 8, -8, 8, -8, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 0, 8, -8, -8, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, 0, -8, -8, 8, 0, 0, 0, -8, }, +{3: 16, -8, 0, 8, 8, 0, -8, 0, -8, -8, 0, 8, 0, -8, -8, 8, }, +{5: 16, -8, 0, 0, 8, -8, 0, -8, 0, 8, -8, 8, -16, 8, 0, 0, }, +{6: 16, 0, -8, 0, 8, 0, 0, 0, 0, -16, 0, 8, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -8, -8, 0, 0, 0, -8, -8, -8, 16, 0, 0, 8, }, +{a: 16, 8, -8, 0, -8, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 8, 8, 0, -8, 8, 0, 0, -8, -8, 8, -8, -16, 0, 0, 0, }, +{7: 16, 0, -8, -8, 8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, -8, 0, -8, 8, 8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, -8, 8, 0, 8, 0, 0, -8, 0, }, +{f: 16, -8, 0, 0, -8, 0, -8, 8, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , , x, x, }, +{7: , , x, x, x, x, x, , x, , x, x, , x, , x, }, +{b: , x, x, , , , x, , x, , x, , x, x, , x, }, +{d: , x, , x, x, x, x, , x, , x, , , , , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0111,0001,1,}, +{1000,1011,1,}, +{1010,0110,1,}, +{1011,0101,1,}, +{1011,1001,0,}, +{1011,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x09,0x0a,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0a,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x09,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +174 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, }, +{4: 0, 4, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 4, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 2, 0, 2, 0, 0, 0, 0, 4, 4, 0, 0, 2, 0, 2, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, }, +{7: 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 4, 2, 6, 0, 4, 0, 6, 0, 0, 4, 0, 2, }, +{2: 16, 0, 6, 0, 0, 0, 6, 2, 4, 2, 6, 6, 4, 0, 4, 0, }, +{4: 16, 8, 2, 4, 0, 0, 4, 0, 0, 2, 4, 2, 0, 4, 0, 2, }, +{8: 16, 8, 0, 0, 4, 2, 0, 2, 4, 0, 4, 0, 2, 4, 2, 0, }, +{3: 16, 0, 0, 0, 0, 6, 4, 8, 10, 4, 4, 2, 0, 2, 0, 8, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 0, 2, 2, 6, 6, 4, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 4, 6, 0, 6, 6, 0, 4, 10, 4, 0, 0, 4, 0, 0, 4, }, +{a: 16, 2, 0, 2, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 2, 4, }, +{c: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{7: 16, 2, 6, 2, 2, 0, 4, 2, 2, 0, 0, 4, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 4, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 4, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 0, 2, 0, 4, 0, 0, 0, 2, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:48, 4:51, 6:19, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:9, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, -8, 8, 8, -8, -8, -8, 0, 0, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 0, -8, 0, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, -16, 0, -8, 0, -8, }, +{8: 16, 8, 0, 0, -8, 8, -8, 0, -8, -8, 0, 8, -8, 0, 0, 0, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, 0, -16, 0, 8, 8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 8, 0, 0, 0, 0, -8, -8, 8, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, -8, 0, -8, 0, 0, -16, 8, }, +{a: 16, 0, 0, 8, -8, -8, -8, 0, 0, 8, -8, -8, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 16, 0, }, +{7: 16, 0, 0, 0, 8, 0, 0, 8, 0, -8, -8, -8, 0, 0, 0, -8, }, +{b: 16, -8, 0, 0, -8, 0, 8, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, -8, 8, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, , x, , x, , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, x, , , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0111,0100,1,}, +{1000,1110,1,}, +{1010,0011,1,}, +{1110,0101,1,}, +{1110,1001,1,}, +{1110,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,0x09,0x0e,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x07,0x08,0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_175.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_175.txt new file mode 100644 index 0000000..a9ff3ec --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_175.txt @@ -0,0 +1,424 @@ +175 Sbox: +LUT = { +0x08,0x00,0x01,0x0d,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x02,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 4, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 4, 0, 2, 0, 0, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 6, 0, 4, 2, 4, 0, 6, 0, 0, 6, 2, 0, }, +{2: 16, 0, 10, 0, 0, 0, 6, 0, 6, 0, 4, 4, 4, 4, 6, 4, }, +{4: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{8: 16, 4, 0, 0, 4, 0, 0, 2, 6, 0, 2, 2, 2, 0, 0, 2, }, +{3: 16, 2, 0, 2, 0, 6, 6, 4, 4, 4, 6, 0, 0, 0, 0, 6, }, +{5: 16, 4, 4, 4, 0, 10, 10, 8, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 0, 2, 0, 2, 4, 4, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 16, 8, 4, 2, 4, 4, 0, 0, 6, 10, 0, 2, 8, 0, 0, 0, }, +{a: 16, 0, 2, 2, 0, 8, 4, 4, 4, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 4, 8, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 8, 4, 10, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 10, 0, 0, 0, 2, 0, 0, 0, 4, 6, 0, 4, 4, 2, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 0, 0, 2, 8, 4, 4, 0, 0, 4, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:46, 4:47, 6:19, 8:8, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{3: 0, 4, 0, 4, 4, 12, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{5: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, -8, 8, -8, 0, 8, 0, -8, -8, 8, -8, }, +{2: 16, 0, 0, 0, 0, -16, 8, -8, 8, -8, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, -8, 0, -8, 8, -8, 0, -8, 0, 0, -8, 16, -8, 0, 0, 8, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, 0, -8, -8, 8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, -8, 0, 8, 0, -8, 0, -8, 8, -16, -8, 8, 0, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, -8, 0, 8, 0, 8, -8, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, -8, 0, 0, 8, 0, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, , x, x, x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , , x, x, }, +{7: , x, x, , , , x, , x, , x, x, , x, , x, }, +{b: , , , , x, x, x, , x, , x, , x, x, , x, }, +{d: , x, , x, x, x, x, , x, , x, , , , , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0110,1010,1,}, +{0111,0101,0,}, +{0111,1001,1,}, +{0111,1100,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x09,0x0a,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x07,0x08,0x0f,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +175 Inverse Sbox: +LUT = { +0x01,0x02,0x0d,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 4, 0, 0, }, +{c: 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 6, 0, 2, 2, 0, 0, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 4, 2, 4, 0, 8, 0, 4, 0, 0, 10, 0, 2, }, +{2: 16, 0, 10, 0, 0, 0, 4, 2, 4, 2, 8, 4, 4, 0, 10, 0, }, +{4: 16, 4, 0, 4, 0, 2, 4, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{8: 16, 6, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 16, 0, 0, 0, 0, 6, 10, 4, 4, 8, 4, 0, 2, 2, 0, 8, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 4, 0, 4, 0, 0, 0, 4, }, +{6: 16, 2, 0, 0, 2, 4, 8, 4, 0, 4, 0, 2, 0, 0, 2, 4, }, +{9: 16, 4, 6, 0, 6, 4, 0, 2, 6, 4, 0, 0, 6, 0, 2, 0, }, +{a: 16, 0, 0, 6, 0, 4, 0, 2, 10, 4, 0, 0, 2, 4, 0, 0, }, +{c: 16, 6, 4, 0, 2, 6, 0, 0, 0, 0, 6, 0, 2, 6, 4, 4, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 4, 2, 0, 2, 0, 8, 2, 0, 2, 4, 4, 0, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:46, 4:47, 6:19, 8:8, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{2: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:5, 4:6, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 0, -8, -8, 8, 0, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, -16, -8, 0, 0, 8, 0, -8, 0, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -8, 8, -16, -8, 8, -8, 0, 0, 0, -8, 8, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, -8, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 8, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 8, 0, -8, 8, -8, -8, -8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , x, x, x, }, +{7: , , x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , , , x, x, x, , x, , x, , , , , x, }, +{e: , , x, , x, , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0011,1101,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x01,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x03,0x05,0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x02,0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_176.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_176.txt new file mode 100644 index 0000000..3c3cf6b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_176.txt @@ -0,0 +1,424 @@ +176 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, }, +{4: 0, 2, 0, 6, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 4, 0, 2, 4, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 4, 2, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 6, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:2, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 8, 2, 8, 0, 4, 0, 4, 0, 0, 10, 0, 2, }, +{2: 16, 0, 10, 4, 0, 0, 2, 4, 10, 0, 0, 0, 8, 4, 2, 4, }, +{4: 16, 6, 4, 6, 0, 4, 6, 4, 0, 0, 2, 6, 2, 0, 0, 0, }, +{8: 16, 6, 4, 0, 4, 0, 0, 2, 8, 0, 2, 0, 6, 0, 0, 0, }, +{3: 16, 2, 0, 10, 0, 8, 0, 0, 4, 6, 0, 8, 0, 4, 4, 2, }, +{5: 16, 4, 0, 8, 0, 2, 4, 2, 2, 4, 2, 0, 0, 0, 4, 0, }, +{6: 16, 0, 6, 8, 0, 0, 0, 4, 0, 6, 0, 2, 0, 0, 4, 2, }, +{9: 16, 6, 4, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 6, 0, 0, 4, 2, 0, 8, 6, 0, 0, 4, 2, 0, 0, }, +{c: 16, 4, 4, 0, 4, 0, 6, 0, 0, 4, 4, 6, 0, 10, 0, 6, }, +{7: 16, 2, 0, 4, 0, 4, 0, 2, 0, 0, 0, 4, 2, 2, 2, 2, }, +{b: 16, 0, 4, 0, 2, 2, 0, 2, 4, 2, 2, 0, 6, 0, 0, 0, }, +{d: 16, 4, 0, 0, 6, 0, 4, 0, 0, 2, 6, 0, 0, 8, 2, 0, }, +{e: 16, 0, 6, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 2, 4, }, +{f: 16, 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 4, 0, 4, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:44, 4:43, 6:23, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{c: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, 0, 8, -8, 0, 8, 0, -8, -16, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 16, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 8, -8, -8, 0, 0, 0, -8, }, +{8: 16, 0, 8, 8, -8, 0, -8, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, -8, 8, 0, 0, 0, -8, -8, 8, 0, -8, 8, -16, 0, 8, }, +{5: 16, 0, 8, -8, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, -8, 8, }, +{6: 16, 8, -16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, -8, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, -8, -8, 8, 0, 0, 0, -16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{c: 16, -8, 8, -16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{b: 16, 8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{d: 16, 0, 8, -8, -8, -8, 8, -8, -8, 0, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, 0, 0, 8, 8, 0, 0, -8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 8, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, , x, x, , , , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, , , x, x, , , x, x, }, +{9: , x, x, x, , x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, , x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, , , x, , , , x, x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , , x, x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0110,1,}, +{0100,1100,1,}, +{0110,1010,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x01,0x02,0x03,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +176 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x0c,0x06,0x07,0x00,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{8: 0, 4, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 2, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 6, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, }, +{b: 0, 0, 4, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:2, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 6, 2, 4, 0, 6, 0, 4, 2, 0, 4, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 4, 4, 6, 0, 10, 8, 8, 2, 0, 0, 4, 0, 0, 2, 0, }, +{8: 16, 8, 0, 0, 4, 0, 0, 0, 6, 0, 4, 0, 2, 6, 0, 2, }, +{3: 16, 2, 0, 4, 0, 8, 2, 0, 4, 4, 0, 4, 2, 0, 0, 2, }, +{5: 16, 8, 2, 6, 0, 0, 4, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{6: 16, 0, 4, 4, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 2, }, +{9: 16, 4, 10, 0, 8, 4, 2, 0, 6, 8, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 0, 0, 0, 6, 4, 6, 6, 6, 4, 0, 2, 2, 0, 4, }, +{c: 16, 4, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 6, 0, 2, }, +{7: 16, 0, 0, 6, 0, 8, 0, 2, 0, 0, 6, 4, 0, 0, 2, 4, }, +{b: 16, 0, 8, 2, 6, 0, 0, 0, 4, 4, 0, 2, 6, 0, 0, 0, }, +{d: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{e: 16, 0, 2, 0, 0, 4, 4, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 16, 2, 4, 0, 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:44, 4:43, 6:23, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -8, 8, -8, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 8, -8, 8, 0, -8, -8, 0, 8, -8, 0, 8, 0, -16, 0, }, +{8: 16, -8, 8, 8, -8, 0, 0, 8, 0, 0, 0, 0, -8, -8, 0, -8, }, +{3: 16, -8, -8, 8, 0, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 8, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 0, 0, 0, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, 0, 8, 0, -8, -8, 0, 0, 8, -16, 0, }, +{a: 16, -8, -8, 8, 0, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{7: 16, 0, -8, -16, 0, 8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, 8, -8, 8, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, -8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 16, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, , , x, , , , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, x, , , , x, , , x, x, x, }, +{7: , x, , , , , x, , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , x, x, x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0010,1,}, +{0100,0111,1,}, +{0110,0101,1,}, +{1110,0100,1,}, +{1110,1001,1,}, +{1110,1101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_177.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_177.txt new file mode 100644 index 0000000..5c878e7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_177.txt @@ -0,0 +1,424 @@ +177 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x0e,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x07,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 0, 4, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 2, 0, 0, 2, 0, 2, }, +{6: 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 4, 0, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 2, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 6, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 0, 6, 2, 0, 10, 4, 0, 0, 8, 0, 2, 4, 4, }, +{2: 16, 0, 10, 4, 0, 0, 2, 4, 10, 0, 0, 0, 8, 4, 2, 4, }, +{4: 16, 0, 4, 4, 2, 0, 2, 4, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 16, 4, 4, 0, 6, 0, 0, 0, 8, 0, 2, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 6, 8, 4, 4, 8, 4, 0, 0, 2, 0, 10, }, +{5: 16, 0, 0, 2, 0, 6, 4, 4, 2, 0, 2, 0, 0, 2, 0, 2, }, +{6: 16, 4, 6, 4, 4, 6, 4, 10, 0, 0, 0, 6, 0, 0, 4, 0, }, +{9: 16, 6, 4, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 6, 2, 0, 6, 2, 0, 8, 4, 0, 0, 4, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 4, 2, 2, 0, 0, 4, 2, 0, 4, 0, 8, }, +{7: 16, 6, 0, 2, 4, 0, 0, 8, 0, 0, 0, 4, 2, 0, 6, 0, }, +{b: 16, 0, 4, 0, 2, 2, 0, 2, 4, 2, 2, 0, 6, 0, 0, 0, }, +{d: 16, 2, 0, 2, 0, 0, 4, 0, 0, 6, 2, 0, 0, 2, 2, 4, }, +{e: 16, 0, 6, 0, 4, 0, 4, 0, 2, 4, 0, 6, 0, 6, 2, 6, }, +{f: 16, 0, 0, 0, 6, 4, 0, 0, 0, 2, 6, 4, 0, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:43, 4:42, 6:24, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 0, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{c: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, 0, 8, -8, -8, 0, 8, -8, -16, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 16, -8, -8, }, +{4: 16, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{8: 16, -8, 8, 8, -8, 0, -8, 8, 0, 0, 0, -8, -8, 0, 0, 0, }, +{3: 16, -8, -8, 8, 0, 0, 0, -8, -8, 0, 8, 0, 8, -16, 0, 8, }, +{5: 16, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, -8, 8, }, +{6: 16, 8, -16, -8, 8, -8, -8, 8, 0, -8, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, -8, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, 0, 0, 0, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, -8, 8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{b: 16, 8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, }, +{d: 16, 0, 8, -8, 0, -8, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, -8, -8, -8, -8, 0, 8, 8, 8, 0, 8, -8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 8, 8, -8, 0, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, x, x, , , x, x, , x, , x, x, }, +{5: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{6: , x, , x, x, x, x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, , x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, x, x, x, , , x, }, +{c: , x, x, , x, x, x, , , x, x, x, , x, , x, }, +{7: , x, , x, , x, x, , , x, x, , , , x, x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , , x, , x, , , x, x, x, , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0110,1,}, +{0100,1100,1,}, +{0110,1010,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x01,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x0d,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x0d,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x01,0x02,0x03,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +177 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x0e,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x07,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 0, 6, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 2, 4, 2, 0, 0, 0, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, }, +{b: 0, 0, 4, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 6, 4, }, +}; +Diff: 6, DDT_spectrum: {0:165, 2:66, 4:18, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 0, 4, 2, 0, 4, 6, 0, 0, 6, 0, 2, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 0, 4, 4, 0, 0, 2, 4, 2, 2, 2, 2, 0, 2, 0, 0, }, +{8: 16, 6, 0, 2, 6, 0, 0, 4, 6, 0, 0, 4, 2, 0, 4, 6, }, +{3: 16, 2, 0, 0, 0, 6, 6, 6, 4, 6, 4, 0, 2, 0, 0, 4, }, +{5: 16, 0, 2, 2, 0, 8, 4, 4, 0, 2, 2, 0, 0, 4, 4, 0, }, +{6: 16, 10, 4, 4, 0, 4, 4, 10, 0, 0, 2, 8, 2, 0, 0, 0, }, +{9: 16, 4, 10, 0, 8, 4, 2, 0, 6, 8, 0, 0, 4, 0, 2, 0, }, +{a: 16, 0, 0, 0, 0, 8, 0, 0, 6, 4, 0, 0, 2, 6, 4, 2, }, +{c: 16, 0, 0, 2, 2, 4, 2, 0, 0, 0, 4, 0, 2, 2, 0, 6, }, +{7: 16, 8, 0, 2, 0, 0, 0, 6, 0, 0, 2, 4, 0, 0, 6, 4, }, +{b: 16, 0, 8, 2, 6, 0, 0, 0, 4, 4, 0, 2, 6, 0, 0, 0, }, +{d: 16, 2, 4, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{e: 16, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, 6, 0, 2, 2, 2, }, +{f: 16, 4, 4, 0, 2, 10, 2, 0, 0, 0, 8, 0, 0, 4, 6, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:43, 4:42, 6:24, 8:10, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 8, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{7: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, 0, 8, -8, -8, 0, 0, 0, -8, 0, -8, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, -8, 8, 8, 0, 0, -8, 8, 0, 8, 0, -8, -8, -8, 0, -8, }, +{3: 16, -8, -8, 8, 8, 0, -8, -8, -8, 0, 0, 8, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 8, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 8, 0, -8, 8, 0, -8, -8, 0, -8, 0, 16, 0, }, +{9: 16, 0, 8, 8, -8, -8, 0, 8, 0, -8, -8, 0, 0, 8, -16, 0, }, +{a: 16, -8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{7: 16, 0, -8, -16, 0, 8, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{b: 16, 8, -8, 8, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 8, -8, 8, 8, 8, 0, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{5: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{6: , x, , x, x, x, x, x, , x, x, x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, x, x, x, , , x, }, +{c: , x, x, x, x, , x, , , x, x, x, , x, , x, }, +{7: , x, , , , x, x, , , x, x, , , , x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , x, x, , x, , , x, x, x, , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0010,1,}, +{0100,0111,1,}, +{0110,0101,1,}, +{1110,0110,0,}, +{1110,1001,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_178.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_178.txt new file mode 100644 index 0000000..d9b4688 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_178.txt @@ -0,0 +1,424 @@ +178 Sbox: +LUT = { +0x04,0x08,0x0e,0x02,0x03,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x01,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 0, 4, 0, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 0, 4, 0, }, +{c: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, }, +{d: 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:164, 2:69, 4:15, 6:7, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 0, 0, 10, 2, 8, 8, 4, 4, 4, 2, 0, }, +{2: 16, 0, 10, 8, 8, 0, 2, 8, 0, 10, 8, 0, 0, 2, 8, 0, }, +{4: 16, 0, 4, 4, 2, 0, 2, 4, 0, 0, 2, 2, 2, 2, 0, 0, }, +{8: 16, 2, 4, 4, 4, 0, 0, 0, 2, 8, 0, 2, 0, 0, 4, 2, }, +{3: 16, 0, 0, 2, 0, 6, 4, 8, 4, 8, 10, 0, 2, 0, 0, 4, }, +{5: 16, 2, 0, 2, 0, 4, 4, 4, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 6, 6, 4, 0, 4, 4, 6, 0, 0, 0, 6, 0, 2, 0, 2, }, +{9: 16, 0, 4, 0, 4, 4, 2, 2, 4, 8, 0, 0, 0, 2, 2, 0, }, +{a: 16, 4, 6, 4, 4, 6, 0, 0, 4, 10, 0, 0, 6, 0, 4, 0, }, +{c: 16, 4, 4, 0, 2, 6, 2, 0, 0, 0, 6, 0, 0, 6, 4, 6, }, +{7: 16, 6, 0, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 4, 4, 2, 4, 0, 0, 0, 0, 8, 2, 2, 4, 0, 0, 2, }, +{d: 16, 6, 0, 2, 0, 2, 2, 0, 2, 2, 4, 0, 0, 4, 0, 0, }, +{e: 16, 0, 6, 0, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 4, 2, }, +{f: 16, 0, 0, 0, 2, 6, 0, 0, 2, 0, 4, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:54, 4:43, 6:17, 8:12, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 0, 4, 0, 4, 12, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, -16, 8, -8, 0, 8, -8, -8, 0, 8, 0, }, +{2: 16, 8, -8, 8, 0, -16, 16, -16, 0, 0, 0, -8, 0, 0, 0, 0, }, +{4: 16, 0, 8, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, -8, -8, -8, }, +{3: 16, 0, -8, 0, 8, 8, -16, -8, 0, -8, 0, 8, 0, -8, 0, 8, }, +{5: 16, -8, 8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 8, 8, -8, 0, 0, -8, -8, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, 8, 0, 0, -8, 0, }, +{a: 16, 8, -16, 8, -8, -8, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, -8, -8, 8, 0, -8, 0, 0, 8, }, +{7: 16, -8, -8, 0, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, }, +{b: 16, 0, -8, 0, 0, 8, 0, -8, 8, 0, 0, -8, -8, 8, 0, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{f: 16, -8, -8, 0, -8, 8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , , , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , , , x, , x, x, x, , , x, x, }, +{b: , , , , x, x, , x, , x, x, , x, , x, x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,1010,1,}, +{0011,0010,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x05,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x07,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x02,0x05,0x07,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x02,0x05,0x07,}}, +{{0x0d,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +178 Inverse Sbox: +LUT = { +0x08,0x0e,0x03,0x04,0x00,0x05,0x06,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x02,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, }, +{4: 0, 0, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{6: 0, 2, 0, 0, 0, 4, 0, 6, 2, 0, 0, 0, 0, 0, 2, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 2, }, +{a: 0, 0, 6, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 2, 0, 0, }, +{c: 0, 4, 0, 2, 0, 2, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, }, +{d: 0, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 4, 0, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:164, 2:69, 4:15, 6:7, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 2, 0, 2, 6, 0, 4, 4, 6, 4, 6, 0, 0, }, +{2: 16, 0, 10, 4, 4, 0, 0, 6, 4, 6, 4, 0, 4, 0, 6, 0, }, +{4: 16, 0, 8, 4, 4, 2, 2, 4, 0, 4, 0, 0, 2, 2, 0, 0, }, +{8: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 2, 2, 4, 0, 0, 2, }, +{3: 16, 0, 0, 0, 0, 6, 4, 4, 4, 6, 6, 2, 0, 2, 0, 6, }, +{5: 16, 0, 2, 2, 0, 4, 4, 4, 2, 0, 2, 0, 0, 2, 2, 0, }, +{6: 16, 10, 8, 4, 0, 8, 4, 6, 2, 0, 0, 4, 0, 0, 2, 0, }, +{9: 16, 2, 0, 0, 2, 4, 2, 0, 4, 4, 0, 0, 0, 2, 2, 2, }, +{a: 16, 8, 10, 0, 8, 8, 2, 0, 8, 10, 0, 0, 8, 2, 0, 0, }, +{c: 16, 8, 8, 2, 0, 10, 0, 0, 0, 0, 6, 0, 2, 4, 4, 4, }, +{7: 16, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 4, 0, 2, 0, 2, 2, 0, 0, 6, 0, 2, 4, 0, 0, 2, }, +{d: 16, 4, 2, 2, 0, 0, 2, 2, 2, 0, 6, 0, 0, 4, 0, 0, }, +{e: 16, 2, 8, 0, 4, 0, 0, 0, 2, 4, 4, 2, 0, 0, 4, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:54, 4:43, 6:17, 8:12, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 12, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{b: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, 0, 8, -8, 0, 0, 0, -8, -8, 8, -8, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 8, 0, -8, }, +{4: 16, 0, 8, 0, 0, 8, 0, -8, 0, 0, -8, 8, 0, -8, -8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{3: 16, -8, -8, 0, 0, 8, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, -16, 8, 0, -8, 0, 8, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, -8, 8, 0, -16, 16, -16, 0, 0, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 8, 0, 0, 8, -16, -8, -8, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, 0, 8, 0, -8, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 8, -8, 0, -8, 0, -8, 8, -8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 8, -8, 8, 0, -8, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, x, x, , x, , x, x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , , , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , x, , x, , , , x, , x, x, x, , , x, x, }, +{b: , , , , x, , , x, , x, x, , x, , x, x, }, +{d: , , x, , x, , , x, , x, x, , , x, x, x, }, +{e: , , , , x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0010,1,}, +{0011,1010,1,}, +{0101,0110,1,}, +{0101,1010,0,}, +{0101,1100,1,}, +{0110,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x05,}}, +{{0x01,0x0a,0x0c,}, {0x05,}}, +{{0x09,0x0a,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x06,0x08,}, {0x05,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x03,0x05,0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x03,0x05,0x06,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x05,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x03,0x05,0x06,}}, +{{0x0d,0x0a,}, {0x03,0x05,0x06,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_179.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_179.txt new file mode 100644 index 0000000..0e7b4b8 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_179.txt @@ -0,0 +1,412 @@ +179 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 8, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 2, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:164, 2:65, 4:24, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 6, 6, 0, 0, 6, 4, 0, 0, 4, 2, 2, 0, }, +{2: 16, 6, 8, 4, 0, 4, 6, 4, 6, 0, 4, 4, 4, 6, 4, 4, }, +{4: 16, 0, 4, 4, 2, 0, 2, 8, 0, 2, 0, 2, 4, 4, 0, 0, }, +{8: 16, 4, 4, 2, 4, 0, 0, 0, 8, 0, 2, 2, 4, 0, 0, 2, }, +{3: 16, 6, 4, 2, 0, 8, 0, 0, 0, 2, 4, 0, 0, 0, 0, 6, }, +{5: 16, 0, 6, 2, 0, 2, 4, 2, 2, 2, 0, 4, 0, 0, 0, 0, }, +{6: 16, 0, 6, 4, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, 0, }, +{9: 16, 6, 0, 2, 4, 0, 0, 2, 4, 2, 0, 2, 0, 0, 2, 0, }, +{a: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 16, 4, 4, 0, }, +{c: 16, 0, 4, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 4, 0, 10, }, +{7: 16, 2, 4, 0, 2, 0, 8, 2, 0, 0, 0, 4, 4, 0, 4, 2, }, +{b: 16, 4, 0, 2, 2, 2, 2, 2, 0, 4, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 6, 0, 0, 0, 6, 0, 0, 2, 4, 0, 4, 2, 8, 0, }, +{e: 16, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 10, 2, 4, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:45, 4:53, 6:18, 8:6, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:10, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +{2: 16, 0, 0, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 8, -8, -8, -8, 0, 8, -8, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, -8, 0, 0, 0, -8, 8, }, +{6: 16, 8, -8, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{a: 16, -8, 0, 0, -8, -8, 8, -16, 0, 8, -8, 8, 0, 0, 8, 0, }, +{c: 16, -8, 0, -8, 0, 8, 0, -8, 0, -8, 8, 0, 8, -8, 0, 0, }, +{7: 16, -8, -8, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, 0, 8, -8, }, +{b: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{d: 16, 8, 0, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 8, 0, 8, 0, -8, -8, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, , x, x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , , , , x, x, x, , , x, , , x, , , x, }, +{d: , x, , x, x, x, x, , , x, , , , x, , x, }, +{e: , x, x, x, x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{0110,1010,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x01,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +179 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x0a,0x06,0x07,0x00,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 4, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 0, 4, 0, }, +{9: 0, 2, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:164, 2:65, 4:24, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 0, 4, 6, 0, 0, 6, 4, 0, 2, 4, 0, 2, 0, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 0, 4, 4, 4, 0, 6, 6, 4, }, +{4: 16, 0, 4, 4, 2, 2, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, }, +{8: 16, 6, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 16, 6, 4, 0, 0, 8, 2, 0, 0, 0, 4, 0, 2, 0, 0, 6, }, +{5: 16, 0, 6, 2, 0, 0, 4, 0, 0, 4, 0, 8, 2, 6, 0, 0, }, +{6: 16, 0, 4, 8, 0, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{9: 16, 6, 6, 0, 8, 0, 2, 2, 4, 4, 0, 0, 0, 0, 0, 0, }, +{a: 16, 4, 0, 2, 0, 2, 2, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 4, 0, 10, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 4, 4, 4, 4, 0, 0, 0, 0, 16, 0, 4, 4, 4, 4, 0, }, +{d: 16, 2, 6, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 10, 0, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 4, 0, 4, 0, 8, 2, 4, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:45, 4:53, 6:18, 8:6, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 8, 4, 0, 0, 4, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:10, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 8, -8, 0, 8, -8, 0, 0, 0, -8, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{3: 16, -8, 0, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, 0, 0, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 0, -8, -8, 8, 0, 0, -8, 8, 0, 8, 0, 0, }, +{9: 16, 0, 8, 8, 0, -8, 0, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, -8, 0, 0, -8, 8, 0, -8, 0, -8, 8, 8, 0, -8, 0, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, }, +{b: 16, 0, -8, 0, 0, 8, 0, -8, 0, 8, -16, -8, 8, 0, 8, -8, }, +{d: 16, 8, 0, 0, -8, -8, 0, -8, -8, 0, 8, -8, 0, 0, 8, 0, }, +{e: 16, -8, 0, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , x, x, x, , , x, , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , x, , , x, , x, , , x, , , , x, , x, }, +{e: , x, x, , x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_180.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_180.txt new file mode 100644 index 0000000..a9662c8 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_180.txt @@ -0,0 +1,412 @@ +180 Sbox: +LUT = { +0x04,0x00,0x08,0x02,0x03,0x05,0x0b,0x07,0x01,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{4: 0, 0, 0, 4, 0, 2, 4, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 2, 2, 4, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 2, 6, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, }, +{5: 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{c: 0, 4, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 0, 2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{e: 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, }, +{f: 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:164, 2:65, 4:24, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:5, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 2, 4, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, }, +{2: 16, 4, 8, 0, 6, 4, 4, 0, 4, 4, 6, 4, 6, 4, 4, 6, }, +{4: 16, 0, 4, 4, 0, 6, 4, 0, 2, 0, 0, 10, 0, 2, 0, 0, }, +{8: 16, 0, 6, 2, 4, 0, 4, 0, 2, 8, 0, 0, 0, 0, 0, 6, }, +{3: 16, 4, 4, 6, 2, 6, 4, 6, 0, 0, 0, 6, 0, 0, 2, 0, }, +{5: 16, 2, 0, 0, 2, 6, 4, 4, 2, 0, 2, 0, 0, 0, 0, 2, }, +{6: 16, 0, 4, 0, 0, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 16, 2, 4, 2, 2, 0, 4, 0, 4, 0, 0, 0, 8, 2, 4, 0, }, +{a: 16, 0, 4, 0, 4, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{c: 16, 4, 6, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 8, 0, 4, }, +{7: 16, 2, 0, 4, 0, 6, 0, 0, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 16, 2, 6, 0, 0, 2, 0, 2, 4, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 4, 2, 0, 2, 4, 0, 2, 4, 0, 0, 0, 4, 2, 8, }, +{f: 16, 0, 6, 0, 0, 0, 4, 2, 0, 0, 4, 0, 6, 0, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:97, 2:47, 4:53, 6:18, 8:8, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{2: 0, 4, 12, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{4: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, -8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 0, 0, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, -8, 8, -8, 8, 0, 0, -8, 0, 0, -8, 0, 8, 0, -8, 0, }, +{8: 16, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, 0, -8, 0, -16, 0, }, +{3: 16, 0, -8, 0, 8, 8, -8, 0, -8, -8, 0, 8, 8, -8, -8, 0, }, +{5: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, }, +{6: 16, -8, -16, -8, 0, 8, 0, 8, 8, 0, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, 0, 0, -8, 0, 0, 0, -8, 8, 0, -8, -8, 8, -8, }, +{7: 16, -8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, 0, 0, -8, 0, -8, 0, -8, 8, 0, 8, 0, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, -8, 8, -8, -8, 8, }, +{f: 16, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, 8, -8, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, x, x, x, , , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , , , x, , x, , x, x, x, , x, x, , , x, }, +{b: , , x, , x, , , x, x, x, , , , , , x, }, +{d: , x, x, , x, x, , , , , , , , x, , x, }, +{e: , x, , x, x, , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0010,0110,1,}, +{1011,0010,1,}, +{1110,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x07,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x0b,}}, +{{0x09,0x02,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +180 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x00,0x05,0x0b,0x07,0x02,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 0, 0, 0, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{4: 0, 2, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{8: 0, 2, 2, 0, 4, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 2, 0, 6, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, }, +{5: 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{6: 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 4, 0, }, +{c: 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, }, +{7: 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{b: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 2, 4, }, +{f: 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:164, 2:65, 4:24, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:5, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 4, 2, 0, 2, 0, 4, 2, 2, 4, 0, 0, }, +{2: 16, 4, 8, 4, 6, 4, 0, 4, 4, 4, 6, 0, 6, 4, 4, 6, }, +{4: 16, 2, 0, 4, 2, 6, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, }, +{8: 16, 2, 6, 0, 4, 2, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, }, +{3: 16, 4, 4, 6, 0, 6, 6, 4, 0, 0, 0, 6, 2, 0, 2, 0, }, +{5: 16, 0, 4, 4, 4, 4, 4, 16, 4, 0, 0, 0, 0, 0, 4, 4, }, +{6: 16, 2, 0, 0, 0, 6, 4, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{9: 16, 0, 4, 2, 2, 0, 2, 0, 4, 2, 0, 0, 4, 2, 2, 0, }, +{a: 16, 2, 4, 0, 8, 0, 0, 4, 0, 4, 0, 2, 2, 2, 4, 0, }, +{c: 16, 4, 6, 0, 0, 0, 2, 0, 0, 0, 6, 0, 2, 8, 0, 4, }, +{7: 16, 0, 4, 10, 0, 6, 0, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{b: 16, 0, 6, 0, 0, 0, 0, 4, 8, 2, 0, 2, 4, 0, 0, 6, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 4, 0, 0, 2, 0, 4, 4, 2, 0, 2, 0, 4, 2, 8, }, +{f: 16, 0, 6, 0, 6, 0, 2, 4, 0, 0, 4, 0, 0, 0, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:97, 2:47, 4:53, 6:18, 8:8, 10:1, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{5: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 0, 4, 4, 4, 4, 8, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 12, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, -8, -8, 8, 8, 0, }, +{2: 16, 8, -8, 8, 0, 0, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, 0, 0, 0, 0, -8, -8, 0, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 0, 8, 8, -8, -8, -8, 0, 0, 8, 8, 0, -8, 0, }, +{5: 16, 0, 8, -8, 0, 8, 8, 0, 0, 8, -8, 0, -8, -8, -16, 0, }, +{6: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 8, 8, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, -8, 8, 0, 0, 8, 0, 8, -8, }, +{c: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 8, -8, }, +{7: 16, 0, -8, -8, 8, 0, 0, 0, 0, -8, -8, 0, 8, -8, 8, 0, }, +{b: 16, 0, -16, 0, 0, 0, 0, 0, 8, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, 0, 0, -8, 0, -8, 0, -8, 8, 0, 8, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 8, 0, 0, 0, -8, 8, 0, -8, 8, }, +{f: 16, 8, -8, -8, 0, -8, 0, 8, 0, 0, 0, 8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, x, , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{7: , x, x, x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , , x, x, , x, x, x, , , , , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, x, , , , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0010,1011,1,}, +{1011,0010,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x07,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x02,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_181.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_181.txt new file mode 100644 index 0000000..235bc20 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_181.txt @@ -0,0 +1,412 @@ +181 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x09,0x07,0x04,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 0, 4, 2, 2, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, 4, 0, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:164, 2:65, 4:24, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 4, 2, 6, 4, 6, 0, 0, 0, 4, 0, 0, 2, 0, }, +{2: 16, 4, 8, 0, 4, 4, 4, 0, 6, 6, 4, 4, 4, 6, 6, 4, }, +{4: 16, 4, 4, 4, 4, 0, 16, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{8: 16, 0, 4, 0, 4, 0, 0, 2, 2, 4, 2, 2, 2, 0, 0, 2, }, +{3: 16, 6, 4, 2, 0, 8, 0, 0, 0, 2, 4, 0, 0, 0, 0, 6, }, +{5: 16, 4, 0, 4, 0, 2, 4, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{6: 16, 6, 6, 0, 0, 0, 4, 4, 2, 2, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 4, 2, 2, 0, 4, 2, 4, 2, 0, 0, 8, 0, 4, 0, }, +{a: 16, 0, 6, 2, 8, 0, 4, 0, 0, 4, 0, 0, 2, 6, 0, 0, }, +{c: 16, 0, 4, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 4, 0, 10, }, +{7: 16, 6, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 2, 0, 2, 0, 2, 4, 2, 2, 2, 4, 0, 0, 0, }, +{d: 16, 2, 6, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 2, 10, 0, }, +{e: 16, 2, 4, 0, 4, 0, 4, 2, 2, 0, 0, 0, 0, 8, 2, 4, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:45, 4:53, 6:18, 8:6, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +{b: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{e: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:10, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -8, -8, 8, -8, 0, 8, 0, -8, -8, 0, -8, }, +{2: 16, 8, -8, 8, 0, -16, 8, -8, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 8, 0, -8, 0, 8, -16, 8, -8, 0, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, 0, 0, 0, 8, -8, -8, -8, 0, 8, -8, 0, -8, 0, 8, }, +{5: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, -8, 0, 0, 8, 0, }, +{9: 16, 8, 0, 0, -8, -8, -8, 8, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, -8, 0, -8, 0, 8, 0, -8, 0, -8, 8, 0, 8, -8, 0, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, -8, 0, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, 0, -8, 0, -8, -8, 0, 8, 0, -8, 8, 0, 0, }, +{e: 16, -8, 0, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, x, , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , x, x, , , , , x, x, , , x, , , , x, }, +{b: , , , , x, x, , x, x, , , , x, , , x, }, +{d: , x, , x, x, x, , x, x, , , , , x, , x, }, +{e: , x, x, x, x, x, , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{0110,1010,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +181 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x09,0x07,0x00,0x06,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 2, 8, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 4, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 2, 2, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 4, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:164, 2:65, 4:24, 6:1, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{2: 16, 6, 8, 4, 4, 4, 0, 6, 4, 6, 4, 0, 4, 6, 4, 4, }, +{4: 16, 4, 0, 4, 0, 2, 4, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{8: 16, 2, 4, 4, 4, 0, 0, 0, 2, 8, 0, 2, 0, 0, 4, 2, }, +{3: 16, 6, 4, 0, 0, 8, 2, 0, 0, 0, 4, 0, 2, 0, 0, 6, }, +{5: 16, 4, 4, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 16, 6, 0, 0, 2, 0, 2, 4, 2, 0, 0, 4, 2, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, 2, 4, 0, 2, 0, }, +{a: 16, 0, 6, 0, 4, 2, 2, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 16, 0, 4, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 4, 0, 10, }, +{7: 16, 4, 4, 4, 2, 0, 0, 8, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 4, 2, 0, 2, 0, 8, 2, 0, 2, 4, 4, 0, 0, }, +{d: 16, 0, 6, 4, 0, 0, 2, 0, 0, 6, 4, 0, 0, 2, 8, 0, }, +{e: 16, 2, 6, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 2, 4, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:45, 4:53, 6:18, 8:6, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:1, 4:10, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 0, 0, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{8: 16, 0, 8, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, -8, -8, -8, }, +{3: 16, -8, 0, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, 0, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 8, -16, 0, 8, -8, 0, 8, -8, 0, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{c: 16, -8, 0, 0, -8, 8, 0, -8, 0, -8, 8, 8, 0, -8, 0, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 8, 0, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, }, +{e: 16, -8, 0, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, x, , , x, x, , , x, }, +{5: , x, x, x, x, , x, x, x, , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, x, , , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, , , , x, x, , x, }, +{a: , x, x, , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, , x, , , x, x, x, }, +{7: , x, x, x, , , , x, x, , , x, , , , x, }, +{b: , x, x, , , , , x, x, , , , x, , , x, }, +{d: , x, , , x, , , x, x, , , , , x, , x, }, +{e: , x, x, , x, x, , x, x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x0d,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_182.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_182.txt new file mode 100644 index 0000000..2db5715 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_182.txt @@ -0,0 +1,412 @@ +182 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x0b,0x07,0x04,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 2, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 0, 2, 2, 4, 2, 4, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, }, +{9: 0, 2, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 2, 6, }, +{f: 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:163, 2:68, 4:21, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 2, 6, 0, 2, 0, 0, 4, 0, 0, 6, 0, 0, }, +{2: 16, 4, 8, 0, 6, 4, 4, 0, 6, 4, 4, 4, 4, 4, 6, 6, }, +{4: 16, 0, 4, 4, 2, 4, 4, 0, 2, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 0, 4, 2, 4, 0, 2, 0, 2, 4, 2, 0, 2, 0, 0, 2, }, +{3: 16, 6, 6, 6, 0, 6, 4, 4, 0, 2, 0, 4, 0, 0, 2, 0, }, +{5: 16, 0, 0, 0, 2, 6, 4, 10, 4, 0, 0, 0, 0, 2, 0, 4, }, +{6: 16, 0, 6, 0, 0, 6, 8, 4, 0, 2, 0, 4, 2, 0, 0, 0, }, +{9: 16, 2, 4, 4, 2, 0, 0, 0, 4, 0, 0, 2, 8, 0, 2, 4, }, +{a: 16, 0, 6, 0, 4, 0, 2, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 16, 4, 4, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 8, 0, 6, }, +{7: 16, 2, 0, 10, 0, 4, 0, 0, 0, 2, 0, 4, 4, 0, 0, 6, }, +{b: 16, 0, 4, 0, 2, 0, 0, 4, 8, 2, 2, 0, 4, 0, 2, 4, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 4, 4, 0, 2, 0, 6, 6, 0, 0, 0, 4, 6, 2, 6, }, +{f: 16, 0, 6, 0, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:43, 4:46, 6:25, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:6, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, 0, -8, 0, -8, -8, 8, 0, -8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 0, -8, 8, 0, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, -8, 8, 8, 0, -8, -8, -8, 0, 8, 0, 8, -8, -8, 0, }, +{5: 16, -8, 8, 0, 0, -8, 0, 0, 0, -8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 0, -16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, -8, 8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, -8, 8, -8, }, +{7: 16, -8, -8, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 8, -8, 0, -8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, -8, -8, -8, -8, 0, 0, 8, 8, 0, 8, 0, 0, -8, -8, 8, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, x, x, x, , , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{7: , x, , , , x, , x, x, x, , x, x, , , x, }, +{b: , , x, , x, , , x, x, x, , , , , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, x, , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0010,0110,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x04,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +182 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x0b,0x07,0x00,0x09,0x0a,0x06,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 4, 2, 2, 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 2, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 4, 0, 2, 0, }, +{9: 0, 0, 2, 2, 2, 0, 4, 0, 4, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, }, +{f: 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 2, }, +}; +Diff: 8, DDT_spectrum: {0:163, 2:68, 4:21, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 6, 0, 0, 2, 0, 4, 2, 0, 6, 0, 0, }, +{2: 16, 4, 8, 4, 4, 6, 0, 6, 4, 6, 4, 0, 4, 4, 4, 6, }, +{4: 16, 0, 0, 4, 2, 6, 0, 0, 4, 0, 2, 10, 0, 0, 4, 0, }, +{8: 16, 2, 6, 2, 4, 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, }, +{3: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 0, 4, 0, 0, 2, 2, }, +{5: 16, 0, 4, 4, 2, 4, 4, 8, 0, 2, 0, 0, 0, 2, 0, 2, }, +{6: 16, 2, 0, 0, 0, 4, 10, 4, 0, 2, 0, 0, 4, 0, 6, 0, }, +{9: 16, 0, 6, 2, 2, 0, 4, 0, 4, 0, 0, 0, 8, 0, 6, 0, }, +{a: 16, 0, 4, 2, 4, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 16, 4, 4, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 8, 0, 6, }, +{7: 16, 0, 4, 8, 0, 4, 0, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 2, 2, 0, 0, 2, 8, 2, 0, 4, 4, 0, 4, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 6, 2, 4, }, +{f: 16, 0, 6, 0, 2, 0, 4, 0, 4, 0, 6, 6, 4, 0, 6, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:101, 2:43, 4:46, 6:25, 8:8, 10:2, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:6, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, -8, 0, -8, -8, 8, -8, 0, 0, 8, 0, }, +{2: 16, 8, -16, 8, 8, -8, 8, -8, 8, -8, 8, -8, -8, 0, -8, 0, }, +{4: 16, 0, 8, 0, 0, 8, -8, 0, 0, -8, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 8, -8, 0, 8, -8, 0, 0, -8, -8, 0, }, +{6: 16, 0, -8, 0, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, -16, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, -8, 8, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, -8, 8, -8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, -8, -8, 0, 0, 8, 8, }, +{b: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 8, -8, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 8, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{6: , x, , x, x, x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , , x, , x, }, +{a: , x, , , x, x, , x, x, x, , , x, , x, x, }, +{c: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{7: , x, , x, , x, , x, x, x, , x, x, , , x, }, +{b: , x, , , , x, , x, x, x, , , , , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , x, , , x, x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0010,0010,1,}, +{1100,1011,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_183.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_183.txt new file mode 100644 index 0000000..66c7cc7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_183.txt @@ -0,0 +1,424 @@ +183 Sbox: +LUT = { +0x08,0x06,0x01,0x0d,0x03,0x05,0x00,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x02,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + x0 + + + x3 + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 4, 0, }, +{2: 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, }, +{4: 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +{3: 0, 0, 0, 2, 0, 4, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, }, +{a: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{c: 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 4, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 4, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 0, 0, 4, 2, 0, 4, 2, 2, 0, 2, 4, 0, }, +{2: 16, 0, 6, 0, 0, 2, 4, 0, 6, 0, 4, 4, 6, 2, 6, 0, }, +{4: 16, 10, 0, 4, 2, 2, 4, 0, 0, 6, 0, 0, 4, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 4, 2, 0, 4, 2, 2, 2, 0, 2, 4, }, +{3: 16, 0, 0, 2, 4, 4, 8, 4, 0, 0, 2, 2, 0, 4, 0, 2, }, +{5: 16, 4, 4, 4, 8, 8, 16, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 16, 2, 2, 0, 4, 4, 8, 4, 2, 2, 0, 0, 0, 4, 0, 0, }, +{9: 16, 4, 6, 0, 0, 0, 0, 0, 4, 6, 0, 2, 8, 0, 0, 2, }, +{a: 16, 0, 2, 2, 4, 4, 8, 4, 0, 2, 2, 0, 0, 4, 0, 0, }, +{c: 16, 0, 6, 4, 0, 0, 0, 0, 0, 6, 4, 2, 0, 0, 8, 2, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 6, 0, 2, 2, 4, 0, 10, 0, 4, 0, 4, 0, 0, 0, }, +{d: 16, 6, 0, 4, 0, 2, 4, 0, 0, 6, 0, 0, 6, 2, 6, 4, }, +{e: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{f: 16, 2, 0, 0, 4, 4, 8, 4, 2, 0, 0, 2, 0, 4, 0, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:48, 4:54, 6:14, 8:12, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{4: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{3: 0, 4, 0, 4, 4, 12, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{5: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:10, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 8, -8, }, +{2: 16, 0, -8, 8, 0, -8, 0, -8, 8, -8, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 0, 8, 0, 8, -8, -8, 0, 8, -8, 0, 0, -8, 0, -8, }, +{8: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, -8, 8, 8, 0, -8, -8, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, -8, 8, -16, 8, -16, 8, -8, 0, 0, -8, 16, -8, 0, 0, 8, }, +{6: 16, 8, 0, 8, 0, -8, 0, 8, 0, -8, -8, 0, -8, -8, 0, 0, }, +{9: 16, -8, 0, 8, 0, -8, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{a: 16, 0, 8, -8, 0, -8, 8, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, -8, 0, 8, 0, -8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 0, -8, 0, 0, -8, 8, 0, 0, }, +{d: 16, 0, -8, 8, -8, -8, 0, -8, -8, 8, 0, 0, 8, -8, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, -8, 0, 8, 0, 8, 0, 8, -8, -8, 0, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, , x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , x, x, , , , x, , x, , x, x, , x, , x, }, +{b: , , x, x, x, x, x, x, x, , x, , x, x, , x, }, +{d: , x, x, , x, x, x, x, x, , x, , , , , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0101,1,}, +{0100,0101,1,}, +{0110,1010,1,}, +{0111,0101,0,}, +{0111,1001,1,}, +{0111,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x09,0x0a,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x06,0x07,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x0b,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x0c,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +183 Inverse Sbox: +LUT = { +0x06,0x02,0x0d,0x04,0x08,0x05,0x01,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + + x2 + + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, }, +{8: 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 4, }, +{3: 0, 0, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, }, +{5: 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 4, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 6, 0, 0, }, +{c: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 0, 4, 0, 0, 0, }, +{7: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 2, 2, 0, }, +{e: 0, 4, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:3, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 10, 0, 0, 4, 2, 4, 0, 0, 0, 0, 6, 0, 2, }, +{2: 16, 0, 6, 0, 0, 0, 4, 2, 6, 2, 6, 4, 6, 0, 4, 0, }, +{4: 16, 8, 0, 4, 0, 2, 4, 0, 0, 2, 4, 2, 0, 4, 2, 0, }, +{8: 16, 0, 0, 2, 2, 4, 8, 4, 0, 4, 0, 2, 2, 0, 0, 4, }, +{3: 16, 0, 2, 2, 0, 4, 8, 4, 0, 4, 0, 0, 2, 2, 0, 4, }, +{5: 16, 4, 4, 4, 4, 8, 16, 8, 0, 8, 0, 4, 4, 4, 4, 8, }, +{6: 16, 2, 0, 0, 2, 4, 8, 4, 0, 4, 0, 2, 0, 0, 2, 4, }, +{9: 16, 0, 6, 0, 0, 0, 4, 2, 4, 0, 0, 0, 10, 0, 4, 2, }, +{a: 16, 4, 0, 6, 4, 0, 4, 2, 6, 2, 6, 0, 0, 6, 0, 0, }, +{c: 16, 2, 4, 0, 2, 2, 4, 0, 0, 2, 4, 0, 4, 0, 8, 0, }, +{7: 16, 2, 4, 0, 2, 2, 4, 0, 2, 0, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 6, 4, 2, 0, 0, 0, 8, 0, 0, 2, 4, 6, 0, 0, }, +{d: 16, 2, 2, 0, 0, 4, 8, 4, 0, 4, 0, 0, 0, 2, 2, 4, }, +{e: 16, 4, 6, 0, 2, 0, 0, 0, 0, 0, 8, 2, 0, 6, 4, 0, }, +{f: 16, 0, 0, 0, 4, 2, 4, 0, 2, 0, 2, 2, 0, 4, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:48, 4:54, 6:14, 8:12, 10:2, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 0, 4, 4, 4, 4, 8, }, +{4: 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{b: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{d: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:10, 8:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, -8, 8, 8, 0, 0, -8, 0, -8, 0, 0, }, +{2: 16, 8, -8, 8, 0, -8, 0, -8, 8, -8, 0, -8, -8, 8, 0, 0, }, +{4: 16, 8, 0, -8, 0, 8, -8, -8, -8, 0, 0, -8, 8, 0, 0, 0, }, +{8: 16, 0, -8, -8, 0, 8, 0, 8, 8, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, -8, 0, 0, 8, 0, -8, 8, 0, 8, 0, 0, -8, -8, 0, }, +{5: 16, -8, 0, 0, 8, -8, 8, -16, -16, 8, -8, 8, 0, 0, -8, 16, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, -8, 0, -8, 8, -8, 0, 0, 0, }, +{9: 16, 0, -8, 0, -8, -8, -8, 8, 8, 0, 0, 0, 0, 8, -8, 0, }, +{a: 16, 0, 8, -8, -8, -8, 0, -8, 8, -8, 0, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, 8, -8, 8, -8, -8, -8, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, -8, 0, 0, 0, 8, 0, 8, -8, -8, 0, -8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 8, 0, -8, 0, 0, 0, 0, -16, }, +{d: 16, 0, 0, 0, 0, -16, 8, -8, -8, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, 0, -8, 0, 8, -8, 0, 8, 0, 0, 0, 0, -16, }, +{f: 16, 0, 0, 0, -8, 8, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , x, , x, , x, x, x, x, , x, , x, x, , x, }, +{d: , x, x, x, x, x, x, x, x, , x, , , , , x, }, +{e: , , x, , x, , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,1101,1,}, +{0110,0101,1,}, +{1001,0101,1,}, +{1111,0101,0,}, +{1111,1011,1,}, +{1111,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x0f,}}, +{{0x01,0x0a,0x04,}, {0x0f,}}, +{{0x09,0x02,0x0c,}, {0x0f,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x0a,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x01,}}, +{{0x0a,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x07,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x03,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x07,}}, +{{0x05,0x02,}, {0x06,0x09,0x0f,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_184.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_184.txt new file mode 100644 index 0000000..ec03bc2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_184.txt @@ -0,0 +1,424 @@ +184 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x04,0x0d,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{8: 0, 0, 2, 2, 4, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 0, 2, 2, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 4, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 2, 2, }, +{7: 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 4, 0, 0, 0, }, +{d: 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 4, }, +{f: 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 16, 4, 8, 4, 0, 6, 10, 4, 2, 0, 0, 8, 0, 0, 0, 2, }, +{4: 16, 4, 0, 8, 4, 4, 4, 0, 6, 6, 6, 4, 4, 4, 4, 6, }, +{8: 16, 0, 2, 6, 4, 2, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, }, +{3: 16, 4, 4, 0, 2, 8, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{5: 16, 4, 4, 4, 2, 10, 10, 8, 0, 0, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 0, 4, 0, 8, 4, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{9: 16, 0, 2, 4, 2, 0, 2, 0, 4, 2, 0, 0, 2, 4, 2, 0, }, +{a: 16, 4, 0, 6, 2, 0, 0, 2, 0, 6, 0, 0, 8, 0, 0, 4, }, +{c: 16, 4, 0, 4, 4, 0, 0, 2, 0, 0, 8, 2, 0, 4, 2, 2, }, +{7: 16, 0, 4, 0, 0, 4, 8, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 2, 2, 8, 0, 2, 4, 0, 4, 0, }, +{d: 16, 4, 0, 6, 0, 0, 0, 2, 4, 0, 6, 0, 0, 8, 2, 0, }, +{e: 16, 0, 2, 4, 2, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 4, }, +{f: 16, 0, 2, 6, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:50, 4:57, 6:11, 8:11, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{2: 0, 8, 8, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{5: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 8, 0, -8, 0, -8, -8, 0, 8, -16, -8, 0, 8, 0, }, +{2: 16, -8, -8, 8, 8, 0, 0, -8, 0, -8, 8, 0, 0, 0, -16, 8, }, +{4: 16, 8, 8, -8, 0, 8, -8, -8, 8, 8, -8, -16, 8, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, -8, 16, -8, 0, -8, 8, }, +{6: 16, -8, -8, -8, 0, 0, 0, 8, 8, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, 0, 0, -8, 0, 0, 8, -8, 0, -8, -8, 8, -8, }, +{c: 16, 0, 0, -16, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 0, 0, 8, -8, -8, 0, -8, 0, 0, 8, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, 0, -8, -8, 0, 0, 0, 8, 0, 0, -8, 8, -8, }, +{e: 16, 0, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, -8, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, , x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, , x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, , x, , x, x, x, , x, , , x, x, x, }, +{7: , , x, x, , , , x, x, , x, x, , x, , x, }, +{b: , x, , x, x, , x, , , , , , x, , , x, }, +{d: , , , , x, , x, x, x, , x, , , , , x, }, +{e: , x, x, , x, , , x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0100,1100,1,}, +{0111,0001,1,}, +{0111,0100,1,}, +{0111,0101,0,}, +{1100,1011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x01,0x0a,0x04,}, {0x07,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x07,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +184 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x08,0x0d,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, }, +{2: 0, 4, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 0, 8, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 6, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 6, 0, 2, 0, 0, 4, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{9: 0, 0, 2, 2, 2, 2, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, }, +{c: 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 2, 2, }, +{e: 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 4, }, +{f: 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 16, 4, 8, 0, 2, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{4: 16, 4, 4, 8, 6, 0, 4, 4, 4, 6, 4, 0, 4, 6, 4, 6, }, +{8: 16, 0, 0, 4, 4, 2, 2, 0, 2, 2, 4, 0, 2, 0, 2, 0, }, +{3: 16, 4, 6, 4, 2, 8, 10, 8, 0, 0, 0, 4, 0, 0, 0, 2, }, +{5: 16, 4, 10, 4, 0, 4, 10, 4, 2, 0, 0, 8, 0, 0, 2, 0, }, +{6: 16, 0, 4, 0, 0, 4, 8, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{9: 16, 0, 2, 6, 2, 2, 0, 2, 4, 0, 0, 0, 2, 4, 0, 0, }, +{a: 16, 4, 0, 6, 0, 0, 0, 0, 2, 6, 0, 2, 8, 0, 0, 4, }, +{c: 16, 4, 0, 6, 4, 0, 0, 0, 0, 0, 8, 2, 0, 6, 2, 0, }, +{7: 16, 0, 8, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 4, 0, 4, 2, 0, 0, 2, 2, 8, 0, 2, 4, 0, 4, 0, }, +{d: 16, 4, 0, 4, 0, 0, 0, 2, 4, 0, 4, 2, 0, 8, 2, 2, }, +{e: 16, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, 0, 4, 2, 2, 4, }, +{f: 16, 0, 2, 6, 0, 2, 0, 2, 0, 4, 2, 0, 0, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:50, 4:57, 6:11, 8:11, 10:3, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 8, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, 0, -8, -8, 0, 8, 0, 8, -16, 8, 0, }, +{2: 16, 0, 0, 8, 0, -8, 0, 8, 0, 0, 8, -8, -8, 0, -8, -8, }, +{4: 16, 8, 8, -8, 0, 8, 0, -8, 8, 8, -8, -8, 8, -16, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, -8, 0, -8, 8, 0, 0, -8, 0, }, +{3: 16, 0, -8, 8, 8, 0, 8, -8, 0, -8, 8, 0, -8, 0, -16, 0, }, +{5: 16, -8, 0, -8, 8, -8, 8, 0, -8, 0, -8, 0, 0, 16, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{9: 16, 0, 0, 8, 0, 0, -8, 0, 8, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, -8, 0, 8, 0, 0, -8, 0, 0, 8, -8, -8, 0, 0, 8, -8, }, +{c: 16, 0, 8, -8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 0, 8, -8, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -16, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 8, 0, }, +{e: 16, -8, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 8, }, +{f: 16, 8, -8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, , x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, , x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{c: , x, , x, x, , x, x, x, , x, , , x, x, x, }, +{7: , x, x, x, , , x, x, x, , x, x, , x, , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , , x, , x, x, x, , x, , , , , x, }, +{e: , x, , x, , , , x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0100,1101,1,}, +{1100,1011,1,}, +{1101,0001,1,}, +{1101,0100,1,}, +{1101,0101,0,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x0a,0x04,}, {0x0d,}}, +{{0x04,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x0d,}}, +{{0x0a,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x02,0x0c,}, {0x07,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x04,0x09,0x0d,}}, +{{0x0b,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x04,0x09,0x0d,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_185.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_185.txt new file mode 100644 index 0000000..94be54c --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_185.txt @@ -0,0 +1,424 @@ +185 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x0a,0x07,0x03,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, }, +{8: 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, }, +{5: 0, 2, 4, 0, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 4, 2, 0, }, +{9: 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, 2, 2, 2, }, +{a: 0, 2, 4, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, }, +{d: 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 0, 4, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 0, 4, 8, 2, 0, 2, 6, 0, 0, 0, 0, 6, 0, 0, 4, }, +{8: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{3: 16, 6, 4, 0, 2, 8, 2, 0, 0, 0, 6, 0, 0, 0, 0, 4, }, +{5: 16, 2, 8, 0, 4, 0, 4, 2, 2, 4, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 4, 4, 0, 2, 0, 8, 0, 2, 0, 2, 4, 4, 2, 0, }, +{9: 16, 0, 4, 0, 0, 2, 2, 0, 4, 2, 0, 0, 4, 2, 2, 2, }, +{a: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{c: 16, 6, 4, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 6, 4, 6, }, +{7: 16, 0, 8, 2, 4, 2, 4, 0, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 4, 2, 0, 0, 6, 4, 0, 0, 2, 6, 6, 0, 6, }, +{d: 16, 4, 0, 0, 0, 0, 0, 4, 2, 0, 6, 0, 6, 8, 2, 0, }, +{e: 16, 0, 4, 2, 0, 0, 2, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:48, 4:52, 6:16, 8:14, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 8, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 0, 4, 0, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 8, -8, 8, -8, }, +{2: 16, 8, 0, 8, 8, -8, 16, -8, 0, -8, 0, 0, -16, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 8, 8, -8, 0, -8, -8, -8, 0, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, -8, -8, -8, 0, 8, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 8, 0, 0, -8, 0, 8, 0, -8, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -16, 0, 0, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 0, -8, 0, 0, 0, -8, 0, 8, 8, -8, 8, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 8, }, +{a: 16, 8, -8, 8, 0, -8, 0, -8, 0, 0, 0, -8, -8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, -8, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, 0, 0, 8, 0, -8, -8, 0, -8, -8, 8, 0, 8, 0, }, +{b: 16, -8, -8, 0, -8, 8, 0, 0, 8, 0, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 0, 0, 0, -8, -16, 8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 8, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 8, -16, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , , x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, , x, , x, , x, , , , x, }, +{b: , , x, , x, , , x, , x, , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0101,1,}, +{0101,0010,0,}, +{0101,1101,1,}, +{0101,1111,1,}, +{1011,0010,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x05,}}, +{{0x09,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,0x05,0x06,}}, +{{0x07,0x08,}, {0x05,0x09,0x0c,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +185 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x0a,0x07,0x03,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = + x0 + x1 + + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +{8: 0, 0, 4, 2, 4, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{3: 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 0, 2, 4, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 2, 2, 2, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 4, 0, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 4, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 6, 2, 0, 2, }, +{d: 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 6, 2, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 2, 4, 8, 2, 0, 0, 4, 0, 0, 0, 2, 4, 0, 2, 4, }, +{8: 16, 0, 8, 2, 4, 2, 4, 0, 0, 4, 2, 4, 2, 0, 0, 0, }, +{3: 16, 4, 4, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 0, 0, 4, }, +{5: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 4, 6, 0, 0, 2, 8, 0, 2, 0, 0, 6, 4, 0, 0, }, +{9: 16, 2, 4, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 2, 2, 2, }, +{a: 16, 2, 8, 0, 4, 0, 4, 2, 2, 4, 0, 4, 0, 0, 2, 0, }, +{c: 16, 4, 4, 0, 0, 6, 0, 0, 0, 2, 6, 2, 0, 6, 4, 6, }, +{7: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 6, 0, 0, 0, 4, 4, 2, 0, 2, 6, 6, 0, 6, }, +{d: 16, 4, 0, 0, 0, 0, 0, 4, 2, 0, 6, 0, 6, 8, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:48, 4:52, 6:16, 8:14, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 0, 0, 8, 8, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{2: 16, 8, -8, 8, 8, -16, 16, -16, 0, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 0, 8, 0, 8, 0, 8, 0, -8, 0, -8, -8, -8, }, +{8: 16, 8, 0, 8, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 0, 8, 0, 8, 0, -8, 0, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, -8, 8, 0, -8, 8, 0, -8, 8, 0, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, -8, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, }, +{7: 16, 0, 0, 0, 0, 8, 0, 8, -8, -8, -8, 0, -8, 0, 8, -8, }, +{b: 16, -8, -8, 0, -8, 8, 0, -8, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, 0, -8, -16, 8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, 0, 8, -16, -8, 0, 0, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, , x, x, x, , x, x, x, , , x, x, , x, }, +{a: , , , , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, , x, , x, , x, , , , x, }, +{b: , , , , x, , , x, , x, , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0101,0010,0,}, +{0101,1101,1,}, +{0101,1111,1,}, +{0110,0010,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x05,}}, +{{0x09,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x07,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_186.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_186.txt new file mode 100644 index 0000000..70215ce --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_186.txt @@ -0,0 +1,424 @@ +186 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x0d,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{8: 0, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 4, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 2, 6, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{6: 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{9: 0, 2, 2, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, }, +{a: 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:3, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 8, 0, 0, 0, 8, 0, 16, 0, 8, 16, 8, 0, 16, 0, }, +{4: 16, 4, 4, 4, 2, 0, 8, 0, 0, 0, 2, 4, 2, 0, 0, 2, }, +{8: 16, 0, 4, 0, 6, 4, 0, 0, 4, 0, 2, 0, 10, 0, 0, 2, }, +{3: 16, 2, 0, 2, 4, 8, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 16, 4, 6, 4, 0, 6, 6, 6, 0, 0, 0, 4, 0, 2, 0, 2, }, +{6: 16, 0, 6, 0, 0, 4, 10, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{9: 16, 2, 6, 2, 2, 0, 2, 0, 4, 2, 0, 0, 4, 0, 0, 0, }, +{a: 16, 4, 6, 0, 0, 0, 2, 0, 4, 6, 0, 0, 8, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 4, 0, 2, 8, 2, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 4, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 2, 4, 0, 0, 0, 0, 2, 4, 2, 4, 4, 0, 2, 8, 0, }, +{e: 16, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 4, 0, 2, 8, 2, }, +{f: 16, 0, 4, 2, 2, 2, 0, 0, 4, 0, 4, 4, 0, 0, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:49, 4:47, 6:13, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -16, 8, 0, }, +{2: 16, 8, -8, 8, 0, -16, 0, 0, 8, -8, 8, -8, 0, 16, -16, -8, }, +{4: 16, 0, 8, -8, 0, 8, 0, -8, 0, 8, -8, 0, -8, 0, -8, 0, }, +{8: 16, -8, 0, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 8, }, +{3: 16, 0, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -16, -8, 0, }, +{5: 16, -8, 0, -8, 8, -8, 8, -8, 0, 0, 0, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, -8, 8, -8, 8, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, 0, -8, 0, 0, 0, 0, -8, -8, 0, 0, -8, 0, }, +{a: 16, -8, 0, 8, 0, -8, 0, -8, 0, 8, 0, 0, -8, 0, 8, -8, }, +{c: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 8, 0, -8, -8, -8, -8, 0, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 8, 0, 8, -8, 0, 0, 0, 8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, , x, , , x, x, x, }, +{7: , x, x, x, , , x, x, x, , x, x, , x, , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, , , x, x, x, x, x, , x, , , , , x, }, +{e: , x, x, , x, x, x, x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,1100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x01,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +186 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x0d,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x06,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{8: 0, 2, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 4, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{9: 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{a: 0, 4, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:3, 4:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 8, 4, 4, 0, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, }, +{4: 16, 4, 0, 4, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +{8: 16, 2, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, }, +{3: 16, 2, 0, 0, 4, 8, 6, 4, 0, 0, 0, 0, 6, 0, 0, 2, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 2, 2, 0, 4, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 6, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 4, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 8, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 4, 4, }, +{7: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 16, 4, 8, 2, 10, 4, 0, 0, 4, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:49, 4:47, 6:13, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 8, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:10, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, -8, 0, 0, -8, 0, 0, -8, 8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, 8, 0, -8, 0, }, +{8: 16, -8, 0, 8, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 8, -8, -8, -8, 0, }, +{5: 16, 0, 8, -8, 8, -8, 0, -8, 0, 8, -16, 0, 0, 0, -8, 8, }, +{6: 16, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 8, 0, }, +{9: 16, 8, 0, 8, -8, -8, 0, 8, 0, -8, 0, 0, 0, 8, -16, -8, }, +{a: 16, -8, 0, 8, 0, -8, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, }, +{7: 16, 0, -8, -16, 0, 8, 0, 8, 0, -8, 0, -8, -8, 0, 8, 8, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , x, x, x, x, , x, x, x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, , , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , x, x, , , , x, x, x, , x, x, , x, , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , x, x, , x, x, x, , x, , , , , x, }, +{e: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,0111,1,}, +{1100,0101,1,}, +{1100,1011,1,}, +{1100,1110,0,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 4, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_187.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_187.txt new file mode 100644 index 0000000..7c3ec34 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_187.txt @@ -0,0 +1,424 @@ +187 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0e,0x0d,0x0c,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 4, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, }, +{3: 0, 6, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, }, +{6: 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 2, }, +{a: 0, 2, 2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 0, 4, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, }, +{7: 0, 0, 0, 2, 0, 2, 4, 2, 0, 2, 2, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, 4, 0, }, +{e: 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 0, 4, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 0, 4, 4, 4, 0, 2, 8, 0, 0, 0, 2, 0, 2, 4, 2, }, +{8: 16, 0, 4, 0, 4, 2, 0, 0, 2, 6, 2, 2, 2, 0, 0, 0, }, +{3: 16, 6, 4, 0, 2, 8, 2, 0, 0, 0, 10, 0, 0, 4, 4, 8, }, +{5: 16, 2, 6, 0, 0, 0, 10, 2, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 6, 6, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 16, 0, 6, 0, 0, 2, 0, 0, 6, 2, 0, 0, 4, 2, 0, 2, }, +{a: 16, 2, 6, 0, 10, 0, 0, 4, 0, 4, 0, 0, 2, 0, 4, 0, }, +{c: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{7: 16, 0, 4, 2, 0, 2, 4, 2, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 8, 0, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 4, 4, 4, }, +{e: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 16, 4, }, +{f: 16, 4, 0, 2, 0, 4, 0, 2, 2, 0, 8, 0, 2, 4, 0, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:46, 4:55, 6:13, 8:9, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 8, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 0, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 0, -16, 8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 0, 8, -8, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 8, 8, 8, 0, -8, 0, -16, 0, 8, 0, -8, -8, 0, 0, }, +{5: 16, 0, -8, -8, 8, -8, 0, 8, -8, 0, 0, 0, 0, 8, 0, -8, }, +{6: 16, 0, -8, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, }, +{9: 16, -8, -8, 8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 8, -8, 8, -8, -8, 0, 0, -8, 8, 0, 0, 0, 0, 0, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 16, 0, }, +{7: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, }, +{b: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, -8, -8, 0, 8, 0, 0, 8, 8, 0, 0, -8, }, +{e: 16, 0, 0, -8, -8, 0, 8, 8, -8, 8, 0, 8, -8, 0, -16, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, , x, x, x, x, , x, , x, , x, x, x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, x, , x, x, x, , , x, x, x, x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, , x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , x, , x, x, , x, , x, , , , x, x, x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0100,0100,1,}, +{1000,1011,1,}, +{1001,0011,1,}, +{1110,0010,1,}, +{1110,1100,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0e,}}, +{{0x01,0x02,0x0c,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x04,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +187 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0e,0x0d,0x0c,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 6, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, }, +{3: 0, 4, 0, 0, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 4, 0, }, +{6: 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, }, +{a: 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 6, 2, 0, 0, 0, 4, }, +{7: 0, 2, 0, 2, 2, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 4, 0, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 6, 2, 0, 0, 2, 10, 0, 0, 8, 4, 4, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 0, 4, 0, }, +{4: 16, 2, 6, 4, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 16, 0, 6, 4, 4, 2, 0, 0, 0, 10, 0, 0, 2, 0, 4, 0, }, +{3: 16, 4, 4, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 0, 0, 4, }, +{5: 16, 0, 6, 2, 0, 2, 10, 0, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 0, 4, 8, 0, 0, 2, 4, 0, 4, 0, 2, 0, 2, 4, 2, }, +{9: 16, 2, 6, 0, 2, 0, 0, 0, 6, 0, 0, 0, 4, 2, 0, 2, }, +{a: 16, 2, 4, 0, 6, 0, 0, 0, 2, 4, 2, 2, 2, 0, 0, 0, }, +{c: 16, 4, 4, 0, 2, 10, 0, 0, 0, 0, 10, 2, 0, 4, 4, 8, }, +{7: 16, 2, 4, 2, 2, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 4, 0, 2, 0, 4, 0, 2, 2, 0, 8, 0, 2, 4, 0, 4, }, +{e: 16, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 16, 0, }, +{f: 16, 0, 0, 2, 0, 8, 0, 2, 2, 0, 4, 0, 2, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:46, 4:55, 6:13, 8:9, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, 4, 0, }, +{b: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, -8, -16, 0, 8, 0, 0, -8, 0, 8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 8, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, -8, 8, -8, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, }, +{3: 16, -8, 0, 8, 8, 0, -8, 8, -8, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, 0, 8, 8, -8, -8, }, +{6: 16, 0, 0, -16, 8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, -8, }, +{a: 16, 0, 0, 8, -8, 0, 0, 0, -8, 0, -8, -8, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 16, 0, 0, -8, -8, 8, -8, -8, 0, 0, 8, }, +{7: 16, 0, 8, -8, 8, 0, 0, 0, -8, 0, -8, 0, -8, 0, 0, 0, }, +{b: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 8, -8, -8, 0, -8, -8, 8, -8, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -16, 8, -8, -8, 8, 0, 8, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 0, -8, 8, 8, 8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, x, x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, x, x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, x, x, x, x, , x, , x, , , , x, x, x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0011,1100,0,}, +{0011,1110,1,}, +{0100,0110,1,}, +{1000,1011,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_188.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_188.txt new file mode 100644 index 0000000..fe48eae --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_188.txt @@ -0,0 +1,424 @@ +188 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0e,0x0b,0x0c,0x0d,0x0a,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, }, +{3: 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, }, +{5: 0, 4, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 2, 6, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 0, 4, 0, 2, 2, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 2, 2, 4, 2, 0, 4, 0, 0, 4, 2, 0, 0, }, +{2: 16, 0, 8, 4, 4, 0, 6, 6, 6, 6, 4, 4, 4, 4, 4, 4, }, +{4: 16, 4, 8, 6, 2, 4, 8, 4, 0, 0, 0, 10, 2, 0, 0, 0, }, +{8: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 2, 0, 6, 0, 8, 0, 0, 4, 6, 0, 4, 0, 0, 0, 2, }, +{5: 16, 4, 0, 6, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 16, 2, 0, 2, 0, 4, 0, 0, 4, 6, 2, 0, 0, 2, 2, 0, }, +{a: 16, 4, 8, 0, 4, 4, 2, 2, 10, 6, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 8, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 4, 4, }, +{7: 16, 2, 0, 6, 0, 4, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 4, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 4, 0, 2, 2, }, +{d: 16, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:49, 4:47, 6:13, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 4, 0, 0, 0, 8, 0, 8, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, 0, 0, -8, 0, 0, 8, -8, -8, 0, 0, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 8, 0, -8, 0, -8, -8, 0, -8, 8, }, +{3: 16, -8, -8, 0, 8, 8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 0, }, +{5: 16, -8, 8, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{6: 16, 8, -16, -8, 8, -8, 0, 8, 0, -8, 0, 0, 0, 8, 0, -8, }, +{9: 16, 0, 8, 0, -8, -8, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 8, -16, 0, 0, 0, 8, 8, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, }, +{7: 16, -8, -8, 0, 8, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 0, }, +{b: 16, 0, -8, 0, -8, 8, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , x, x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , x, , x, x, x, x, }, +{a: , x, x, , , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , x, , x, , x, x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0110,1,}, +{0011,0010,1,}, +{1000,1000,1,}, +{1100,0100,1,}, +{1100,1010,1,}, +{1100,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 4, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x05,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +188 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0e,0x0b,0x0c,0x0d,0x0a,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 4, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 4, 2, 0, 0, 2, }, +{5: 0, 4, 2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{a: 0, 0, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 2, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 4, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:62, 4:24, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 4, 0, 2, 4, 0, 2, 4, 0, 2, 4, 2, 0, 0, }, +{2: 16, 0, 8, 8, 16, 0, 0, 16, 0, 8, 8, 0, 0, 0, 16, 0, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 2, 0, 2, 6, 0, 0, 0, 0, }, +{8: 16, 2, 4, 2, 4, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, 2, }, +{3: 16, 2, 0, 4, 0, 8, 2, 0, 4, 4, 0, 4, 2, 0, 0, 2, }, +{5: 16, 4, 6, 8, 0, 0, 6, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 16, 2, 6, 4, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 16, 0, 6, 0, 4, 4, 2, 0, 4, 10, 0, 0, 0, 2, 0, 0, }, +{a: 16, 4, 6, 0, 4, 6, 0, 0, 6, 6, 0, 0, 4, 2, 0, 2, }, +{c: 16, 0, 4, 0, 4, 0, 0, 4, 2, 0, 4, 0, 2, 2, 8, 2, }, +{7: 16, 0, 4, 10, 0, 4, 0, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 4, 4, 2, 4, 0, 0, 0, 0, 8, 2, 2, 4, 0, 0, 2, }, +{d: 16, 2, 4, 0, 4, 0, 2, 4, 2, 0, 4, 0, 0, 2, 8, 0, }, +{e: 16, 0, 4, 0, 4, 0, 0, 4, 2, 0, 4, 0, 2, 2, 8, 2, }, +{f: 16, 0, 4, 0, 4, 2, 0, 4, 0, 0, 4, 2, 2, 0, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:99, 2:49, 4:47, 6:13, 8:12, 10:2, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 8, 0, 0, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{f: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -16, 0, 8, -16, 0, 0, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, -8, 0, -8, }, +{3: 16, -16, -8, 0, 8, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 8, 0, 8, -8, 0, -8, 0, 8, 0, -8, 0, -8, 0, -8, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, -8, 8, 0, 0, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 8, -8, 0, 0, 0, -8, 8, -8, 0, 8, }, +{c: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{7: 16, 0, -8, -8, 8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 0, 8, }, +{b: 16, 0, -8, 0, -8, 8, 0, -8, 0, 8, -8, -8, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, -8, 8, 8, 0, 0, 8, 0, 0, 0, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 8, -8, 0, 0, 8, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, x, x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , x, , , x, x, x, , x, x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, x, x, }, +{a: , , , x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , , x, , , x, , , x, , x, , x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{1000,1100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_189.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_189.txt new file mode 100644 index 0000000..ae1305f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_189.txt @@ -0,0 +1,412 @@ +189 Sbox: +LUT = { +0x08,0x0a,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x00,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, }, +{8: 0, 2, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, 0, 2, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, 0, 2, 2, 0, }, +{9: 0, 2, 2, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 4, 0, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:159, 2:80, 4:9, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:5, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 0, 4, 6, 0, 2, 4, 4, 0, 0, 6, 2, 0, 0, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 0, 4, 4, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 2, 2, }, +{8: 16, 6, 4, 0, 6, 6, 0, 0, 6, 4, 2, 0, 4, 0, 0, 2, }, +{3: 16, 4, 4, 2, 4, 6, 0, 0, 6, 6, 0, 0, 6, 0, 0, 2, }, +{5: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 0, 8, 0, 2, 4, 2, }, +{6: 16, 0, 6, 4, 0, 0, 0, 4, 0, 2, 2, 2, 0, 2, 2, 0, }, +{9: 16, 6, 6, 0, 4, 4, 0, 0, 10, 6, 0, 4, 4, 0, 4, 0, }, +{a: 16, 6, 4, 0, 6, 4, 2, 0, 4, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 2, 4, 0, 4, 4, 0, 2, 8, 2, }, +{7: 16, 2, 4, 2, 0, 0, 4, 0, 0, 0, 2, 4, 2, 2, 0, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 4, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:56, 4:46, 6:29, 8:3, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, 0, 0, 8, 0, -8, -8, 8, -8, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, -8, -8, 0, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 0, 8, -8, -8, 0, 0, 0, 0, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -16, -8, 8, 0, 0, 0, -8, 8, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 8, -8, -8, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , , x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , x, x, , , x, x, x, }, +{7: , , x, x, , , , , , x, , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, x, , , , x, , , , x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,1001,1,}, +{0100,1100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x07,0x09,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0f,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +189 Inverse Sbox: +LUT = { +0x0a,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x01,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, }, +{2: 0, 2, 8, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{8: 0, 0, 2, 2, 6, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, }, +{5: 0, 0, 2, 2, 0, 0, 4, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{9: 0, 0, 2, 0, 2, 2, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 2, 0, 2, }, +{b: 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:159, 2:80, 4:9, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:5, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 6, 4, 0, 0, 6, 6, 0, 2, 4, 2, 0, 0, }, +{2: 16, 6, 8, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 0, 6, 4, 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, }, +{8: 16, 4, 6, 2, 6, 4, 0, 0, 4, 6, 0, 0, 6, 0, 0, 2, }, +{3: 16, 6, 4, 0, 6, 6, 0, 0, 4, 4, 0, 0, 6, 0, 2, 2, }, +{5: 16, 0, 6, 2, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 2, }, +{6: 16, 2, 4, 4, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{9: 16, 4, 6, 0, 6, 6, 4, 0, 10, 4, 4, 0, 4, 0, 0, 0, }, +{a: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{7: 16, 0, 4, 2, 0, 0, 8, 2, 4, 0, 4, 4, 0, 2, 0, 2, }, +{b: 16, 6, 4, 2, 4, 6, 0, 0, 4, 6, 0, 2, 6, 0, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, }, +{e: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:56, 4:46, 6:29, 8:3, 10:1, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{3: 0, 4, 0, 0, 4, 12, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:111, 4:117, 8:24, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -16, 0, 0, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, }, +{8: 16, 8, 0, 8, -8, 8, 8, 0, 0, 0, -8, 0, -8, -8, -8, -8, }, +{3: 16, -8, -8, 8, 0, 8, -8, 0, -8, 0, 8, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 8, 0, }, +{9: 16, -8, 8, 8, 0, -8, 0, 0, 0, -8, -8, 0, 0, 8, -16, 8, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 0, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 0, -8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, -8, -8, 8, 0, 8, -8, -8, 0, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, , x, , x, , x, , x, , , x, x, }, +{9: , x, , x, x, , , , x, x, , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, x, , , , , , , x, , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , x, x, , , , , x, , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 3 */ +{0011,0010,1,}, +{0100,0111,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 11, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x04,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x07,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x06,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_190.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_190.txt new file mode 100644 index 0000000..0b3e700 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_190.txt @@ -0,0 +1,424 @@ +190 Sbox: +LUT = { +0x04,0x00,0x01,0x0a,0x02,0x05,0x06,0x07,0x03,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{2: 0, 0, 8, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 0, 2, 0, 0, 6, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{3: 0, 4, 0, 0, 2, 6, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{5: 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 2, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 6, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 4, 0, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:162, 2:74, 4:12, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 2, 4, 6, 0, 0, 4, 6, 0, 2, 6, 0, 0, 0, }, +{2: 16, 4, 8, 6, 4, 4, 6, 4, 4, 6, 4, 4, 6, 0, 4, 0, }, +{4: 16, 0, 4, 4, 0, 0, 2, 8, 0, 4, 4, 2, 0, 2, 0, 2, }, +{8: 16, 10, 4, 0, 10, 4, 0, 0, 8, 4, 0, 2, 4, 0, 2, 0, }, +{3: 16, 8, 4, 0, 10, 6, 2, 0, 8, 4, 0, 0, 4, 0, 2, 0, }, +{5: 16, 2, 6, 0, 0, 0, 4, 2, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 0, 6, 6, 0, 2, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 16, 4, 6, 0, 4, 6, 0, 0, 6, 6, 0, 0, 4, 2, 0, 2, }, +{a: 16, 4, 6, 0, 4, 6, 0, 4, 4, 10, 4, 0, 6, 0, 0, 0, }, +{c: 16, 2, 4, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 2, }, +{7: 16, 0, 4, 2, 2, 2, 6, 2, 0, 0, 2, 4, 0, 0, 0, 0, }, +{b: 16, 8, 4, 0, 8, 4, 0, 0, 10, 4, 0, 0, 6, 2, 0, 2, }, +{d: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 4, 0, 0, 0, 2, 4, 0, 4, 8, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:52, 4:43, 6:23, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, -8, 8, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -8, 8, -16, 8, 0, 0, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -16, 8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 8, 8, -8, 0, 0, 16, -8, -8, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 8, 8, 0, -8, 0, -16, 0, 8, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, -8, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -8, -8, 0, 0, 8, -8, 0, -8, 8, 0, -8, 8, }, +{a: 16, 8, -8, 8, -8, 0, 0, -16, -8, 0, 0, -8, 0, 0, 8, 8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, -8, 0, 8, 0, -8, 0, 0, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -16, 8, 0, 0, 8, 0, -8, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, -8, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , x, , x, x, , , x, }, +{5: , x, x, , x, x, x, , , x, , x, , x, , x, }, +{6: , x, , , x, x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, x, , , x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, , , x, x, , , , x, x, , , x, x, x, }, +{7: , x, , , x, x, , , , x, , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0100,0100,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,1011,1,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x08,}, {0x06,}}, +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x04,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x02,}, {0x06,0x09,0x0f,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0a,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +190 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x0a,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 0, }, +{3: 0, 2, 0, 0, 0, 6, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 0, }, +{b: 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:162, 2:74, 4:12, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 10, 8, 2, 0, 4, 4, 2, 0, 8, 0, 0, 0, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 0, 4, 0, }, +{4: 16, 2, 6, 4, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 2, }, +{8: 16, 4, 4, 0, 10, 10, 0, 0, 4, 4, 2, 2, 8, 0, 0, 0, }, +{3: 16, 6, 4, 0, 4, 6, 0, 2, 6, 6, 0, 2, 4, 0, 0, 0, }, +{5: 16, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 0, 4, 8, 0, 0, 2, 4, 0, 4, 0, 2, 0, 2, 4, 2, }, +{9: 16, 4, 4, 0, 8, 8, 0, 0, 6, 4, 0, 0, 10, 2, 0, 2, }, +{a: 16, 6, 6, 4, 4, 4, 0, 0, 6, 10, 0, 0, 4, 0, 4, 0, }, +{c: 16, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 8, 2, }, +{7: 16, 2, 4, 2, 2, 0, 6, 2, 0, 0, 0, 4, 0, 0, 2, 0, }, +{b: 16, 6, 6, 0, 4, 4, 0, 0, 4, 6, 0, 0, 6, 2, 0, 2, }, +{d: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 4, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:52, 4:43, 6:23, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 0, 0, 0, 8, 8, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -8, 0, -16, 0, 8, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 8, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 0, 8, -8, 16, 0, 0, -8, -8, -8, 8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 8, 8, 0, -8, 0, -8, -8, 0, 0, 8, -8, 0, 8, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -16, 8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, -16, 0, 0, 8, 8, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 8, -8, 8, -8, -16, 0, 0, -8, 8, 0, -8, 8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 8, -8, -8, 0, 0, -8, 0, 0, 8, 8, }, +{7: 16, 0, 0, -8, 8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 0, 0, -8, 8, 8, 0, 0, -8, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , , , x, , , , , x, x, , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{0100,0110,1,}, +{1000,1001,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x03,}}, +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x0f,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_191.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_191.txt new file mode 100644 index 0000000..30ad562 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_191.txt @@ -0,0 +1,424 @@ +191 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x03,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{2: 0, 2, 8, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 4, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 0, 4, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 2, 2, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 4, 0, 0, 2, 2, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:162, 2:74, 4:12, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 0, 8, 4, 4, 2, 0, 0, 10, 0, 0, 0, 2, }, +{2: 16, 6, 8, 4, 6, 4, 6, 4, 4, 4, 6, 4, 4, 0, 4, 0, }, +{4: 16, 4, 6, 6, 0, 4, 6, 6, 0, 2, 0, 4, 0, 0, 0, 2, }, +{8: 16, 0, 6, 0, 4, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{3: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 2, 4, 0, 2, 0, 0, }, +{5: 16, 6, 6, 4, 0, 4, 10, 6, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 4, 4, 8, 2, 10, 4, 6, 0, 0, 0, 8, 0, 2, 0, 0, }, +{9: 16, 0, 6, 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 2, 0, 2, }, +{a: 16, 2, 4, 0, 4, 0, 0, 0, 0, 4, 2, 2, 2, 0, 2, 2, }, +{c: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{7: 16, 4, 4, 10, 0, 8, 4, 4, 2, 2, 0, 10, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:56, 4:47, 6:19, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 4, 4, 12, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:9, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 8, 0, 8, 0, -16, 0, -8, 0, -8, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 0, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 8, 0, -8, 8, 0, 0, -8, 8, 8, -8, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, -8, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, -8, 0, 0, 8, -8, 0, -8, 0, 8, -8, 8, -16, 8, 0, 0, }, +{6: 16, 0, -8, -8, 8, 0, 0, 8, 0, -16, -8, 8, 0, -8, 8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -8, 0, 0, 0, -8, 8, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, }, +{7: 16, -8, -8, 0, 8, 8, 0, 0, -8, -8, -8, -8, 16, 0, 0, 0, }, +{b: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, -8, 8, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , , x, x, , , x, }, +{5: , x, x, x, x, , x, x, , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, x, , , x, , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, , x, x, , , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0111,0001,1,}, +{1000,1011,1,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x07,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x0b,}}, +{{0x01,0x06,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +191 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x05,0x08,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 0, 6, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 2, 6, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 2, 0, 2, 2, 6, 2, 0, 0, 0, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, 0, 2, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{c: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:162, 2:74, 4:12, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 4, 0, 6, 6, 4, 0, 2, 0, 4, 0, 0, 0, 2, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 8, 4, 6, 0, 4, 4, 8, 0, 0, 2, 10, 0, 0, 0, 2, }, +{8: 16, 0, 6, 0, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, 2, 0, }, +{3: 16, 8, 4, 4, 2, 6, 4, 10, 0, 0, 0, 8, 0, 2, 0, 0, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 4, 4, 6, 0, 6, 6, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{9: 16, 2, 4, 0, 2, 0, 0, 0, 4, 0, 2, 2, 4, 2, 0, 2, }, +{a: 16, 0, 4, 2, 4, 0, 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, }, +{c: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{7: 16, 10, 4, 4, 0, 4, 4, 8, 0, 2, 2, 10, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, 2, 2, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:56, 4:47, 6:19, 8:8, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 4, 8, 4, 4, 4, 0, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:9, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, 0, 0, -8, 8, 8, -8, -8, -8, 0, 0, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, 0, 0, 8, 0, -16, 0, -8, 0, -8, }, +{8: 16, 8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 8, 0, 0, -8, -16, 0, 8, 8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, 0, -8, 8, -8, -8, 0, 8, -8, -8, 8, 0, -8, 0, 8, }, +{9: 16, -8, 8, 0, -8, 0, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, -8, 8, 0, 0, 0, }, +{c: 16, 0, 0, 0, -8, 0, 0, -8, 0, -8, 8, -8, 0, 0, 0, 8, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, -8, -8, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, 0, 0, -8, 0, 8, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0111,0100,1,}, +{1000,1110,1,}, +{1010,0011,1,}, +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x04,}, {0x07,0x08,0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x0f,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x0c,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x0a,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_192.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_192.txt new file mode 100644 index 0000000..16b99fd --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_192.txt @@ -0,0 +1,444 @@ +192 Sbox: +LUT = { +0x06,0x00,0x01,0x08,0x03,0x05,0x04,0x07,0x02,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{8: 0, 0, 0, 2, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 2, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{5: 0, 0, 0, 0, 0, 4, 6, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 2, 2, 0, 2, 0, 0, }, +{9: 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 2, 2, }, +{7: 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:167, 2:65, 4:15, 6:7, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 10, 8, 8, 2, 0, 0, 4, 2, 0, 0, 0, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 0, 8, 0, 0, 2, 2, }, +{8: 16, 0, 4, 2, 4, 2, 0, 0, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 8, 4, 10, 0, 6, 8, 4, 2, 0, 0, 4, 0, 0, 2, 0, }, +{5: 16, 4, 4, 4, 0, 8, 10, 10, 0, 0, 2, 4, 0, 0, 0, 2, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 0, 2, 10, 0, 2, 0, 0, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 2, 4, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 6, 2, }, +{7: 16, 10, 4, 8, 0, 4, 8, 4, 0, 0, 0, 6, 2, 2, 0, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{e: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:95, 2:53, 4:37, 6:11, 8:20, 10:8, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 0, 12, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:129, 4:93, 8:30, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -16, 8, 0, 0, 0, 0, -8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 8, 0, 16, 0, 0, -16, 0, -8, -8, 8, -8, -16, }, +{4: 16, 0, 8, -16, 8, 0, 0, -8, 0, 16, -8, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 8, -8, 8, 0, 0, 0, 0, -8, 0, 0, -8, -8, 0, }, +{3: 16, -8, 0, 8, 8, 0, -16, 0, -8, 0, 8, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, -8, 8, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 16, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 8, -16, 0, 0, -8, 0, 8, 0, }, +{9: 16, 0, -8, 8, -8, -8, 0, 0, 8, 0, 0, -8, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 8, 8, 0, 0, 0, 0, -8, -8, 8, 0, 8, -16, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , , x, x, , , x, }, +{5: , , x, , x, x, x, x, , , , x, , x, , x, }, +{6: , , x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , x, , , , , , , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , x, , x, x, , x, , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 12 */ +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1000,1011,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1110,0100,1,}, +{1111,0010,1,}, +{1111,0101,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x05,0x02,0x08,}, {0x0f,}}, +{{0x01,0x02,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x09,0x02,0x0c,}, {0x0f,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x06,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x03,0x05,0x06,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +192 Inverse Sbox: +LUT = { +0x01,0x02,0x08,0x04,0x06,0x05,0x00,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{6: 0, 4, 0, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 2, 2, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 6, 0, 2, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{e: 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:167, 2:65, 4:15, 6:7, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 0, 8, 4, 4, 0, 2, 2, 10, 0, 0, 0, 0, }, +{2: 16, 4, 16, 8, 4, 4, 4, 8, 8, 4, 4, 4, 8, 0, 4, 0, }, +{4: 16, 4, 4, 10, 2, 10, 4, 4, 0, 0, 0, 8, 0, 0, 0, 2, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 10, 4, 8, 2, 6, 8, 4, 0, 2, 0, 4, 0, 0, 0, 0, }, +{5: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 0, 8, 0, 0, 2, 2, }, +{6: 16, 8, 4, 8, 0, 4, 10, 6, 0, 0, 0, 4, 0, 2, 2, 0, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 2, 2, 0, 2, 4, 0, 2, 2, 4, 2, }, +{7: 16, 4, 8, 8, 0, 4, 4, 10, 0, 0, 2, 6, 0, 2, 0, 0, }, +{b: 16, 2, 4, 0, 2, 0, 0, 0, 6, 2, 0, 2, 4, 2, 0, 0, }, +{d: 16, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 2, 2, 2, }, +{e: 16, 0, 4, 2, 0, 2, 0, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:95, 2:53, 4:37, 6:11, 8:20, 10:8, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 8, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 12, 4, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:129, 4:93, 8:30, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, -16, 0, 8, -8, 0, -8, 8, 0, }, +{2: 16, 8, -8, 8, 8, -16, 0, 0, 16, -16, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 16, 0, 0, 0, 0, -8, -8, 8, -8, -8, -8, }, +{8: 16, 8, -8, 8, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, -8, -8, }, +{3: 16, -8, 0, 8, 8, 0, 0, -8, -16, 0, 0, 8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -16, 8, 0, 0, -8, 0, 16, -8, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -8, 8, -16, -8, 8, 0, 0, 0, 8, -8, -8, 8, 0, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 0, 0, 0, 0, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 8, 0, 8, 0, 0, -16, 0, -8, 0, 8, 8, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, , x, x, x, x, , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, x, , x, x, , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 12 */ +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +{1000,1010,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x03,0x09,0x0a,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x09,0x02,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x03,0x04,}, {0x03,0x09,0x0a,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x02,}, {0x03,0x09,0x0a,}}, +{{0x01,0x06,}, {0x03,0x09,0x0a,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x03,0x05,0x06,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_193.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_193.txt new file mode 100644 index 0000000..4ed4632 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_193.txt @@ -0,0 +1,444 @@ +193 Sbox: +LUT = { +0x06,0x08,0x01,0x02,0x03,0x05,0x04,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 4, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 6, 4, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{7: 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:167, 2:65, 4:15, 6:7, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 8, 8, 10, 2, 0, 0, 4, 0, 0, 2, 0, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 2, 8, 0, 2, 0, 0, }, +{8: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 10, 4, 8, 0, 6, 8, 4, 2, 0, 0, 4, 2, 0, 0, 0, }, +{5: 16, 4, 4, 4, 0, 10, 10, 8, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 0, 0, 10, 0, 0, 2, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{7: 16, 8, 4, 10, 0, 4, 8, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:95, 2:53, 4:37, 6:11, 8:20, 10:8, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:129, 4:93, 8:30, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -16, 8, -8, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 8, 8, -8, 16, -8, 0, -8, 0, -16, 0, 8, 0, -8, }, +{4: 16, 0, 16, -16, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -8, 0, 8, 8, 8, -16, -8, 0, 0, 0, 0, 8, -8, -8, 0, }, +{5: 16, -8, 0, -8, 8, -8, 0, -8, 0, 0, -8, 16, -8, 0, 0, 8, }, +{6: 16, 8, -16, -8, 8, -8, 0, 8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{7: 16, -8, 0, -8, 8, 8, 0, 8, -8, 0, 0, -16, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 8, -8, 0, 0, -8, 8, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , , , x, x, , , x, }, +{5: , , , , x, x, x, x, , , , x, , x, , x, }, +{6: , , , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 12 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +193 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x06,0x05,0x00,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 6, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 4, 6, 0, 0, 0, 0, 0, 0, 0, 2, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 4, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:167, 2:65, 4:15, 6:7, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 2, 10, 4, 4, 0, 2, 0, 8, 0, 0, 0, 0, }, +{2: 16, 4, 16, 8, 4, 4, 4, 8, 8, 4, 4, 4, 8, 0, 4, 0, }, +{4: 16, 4, 4, 10, 0, 8, 4, 4, 0, 0, 0, 10, 0, 2, 2, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 8, 4, 8, 0, 6, 10, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{5: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 10, 4, 8, 2, 4, 8, 6, 0, 0, 0, 4, 0, 0, 0, 2, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 4, 8, 8, 0, 4, 4, 10, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 2, 4, 0, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:95, 2:53, 4:37, 6:11, 8:20, 10:8, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:129, 4:93, 8:30, 12:3, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, 0, 8, -16, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -16, 8, 8, -8, 0, -8, 16, -8, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, -8, 0, 0, 0, 0, 16, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, -16, 0, 8, 0, 0, -8, 0, 8, }, +{5: 16, 0, 16, -16, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, 8, -16, -8, 0, 8, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 8, 0, 8, -8, -8, 8, -8, 0, -8, 0, -8, 0, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, 0, -16, -8, 8, 0, 8, 8, 0, -8, 0, -8, 0, 8, 0, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , , , , x, x, , , x, }, +{5: , x, , , x, , x, x, , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, , , , x, x, , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 12 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1000,1000,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,0x09,0x0b,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x02,0x09,0x0b,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x05,0x09,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_194.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_194.txt new file mode 100644 index 0000000..73cc6fb --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_194.txt @@ -0,0 +1,414 @@ +194 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x0f,0x0b,0x06,0x07,0x04,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, }, +{8: 0, 0, 0, 0, 2, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 6, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{6: 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 4, 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 2, 4, 0, 0, 6, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 4, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 6, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 4, 0, 4, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 6, 0, }, +{f: 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:168, 2:60, 4:21, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 0, 4, 0, 2, 0, 4, 0, 0, 4, 2, 0, 2, }, +{2: 16, 4, 10, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 0, 6, 0, }, +{4: 16, 0, 0, 6, 2, 4, 0, 0, 4, 8, 0, 10, 2, 8, 4, 0, }, +{8: 16, 4, 0, 0, 6, 2, 0, 6, 6, 0, 0, 4, 2, 0, 4, 6, }, +{3: 16, 6, 4, 10, 2, 8, 4, 4, 0, 0, 0, 8, 0, 2, 0, 0, }, +{5: 16, 0, 2, 0, 0, 0, 4, 6, 4, 4, 0, 0, 2, 0, 0, 10, }, +{6: 16, 2, 0, 2, 4, 0, 0, 6, 0, 2, 0, 2, 0, 0, 6, 0, }, +{9: 16, 4, 2, 8, 0, 0, 4, 0, 4, 0, 0, 2, 2, 4, 2, 0, }, +{a: 16, 10, 0, 8, 2, 2, 8, 0, 0, 6, 0, 0, 4, 0, 4, 4, }, +{c: 16, 0, 4, 0, 0, 0, 0, 0, 0, 0, 10, 4, 4, 2, 6, 2, }, +{7: 16, 0, 0, 4, 0, 4, 2, 2, 2, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 8, 0, 0, 2, 0, 2, 4, 0, 10, 4, 6, 8, 4, 0, 0, }, +{d: 16, 0, 0, 4, 0, 2, 0, 6, 10, 0, 2, 0, 0, 4, 0, 4, }, +{e: 16, 0, 6, 4, 6, 0, 2, 4, 0, 4, 6, 0, 0, 2, 6, 0, }, +{f: 16, 2, 0, 0, 0, 2, 4, 0, 0, 8, 2, 4, 0, 4, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:40, 4:47, 6:18, 8:12, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 12, 0, 4, 4, 0, 4, 0, 0, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 8, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 12, }, +{6: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 4, 8, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -8, 0, 0, 8, 0, 8, -8, -8, -8, 0, -8, }, +{2: 16, 0, 0, 0, 0, 0, -8, -8, -8, -8, 8, 0, 0, 8, -8, 8, }, +{4: 16, 0, 8, -8, 0, 8, 0, -8, 8, 0, -8, 0, 8, -8, 0, -16, }, +{8: 16, 0, -8, 0, 0, 0, -8, 8, 8, -8, -8, 8, -8, -8, 0, 8, }, +{3: 16, -8, 8, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -16, 0, -8, }, +{5: 16, -8, 0, 0, 0, -8, 0, 0, 8, 0, -8, 0, -8, 8, -8, 8, }, +{6: 16, 8, 0, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, -8, 0, -8, }, +{9: 16, 0, 0, 0, 0, 0, -8, 0, 8, 0, -8, -8, 8, 8, -8, -8, }, +{a: 16, 0, 0, 8, 0, -8, 8, -8, -16, 8, -8, 0, 0, -8, 0, 8, }, +{c: 16, 0, -8, 0, -8, 0, 0, -8, 8, 0, 8, 0, -8, 8, 0, -8, }, +{7: 16, 0, 0, -8, 0, 0, 0, 0, -8, -8, -8, -8, 0, 8, 8, 8, }, +{b: 16, -8, -8, 0, 0, 8, 8, 0, -8, 0, -16, 0, 0, 8, 8, -8, }, +{d: 16, -8, 0, -8, -8, 0, 0, 0, 8, -8, 8, 0, 0, -8, 0, 8, }, +{e: 16, 8, 0, -8, -8, -8, 0, 0, -8, 0, 8, 8, 0, 8, -8, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, -8, 8, 8, -8, 0, -8, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, , , x, x, x, }, +{5: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, , , x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, , x, , , , x, , , x, , , x, x, x, }, +{b: , , x, , , x, x, , x, x, , , , , , x, }, +{d: , , x, , x, , , x, , , x, x, , , x, x, }, +{e: , , x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{1001,1010,1,}, +{1100,1011,1,}, +{1101,0011,1,}, +{1111,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x09,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,}}, +{{0x02,0x04,}, {0x0f,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x09,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x0b,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x07,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x05,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +194 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x08,0x0b,0x06,0x07,0x0f,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 4, 2, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 6, 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 2, 2, 0, 4, 0, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 4, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 0, 2, 0, }, +{6: 0, 2, 0, 0, 6, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 2, 2, 0, 0, 4, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 6, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 4, 0, 4, 0, 0, 0, }, +{d: 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 6, 2, }, +{f: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 4, }, +}; +Diff: 6, DDT_spectrum: {0:168, 2:60, 4:21, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 4, 6, 0, 2, 4, 10, 0, 0, 8, 0, 0, 2, }, +{2: 16, 4, 10, 0, 0, 4, 2, 0, 2, 0, 4, 0, 0, 0, 6, 0, }, +{4: 16, 2, 0, 6, 0, 10, 0, 2, 8, 8, 0, 4, 0, 4, 4, 0, }, +{8: 16, 0, 0, 2, 6, 2, 0, 4, 0, 2, 0, 0, 2, 0, 6, 0, }, +{3: 16, 4, 4, 4, 2, 8, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, }, +{5: 16, 0, 2, 0, 0, 4, 4, 0, 4, 8, 0, 2, 2, 0, 2, 4, }, +{6: 16, 2, 0, 0, 6, 4, 6, 6, 0, 0, 0, 2, 4, 6, 4, 0, }, +{9: 16, 0, 2, 4, 6, 0, 4, 0, 4, 0, 0, 2, 0, 10, 0, 0, }, +{a: 16, 4, 0, 8, 0, 0, 4, 2, 0, 6, 0, 2, 10, 0, 4, 8, }, +{c: 16, 0, 4, 0, 0, 0, 0, 0, 0, 0, 10, 4, 4, 2, 6, 2, }, +{7: 16, 0, 0, 10, 4, 8, 0, 2, 2, 0, 4, 8, 6, 0, 0, 4, }, +{b: 16, 4, 0, 2, 2, 0, 2, 0, 2, 4, 4, 4, 8, 0, 0, 0, }, +{d: 16, 2, 0, 8, 0, 2, 0, 0, 4, 0, 2, 0, 4, 4, 2, 4, }, +{e: 16, 0, 6, 4, 4, 0, 0, 6, 2, 4, 6, 0, 0, 0, 6, 2, }, +{f: 16, 2, 0, 0, 6, 0, 10, 0, 0, 4, 2, 0, 0, 4, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:100, 2:40, 4:47, 6:18, 8:12, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 0, 12, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 4, 0, 0, 12, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:7, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, -8, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -16, 0, 8, }, +{2: 16, 0, 8, 0, 0, -8, -8, 0, -8, 0, 8, -8, -8, 8, 0, 0, }, +{4: 16, 0, 8, 0, 8, 0, -16, 0, 8, 0, -8, -8, 8, -8, -8, 0, }, +{8: 16, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, 8, 0, -8, 0, 0, }, +{3: 16, 0, -8, 8, 0, 0, 8, -8, 0, -8, 8, 0, 0, -8, -8, 0, }, +{5: 16, 0, -8, 0, 0, -8, 8, -8, -8, 8, -8, 0, 0, 8, 0, 0, }, +{6: 16, 0, 8, 0, 0, 0, 8, 8, -8, -8, -8, 8, -8, -8, 0, -8, }, +{9: 16, -8, 8, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -16, 0, -8, 0, 8, 0, 0, 8, -8, -8, 0, -8, 8, 8, }, +{c: 16, 0, -8, -8, 0, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, -8, }, +{7: 16, -8, -8, 0, 0, 8, -8, 0, 8, 0, -16, 0, 0, 8, 8, -8, }, +{b: 16, 0, 8, 0, -8, 8, -8, -8, 0, 0, -8, 0, -8, 8, 0, 0, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, 0, 0, 8, 0, 8, -8, 0, -8, }, +{e: 16, 8, -8, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, -8, 8, -8, -8, 0, 8, 0, 0, 0, 8, 0, -8, -8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{a: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , x, , , x, x, , x, x, , x, x, , , x, }, +{b: , x, , , x, , , x, , , x, x, x, x, x, x, }, +{d: , x, x, x, , , , x, , , x, x, , , x, x, }, +{e: , , , , x, x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,1010,1,}, +{0101,0100,1,}, +{1100,0111,1,}, +{1101,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x05,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,}}, +{{0x02,0x04,}, {0x05,}}, +{{0x0a,0x04,}, {0x02,0x05,0x07,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x04,0x09,0x0d,}}, +{{0x05,0x02,}, {0x0c,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x02,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_195.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_195.txt new file mode 100644 index 0000000..4c45246 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_195.txt @@ -0,0 +1,414 @@ +195 Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x05,0x0f,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, }, +{8: 0, 4, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 0, 2, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 4, 2, 2, }, +{9: 0, 0, 2, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{7: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:168, 2:60, 4:21, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 0, 4, 0, 0, 4, 4, 6, 6, 6, 4, 4, 0, 0, }, +{2: 16, 0, 6, 0, 2, 0, 6, 0, 6, 0, 4, 4, 6, 2, 4, 0, }, +{4: 16, 0, 0, 8, 0, 6, 2, 0, 0, 0, 0, 4, 6, 2, 0, 4, }, +{8: 16, 4, 2, 0, 10, 2, 0, 4, 6, 0, 0, 0, 0, 0, 4, 0, }, +{3: 16, 0, 0, 6, 2, 8, 2, 0, 6, 4, 0, 4, 0, 0, 0, 0, }, +{5: 16, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 4, 0, 0, 4, 0, 0, 10, 4, 0, 0, 6, 4, 4, 6, 6, }, +{9: 16, 4, 6, 0, 6, 6, 0, 4, 10, 4, 0, 0, 4, 0, 0, 4, }, +{a: 16, 6, 0, 0, 0, 4, 0, 0, 4, 10, 2, 2, 4, 0, 0, 0, }, +{c: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{7: 16, 6, 4, 4, 0, 4, 6, 6, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 16, 4, 6, 6, 0, 0, 0, 4, 4, 4, 0, 0, 10, 6, 0, 4, }, +{d: 16, 4, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 6, 10, 0, 0, }, +{e: 16, 0, 4, 0, 4, 0, 2, 6, 0, 0, 6, 0, 0, 0, 8, 2, }, +{f: 16, 0, 0, 4, 0, 0, 0, 6, 4, 0, 0, 2, 4, 0, 2, 10, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:24, 4:47, 6:34, 8:4, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{5: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, 0, 8, -16, 0, 0, -8, -8, -8, 8, -8, }, +{2: 16, 0, 0, 8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, -8, }, +{4: 16, -8, 0, -8, 0, 8, 0, -8, 8, 8, 0, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, -8, -8, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, -8, 0, 8, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, -8, -16, 0, -8, 0, 8, 8, -8, 0, 8, 0, -8, 8, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, -8, 0, -8, 0, 0, -16, 8, }, +{a: 16, -8, -8, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 8, 8, -8, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, -16, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 8, 0, -8, 0, 0, -8, -8, 8, -8, 0, 0, -8, 0, 8, 0, }, +{e: 16, 8, 0, -8, -8, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 0, -8, 8, 8, 0, -8, -8, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{7: , , x, , , , x, , x, x, x, , x, x, x, x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, x, , , , x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0110,1,}, +{0110,1011,1,}, +{1001,0001,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x04,}, {0x04,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x0b,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +195 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x05,0x0f,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 4, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{4: 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, }, +{8: 0, 4, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 0, 2, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 4, 2, 2, }, +{9: 0, 0, 2, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{7: 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, }, +{d: 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:168, 2:60, 4:21, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 0, 4, 0, 0, 4, 4, 6, 6, 6, 4, 4, 0, 0, }, +{2: 16, 0, 6, 0, 2, 0, 6, 0, 6, 0, 4, 4, 6, 2, 4, 0, }, +{4: 16, 0, 0, 8, 0, 6, 2, 0, 0, 0, 0, 4, 6, 2, 0, 4, }, +{8: 16, 4, 2, 0, 10, 2, 0, 4, 6, 0, 0, 0, 0, 0, 4, 0, }, +{3: 16, 0, 0, 6, 2, 8, 2, 0, 6, 4, 0, 4, 0, 0, 0, 0, }, +{5: 16, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 4, 0, 0, 4, 0, 0, 10, 4, 0, 0, 6, 4, 4, 6, 6, }, +{9: 16, 4, 6, 0, 6, 6, 0, 4, 10, 4, 0, 0, 4, 0, 0, 4, }, +{a: 16, 6, 0, 0, 0, 4, 0, 0, 4, 10, 2, 2, 4, 0, 0, 0, }, +{c: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{7: 16, 6, 4, 4, 0, 4, 6, 6, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 16, 4, 6, 6, 0, 0, 0, 4, 4, 4, 0, 0, 10, 6, 0, 4, }, +{d: 16, 4, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 6, 10, 0, 0, }, +{e: 16, 0, 4, 0, 4, 0, 2, 6, 0, 0, 6, 0, 0, 0, 8, 2, }, +{f: 16, 0, 0, 4, 0, 0, 0, 6, 4, 0, 0, 2, 4, 0, 2, 10, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:108, 2:24, 4:47, 6:34, 8:4, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{5: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, 0, 0, 8, -16, 0, 0, -8, -8, -8, 8, -8, }, +{2: 16, 0, 0, 8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, -8, }, +{4: 16, -8, 0, -8, 0, 8, 0, -8, 8, 8, 0, 0, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, -8, -8, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, -8, 0, 8, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, -8, -16, 0, -8, 0, 8, 8, -8, 0, 8, 0, -8, 8, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, -8, 0, -8, 0, 0, -16, 8, }, +{a: 16, -8, -8, 8, 0, 8, -8, -8, -8, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 8, 8, -8, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, -16, 8, 8, -8, 0, 0, 0, 8, -8, }, +{d: 16, 8, 0, -8, 0, 0, -8, -8, 8, -8, 0, 0, -8, 0, 8, 0, }, +{e: 16, 8, 0, -8, -8, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 0, -8, 8, 8, 0, -8, -8, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{7: , , x, , , , x, , x, x, x, , x, x, x, x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , x, x, , , , x, , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0100,0110,1,}, +{0110,1011,1,}, +{1001,0001,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x04,}, {0x04,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x0b,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_196.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_196.txt new file mode 100644 index 0000000..7058873 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_196.txt @@ -0,0 +1,414 @@ +196 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x06,0x07,0x03,0x0e,0x0a,0x0b,0x0c,0x0d,0x09,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 4, 2, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, }, +{3: 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 2, 2, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 0, 6, 0, 0, 4, 0, 2, 0, }, +{c: 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, }, +{7: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 6, 2, 0, 4, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 4, 2, 2, }, +{f: 0, 0, 0, 4, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +}; +Diff: 6, DDT_spectrum: {0:168, 2:60, 4:21, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 2, 0, 0, 0, 6, 2, 4, 4, 6, 4, 6, 0, 0, }, +{2: 16, 0, 8, 2, 10, 0, 6, 0, 2, 8, 0, 4, 0, 4, 0, 4, }, +{4: 16, 0, 0, 10, 0, 4, 2, 2, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 0, 8, 0, 4, 2, 0, 0, 0, 4, 4, 2, 2, 0, 4, 2, }, +{3: 16, 2, 0, 4, 2, 8, 2, 0, 4, 4, 2, 4, 0, 0, 0, 0, }, +{5: 16, 2, 6, 0, 0, 0, 10, 2, 4, 0, 4, 4, 8, 0, 8, 0, }, +{6: 16, 6, 2, 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{9: 16, 0, 2, 0, 0, 6, 4, 0, 4, 8, 0, 0, 0, 0, 2, 6, }, +{a: 16, 4, 10, 0, 4, 4, 0, 2, 8, 6, 0, 0, 8, 0, 2, 0, }, +{c: 16, 6, 0, 0, 4, 0, 4, 0, 0, 0, 4, 2, 2, 10, 0, 0, }, +{7: 16, 4, 4, 6, 0, 6, 4, 6, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 0, 4, 0, 0, 8, 0, 0, 10, 2, 0, 6, 2, 4, 8, }, +{d: 16, 6, 4, 0, 0, 0, 0, 2, 2, 0, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 0, 0, 6, 0, 8, 0, 2, 0, 0, 0, 4, 4, 6, 2, }, +{f: 16, 0, 4, 4, 2, 0, 0, 0, 4, 0, 2, 0, 10, 0, 0, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:36, 4:42, 6:23, 8:13, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 0, 12, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:10, 8:1, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 0, 8, 0, 8, -8, 8, -8, 0, 0, -8, 0, -8, 8, -16, 0, }, +{4: 16, -8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 0, -8, -8, 8, }, +{8: 16, 0, -8, 0, -8, 8, 0, 8, -8, 0, 0, 8, 0, 0, -8, -8, }, +{3: 16, 0, 8, 0, 8, 8, -8, -8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{5: 16, 8, -8, 0, 8, -16, 0, 0, 0, 0, 8, 0, -8, 8, -8, -8, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, 8, 0, }, +{9: 16, 0, -8, 8, -8, -8, 0, 0, 0, 0, 0, -8, 8, 0, -8, 8, }, +{a: 16, 8, -16, 8, -8, -8, 0, -8, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, 0, -8, 8, 0, 0, -8, -8, 0, 0, -8, 0, 8, -8, }, +{7: 16, 0, -8, -8, 8, 8, 0, 0, -8, -8, -8, -8, 8, 0, 8, 0, }, +{b: 16, -8, -8, 0, -16, 8, 0, -8, 8, 8, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, -8, 0, 0, -8, 8, 0, 0, 0, 8, 0, }, +{e: 16, -8, 8, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 8, 0, -8, 8, -8, 0, 8, 0, -8, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, x, , , , x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , x, x, x, , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, , , , , , x, x, x, x, , x, , x, x, }, +{d: , x, x, x, x, x, , x, x, x, x, , , x, x, x, }, +{e: , x, , x, x, x, , x, x, x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0010,1010,1,}, +{0011,0101,1,}, +{1000,1011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x09,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x0f,}}, +{{0x0b,0x04,}, {0x01,0x08,0x09,}}, +{{0x01,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x06,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x01,0x02,0x03,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +196 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x03,0x0e,0x0a,0x0b,0x0c,0x0d,0x09,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 4, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, }, +{3: 0, 0, 0, 4, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 6, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 2, 0, 2, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 2, 4, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 6, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 4, 0, }, +{e: 0, 0, 0, 0, 4, 0, 4, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{f: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, }, +}; +Diff: 6, DDT_spectrum: {0:168, 2:60, 4:21, 6:6, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:4, 4:2, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 2, 6, 0, 4, 6, 4, 4, 6, 0, 0, }, +{2: 16, 0, 8, 0, 8, 0, 6, 2, 2, 10, 0, 4, 0, 4, 0, 4, }, +{4: 16, 2, 2, 10, 0, 4, 0, 0, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 0, 10, 0, 4, 2, 0, 0, 0, 4, 4, 0, 0, 0, 6, 2, }, +{3: 16, 0, 0, 4, 2, 8, 0, 2, 6, 4, 0, 6, 0, 0, 0, 0, }, +{5: 16, 0, 6, 2, 0, 2, 10, 0, 4, 0, 4, 4, 8, 0, 8, 0, }, +{6: 16, 6, 0, 2, 0, 0, 2, 4, 0, 2, 0, 6, 0, 2, 0, 0, }, +{9: 16, 2, 2, 0, 0, 4, 4, 0, 4, 8, 0, 0, 0, 2, 2, 4, }, +{a: 16, 4, 8, 0, 4, 4, 0, 2, 8, 6, 0, 2, 10, 0, 0, 0, }, +{c: 16, 4, 0, 0, 4, 2, 4, 0, 0, 0, 4, 2, 2, 8, 0, 2, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 0, 4, 2, 0, 8, 0, 0, 8, 2, 0, 6, 0, 4, 10, }, +{d: 16, 6, 4, 0, 0, 0, 0, 2, 0, 0, 10, 0, 2, 4, 4, 0, }, +{e: 16, 0, 0, 0, 4, 0, 8, 0, 2, 2, 0, 0, 4, 6, 6, 0, }, +{f: 16, 0, 4, 4, 2, 0, 0, 0, 6, 0, 0, 0, 8, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:104, 2:36, 4:42, 6:23, 8:13, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:10, 8:1, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, -8, 0, 8, 0, -8, -8, 8, 0, }, +{2: 16, 0, 0, 0, 8, -16, 8, -8, 0, 0, -8, 0, -8, 8, -8, 8, }, +{4: 16, -8, -8, 0, 8, 8, 0, 0, 0, 0, 8, -8, 0, -8, -8, 0, }, +{8: 16, 8, 0, 0, -8, 8, 0, 0, -8, -8, 8, 0, -8, 0, -8, 0, }, +{3: 16, 0, 0, 0, 8, 8, -8, 0, 0, -8, -8, 0, 8, -8, -8, 0, }, +{5: 16, 8, -8, 0, 8, -8, 0, -8, 0, 0, 8, 0, 0, 8, -16, -8, }, +{6: 16, 0, 0, -8, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, 0, 0, 0, -16, -8, 8, 0, 8, 8, }, +{c: 16, -8, 0, -8, -8, 8, 0, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -16, 8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, -8, -8, 0, 0, 0, 8, 8, 0, 0, 8, -8, }, +{e: 16, 0, 8, 0, -8, -8, 8, 0, -8, 0, -8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, -8, 0, 8, 8, -8, 0, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, x, , , , x, }, +{9: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, x, , x, x, x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, x, , , , , x, x, x, x, , x, , x, x, }, +{d: , , x, , x, x, , x, x, x, x, , , x, x, x, }, +{e: , x, x, x, x, x, , x, x, x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{1000,1011,1,}, +{1100,1010,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x09,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x01,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_197.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_197.txt new file mode 100644 index 0000000..5941387 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_197.txt @@ -0,0 +1,414 @@ +197 Sbox: +LUT = { +0x08,0x00,0x01,0x03,0x02,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 6, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 6, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 6, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 4, 0, 2, 0, 0, 2, }, +{5: 0, 0, 4, 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 4, 0, 0, 6, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 4, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:167, 2:63, 4:18, 6:7, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:5, 4:1, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 10, 0, 8, 4, 0, 0, 4, 8, 0, 0, 4, 2, 2, 0, }, +{2: 16, 6, 6, 6, 0, 6, 4, 4, 2, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 0, 8, 6, 10, 0, 0, 4, 0, 8, 4, 2, 2, 0, 4, 0, }, +{8: 16, 4, 0, 6, 6, 0, 4, 0, 6, 0, 6, 2, 0, 4, 2, 0, }, +{3: 16, 6, 4, 0, 0, 8, 2, 0, 0, 0, 4, 0, 2, 0, 0, 6, }, +{5: 16, 0, 8, 0, 8, 0, 6, 2, 2, 10, 0, 4, 0, 4, 0, 4, }, +{6: 16, 0, 4, 4, 0, 2, 0, 8, 4, 2, 0, 2, 0, 0, 2, 4, }, +{9: 16, 6, 0, 2, 4, 0, 0, 4, 8, 2, 0, 0, 0, 0, 0, 6, }, +{a: 16, 4, 0, 4, 0, 0, 8, 0, 0, 6, 2, 0, 10, 2, 8, 4, }, +{c: 16, 0, 0, 6, 4, 4, 0, 2, 0, 0, 8, 0, 0, 2, 0, 6, }, +{7: 16, 2, 4, 0, 2, 0, 8, 2, 0, 0, 0, 4, 4, 0, 4, 2, }, +{b: 16, 4, 0, 2, 2, 2, 2, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{d: 16, 0, 2, 0, 4, 0, 10, 0, 0, 0, 2, 0, 6, 4, 4, 0, }, +{e: 16, 2, 2, 4, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 6, 4, 4, 6, 4, 6, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:42, 4:44, 6:23, 8:13, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 0, 4, 4, }, +{2: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {4:9, 8:7, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, -16, }, +{2: 16, 0, 0, 8, 8, -8, 0, -8, 8, -8, 8, -8, 0, 0, -8, -8, }, +{4: 16, 8, 0, 0, 0, 8, 0, -8, 0, 8, -16, -8, 8, -8, 0, -8, }, +{8: 16, 8, 8, 0, -8, 8, 0, 8, -8, -8, -8, 0, 0, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, 0, 0, 8, }, +{5: 16, 0, 0, 0, 8, -16, 8, -8, 0, 0, -8, 0, -8, 8, -8, 8, }, +{6: 16, 0, -8, 0, 0, -8, -8, 8, 0, -8, -8, 0, 8, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, -8, 8, 8, 0, -8, -8, 0, -8, 0, 8, }, +{a: 16, 0, 0, 0, -8, -8, 8, -16, -8, 8, -8, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, 0, 8, -8, -8, 0, -8, 8, 0, 0, -8, 0, 8, }, +{7: 16, -8, -8, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, 0, 8, -8, }, +{b: 16, -8, 0, 0, 0, 8, 0, -8, 0, 0, -8, 8, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, -8, 0, 0, 8, 8, 0, 8, 0, -8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, , x, x, , x, , x, , , x, x, }, +{9: , x, , x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , , x, x, x, , x, , , x, x, , , x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , x, , , x, , x, , , x, , , x, , , x, }, +{d: , , , x, x, , x, , , x, , , , x, , x, }, +{e: , , x, x, x, , x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0101,1,}, +{0110,1010,1,}, +{1100,0100,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x0a,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x04,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +197 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x08,0x0a,0x06,0x07,0x00,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{2: 0, 2, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 6, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, }, +{8: 0, 4, 0, 2, 6, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 4, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 4, 4, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 4, 0, 0, 2, 2, 2, 6, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:167, 2:63, 4:18, 6:7, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:5, 4:1, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 0, 4, 6, 0, 0, 6, 4, 0, 2, 4, 0, 2, 0, }, +{2: 16, 10, 6, 8, 0, 4, 8, 4, 0, 0, 0, 4, 0, 2, 2, 0, }, +{4: 16, 0, 6, 6, 6, 0, 0, 4, 2, 4, 6, 0, 2, 0, 4, 0, }, +{8: 16, 8, 0, 10, 6, 0, 8, 0, 4, 0, 4, 2, 2, 4, 0, 0, }, +{3: 16, 4, 6, 0, 0, 8, 0, 2, 0, 0, 4, 0, 2, 0, 0, 6, }, +{5: 16, 0, 4, 0, 4, 2, 6, 0, 0, 8, 0, 8, 2, 10, 0, 4, }, +{6: 16, 0, 4, 4, 0, 0, 2, 8, 4, 0, 2, 2, 0, 0, 2, 4, }, +{9: 16, 4, 2, 0, 6, 0, 2, 4, 8, 0, 0, 0, 0, 0, 0, 6, }, +{a: 16, 8, 0, 8, 0, 0, 10, 2, 2, 6, 0, 0, 4, 0, 4, 4, }, +{c: 16, 0, 0, 4, 6, 4, 0, 0, 0, 2, 8, 0, 0, 2, 0, 6, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 4, 0, 2, 0, 2, 0, 0, 0, 10, 0, 4, 4, 6, 0, 0, }, +{d: 16, 2, 2, 0, 4, 0, 4, 0, 0, 2, 2, 0, 2, 4, 2, 0, }, +{e: 16, 2, 0, 4, 2, 0, 0, 2, 0, 8, 0, 4, 0, 4, 4, 2, }, +{f: 16, 0, 0, 0, 0, 6, 4, 4, 6, 4, 6, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:42, 4:44, 6:23, 8:13, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {4:9, 8:7, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 8, -8, 0, 8, -8, 0, 0, 0, -8, }, +{2: 16, 0, 0, 0, 8, -16, 8, -8, 0, 0, 8, 0, -8, 8, -8, -8, }, +{4: 16, 8, 8, 0, 0, 8, -8, -8, 8, 0, -8, -8, 0, 0, -8, -8, }, +{8: 16, 0, 8, 8, 0, 8, 0, 8, -8, 0, -8, 0, -8, -8, 0, -16, }, +{3: 16, 0, -8, 0, 0, 8, -8, -8, 0, -8, 8, 0, -8, 0, 0, 8, }, +{5: 16, -8, 0, 0, 0, -8, 8, -16, -8, 8, -8, 8, 0, 0, 0, 8, }, +{6: 16, 0, 0, -8, 0, -8, -8, 8, 0, -8, -8, 0, 0, 8, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 8, -8, -8, 0, -8, 0, -8, 8, }, +{a: 16, 8, 0, 0, 0, -8, 0, -8, 0, 8, -16, -8, 8, -8, 0, 8, }, +{c: 16, 0, 0, 0, -8, 8, 0, -8, -8, -8, 8, 0, 0, -8, 0, 8, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, 8, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, 0, 0, 8, 0, 0, 0, 8, -8, }, +{e: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 8, 8, 0, -8, 0, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, , x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , x, , x, x, , x, , , x, x, , , x, x, x, }, +{7: , x, x, x, , , x, , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , x, , , x, , x, , , x, , , , x, , x, }, +{e: , , , x, x, , x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1100,1010,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x03,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_198.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_198.txt new file mode 100644 index 0000000..57464c4 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_198.txt @@ -0,0 +1,414 @@ +198 Sbox: +LUT = { +0x08,0x00,0x01,0x0c,0x02,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 6, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 6, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, }, +{e: 0, 2, 4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:66, 4:15, 6:8, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 10, 0, 8, 0, 4, 0, 4, 2, 0, 8, 2, 0, }, +{2: 16, 0, 6, 6, 4, 0, 0, 4, 2, 4, 6, 0, 0, 2, 6, 0, }, +{4: 16, 4, 8, 6, 0, 4, 10, 4, 0, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 6, 4, 0, 6, 4, 0, 0, 6, 4, 2, 2, 6, 0, 0, 0, }, +{3: 16, 2, 0, 6, 4, 6, 2, 0, 0, 0, 6, 4, 4, 0, 0, 6, }, +{5: 16, 4, 2, 4, 0, 0, 8, 2, 2, 4, 0, 0, 0, 2, 0, 4, }, +{6: 16, 0, 4, 4, 0, 2, 0, 8, 4, 2, 0, 2, 0, 0, 2, 4, }, +{9: 16, 6, 0, 2, 4, 0, 0, 4, 8, 2, 0, 0, 0, 0, 0, 6, }, +{a: 16, 0, 10, 0, 8, 0, 6, 0, 0, 8, 2, 4, 2, 4, 0, 4, }, +{c: 16, 4, 4, 0, 0, 6, 0, 2, 0, 0, 6, 0, 2, 6, 4, 6, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 0, 2, 8, 6, 4, 0, 0, 2, 0, 0, 4, 6, 0, 0, }, +{d: 16, 6, 2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 0, }, +{e: 16, 2, 8, 0, 2, 0, 4, 2, 0, 0, 4, 4, 0, 0, 4, 2, }, +{f: 16, 0, 0, 0, 0, 6, 4, 4, 6, 4, 6, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:42, 4:44, 6:29, 8:11, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:9, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, 8, -8, 0, 8, 0, 0, -8, 8, -16, }, +{2: 16, 8, 0, 0, 0, -8, 0, -8, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 0, 8, -16, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, -8, -8, -8, 0, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 0, -16, 8, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 0, -8, -8, 8, 0, -8, -8, 0, 8, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, -8, 8, 8, 0, -8, -8, 0, -8, 0, 8, }, +{a: 16, 0, 0, 0, 0, -8, 8, -16, -8, 8, -8, 0, -8, 8, 0, 8, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, 0, -8, 8, 0, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, 0, -8, 0, 0, -8, 8, 0, -8, 0, -8, }, +{d: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 8, -8, 0, 0, -8, 0, 8, 0, 0, 8, 0, -8, 0, -8, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, , x, x, x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, , , x, , , , , x, x, , , , x, }, +{b: , x, , , x, x, , , , , x, , x, , , x, }, +{d: , , , x, x, x, , , , , x, , , x, , x, }, +{e: , , x, x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0101,1,}, +{0110,1010,1,}, +{1100,0100,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x0f,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x09,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +198 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0c,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, }, +{4: 0, 0, 2, 6, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 6, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 4, 4, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 6, 0, 0, 0, 0, 2, }, +{7: 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:66, 4:15, 6:8, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 6, 2, 4, 0, 6, 0, 4, 0, 0, 6, 2, 0, }, +{2: 16, 0, 6, 8, 4, 0, 2, 4, 0, 10, 4, 0, 0, 2, 8, 0, }, +{4: 16, 4, 6, 6, 0, 6, 4, 4, 2, 0, 0, 6, 2, 0, 0, 0, }, +{8: 16, 10, 4, 0, 6, 4, 0, 0, 4, 8, 0, 2, 8, 0, 2, 0, }, +{3: 16, 0, 0, 4, 4, 6, 0, 2, 0, 0, 6, 4, 6, 2, 0, 6, }, +{5: 16, 8, 0, 10, 0, 2, 8, 0, 0, 6, 0, 0, 4, 2, 4, 4, }, +{6: 16, 0, 4, 4, 0, 0, 2, 8, 4, 0, 2, 2, 0, 0, 2, 4, }, +{9: 16, 4, 2, 0, 6, 0, 2, 4, 8, 0, 0, 0, 0, 0, 0, 6, }, +{a: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{c: 16, 4, 6, 0, 2, 6, 0, 0, 0, 2, 6, 0, 0, 4, 4, 6, }, +{7: 16, 2, 0, 8, 2, 4, 0, 2, 0, 4, 0, 4, 0, 0, 4, 2, }, +{b: 16, 0, 0, 2, 6, 4, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 16, 8, 2, 0, 0, 0, 2, 0, 0, 4, 6, 0, 6, 4, 0, 0, }, +{e: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 6, 4, 4, 6, 4, 6, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:42, 4:44, 6:29, 8:11, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 0, 4, 0, 8, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:9, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 0, 0, -16, 8, -8, 0, 0, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 0, 0, 8, 8, -8, -8, 8, 0, -8, -8, 8, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 8, 0, 8, -8, 0, -8, 8, -8, 0, 0, -16, }, +{3: 16, -8, -8, 0, 0, 8, -8, -8, 0, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, -8, 8, -16, -8, 8, -8, 0, 8, -8, 0, 8, }, +{6: 16, 0, 0, -8, 0, -8, -8, 8, 0, -8, -8, 0, 0, 8, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 8, -8, -8, 0, -8, 0, -8, 8, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{c: 16, 8, 0, 0, -8, 8, 0, -8, -8, -8, 8, -8, -8, 0, 0, 8, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, -8, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 8, -8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, , x, x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, , , , , x, x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , x, , , x, x, , , , , x, , , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1100,1010,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_199.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_199.txt new file mode 100644 index 0000000..3ae788c --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_199.txt @@ -0,0 +1,414 @@ +199 Sbox: +LUT = { +0x08,0x00,0x01,0x0d,0x02,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, }, +{2: 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 6, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 4, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 4, 0, 2, 0, 0, 0, 0, 6, 2, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 2, 4, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 6, 0, 0, 0, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 6, 2, }, +{f: 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:66, 4:15, 6:8, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 6, 0, 4, 0, 4, 0, 6, 2, 0, 6, 0, 2, }, +{2: 16, 0, 6, 2, 0, 0, 4, 0, 6, 0, 6, 4, 4, 2, 6, 0, }, +{4: 16, 8, 0, 8, 2, 0, 10, 0, 0, 6, 0, 2, 4, 0, 4, 4, }, +{8: 16, 4, 0, 0, 8, 0, 0, 4, 6, 0, 2, 0, 2, 0, 6, 0, }, +{3: 16, 2, 0, 0, 0, 6, 8, 4, 4, 8, 4, 0, 0, 2, 0, 10, }, +{5: 16, 4, 6, 4, 0, 4, 6, 6, 0, 0, 0, 6, 2, 2, 0, 0, }, +{6: 16, 0, 0, 0, 4, 6, 4, 8, 0, 2, 0, 2, 0, 0, 6, 0, }, +{9: 16, 8, 4, 2, 4, 4, 0, 0, 6, 10, 0, 2, 8, 0, 0, 0, }, +{a: 16, 0, 2, 4, 0, 4, 2, 0, 4, 8, 2, 0, 2, 0, 4, 0, }, +{c: 16, 4, 6, 2, 0, 6, 0, 2, 0, 0, 6, 0, 0, 4, 4, 6, }, +{7: 16, 0, 4, 2, 0, 0, 8, 2, 2, 4, 0, 4, 2, 0, 0, 4, }, +{b: 16, 0, 4, 0, 2, 2, 2, 0, 6, 2, 0, 0, 4, 2, 0, 0, }, +{d: 16, 10, 0, 0, 0, 2, 0, 0, 0, 4, 6, 0, 4, 4, 2, 0, }, +{e: 16, 0, 6, 4, 6, 0, 0, 6, 0, 4, 4, 0, 0, 2, 6, 2, }, +{f: 16, 2, 2, 0, 0, 6, 0, 0, 2, 0, 4, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:40, 4:43, 6:30, 8:10, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{4: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{5: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, 0, 0, 8, -8, 0, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, 0, 0, 0, -8, 0, -8, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 8, 0, 0, 0, 0, 8, -8, -8, 8, -16, -8, 8, -8, 0, 0, }, +{8: 16, 8, 0, 0, -8, 0, -8, 8, 0, -8, -8, 8, -8, 0, 0, 0, }, +{3: 16, -16, 0, 0, 8, 0, 0, -8, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, -8, 0, -8, 8, -8, 8, -8, 0, 0, -8, 8, -8, 8, 0, 0, }, +{6: 16, 8, -8, 0, 0, 0, 0, 8, -8, -8, -8, 8, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, 0, -8, -8, 8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{a: 16, 8, 0, 0, 0, 0, 0, -16, 0, 8, -8, -8, 0, 0, 0, 0, }, +{c: 16, 8, 0, -8, 0, 8, -8, -8, 0, -8, 8, -8, -8, 0, 0, 8, }, +{7: 16, -8, -8, -8, 0, 8, 0, 8, 8, 0, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, -8, 8, 0, 0, 0, 0, }, +{d: 16, -8, 0, 0, -8, 0, -8, -8, 0, 0, 8, 8, 0, 0, 8, -8, }, +{e: 16, 8, -8, -8, -8, -8, 0, 8, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, , x, x, x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , , x, x, }, +{7: , , x, , , x, x, , x, , x, x, , x, , x, }, +{b: , , , , x, x, x, , x, , x, , x, x, , x, }, +{d: , x, , x, x, x, x, , x, , x, , , , , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0001,0011,1,}, +{0110,1010,1,}, +{0111,1001,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x06,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x02,0x05,0x07,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +199 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0d,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, }, +{4: 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, }, +{5: 0, 0, 0, 2, 0, 4, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 2, }, +{a: 0, 0, 0, 6, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 2, 0, 0, }, +{7: 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 4, 4, 0, 0, }, +{d: 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 6, 2, }, +{f: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:166, 2:66, 4:15, 6:8, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 4:2, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 4, 2, 4, 0, 8, 0, 4, 0, 0, 10, 0, 2, }, +{2: 16, 0, 6, 0, 0, 0, 6, 0, 4, 2, 6, 4, 4, 0, 6, 2, }, +{4: 16, 4, 2, 8, 0, 0, 4, 0, 2, 4, 2, 2, 0, 0, 4, 0, }, +{8: 16, 6, 0, 2, 8, 0, 0, 4, 4, 0, 0, 0, 2, 0, 6, 0, }, +{3: 16, 0, 0, 0, 0, 6, 4, 6, 4, 4, 6, 0, 2, 2, 0, 6, }, +{5: 16, 4, 4, 10, 0, 8, 6, 4, 0, 2, 0, 8, 2, 0, 0, 0, }, +{6: 16, 0, 0, 0, 4, 4, 6, 8, 0, 0, 2, 2, 0, 0, 6, 0, }, +{9: 16, 4, 6, 0, 6, 4, 0, 0, 6, 4, 0, 2, 6, 0, 0, 2, }, +{a: 16, 0, 0, 6, 0, 8, 0, 2, 10, 8, 0, 4, 2, 4, 4, 0, }, +{c: 16, 6, 6, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 6, 4, 4, }, +{7: 16, 2, 4, 2, 0, 0, 6, 2, 2, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 4, 2, 0, 2, 0, 8, 2, 0, 2, 4, 4, 0, 0, }, +{d: 16, 6, 2, 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 4, 2, 0, }, +{e: 16, 0, 6, 4, 6, 0, 0, 6, 0, 4, 4, 0, 0, 2, 6, 2, }, +{f: 16, 2, 0, 4, 0, 10, 0, 0, 0, 0, 6, 4, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:40, 4:43, 6:30, 8:10, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 12, 0, 0, 4, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:5, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 0, -8, -8, 8, 0, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 0, -8, 8, -8, 0, 0, 8, -8, -8, 8, -8, 0, }, +{4: 16, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, -16, 8, 0, 0, 0, }, +{8: 16, 8, 0, 0, 0, 0, -8, 8, 0, 0, -8, 8, -8, -8, 0, -8, }, +{3: 16, -8, -8, 0, 0, 8, -8, -8, 0, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, -8, 0, 0, 8, 0, 0, -16, -8, 8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, 0, -8, 0, 0, 0, 8, -8, -8, -8, 8, -8, 0, 0, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, -8, -8, -8, 0, 8, -8, 0, }, +{a: 16, 8, 0, 0, 0, 0, -8, -8, 8, 8, -16, -8, 8, -8, 0, 0, }, +{c: 16, 8, 8, 0, -8, 0, 0, -8, -8, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 0, -8, 0, 8, -8, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, -8, 0, 0, 0, -8, 0, -8, 0, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 8, -8, -8, -8, -8, 0, 8, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, -8, -8, -8, 0, 8, 0, 8, -8, 0, 8, -8, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , , x, x, }, +{7: , , x, x, , x, x, , x, , x, x, , x, , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , , , x, x, x, , x, , x, , , , , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0001,0001,1,}, +{0110,0101,1,}, +{0111,0100,1,}, +{1100,1010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x0c,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x07,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x07,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,}}, +{{0x03,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_200.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_200.txt new file mode 100644 index 0000000..4b8fb19 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_200.txt @@ -0,0 +1,414 @@ +200 Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x0a,0x06,0x07,0x03,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, }, +{8: 0, 2, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{3: 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 4, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, 4, }, +{a: 0, 2, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 6, 4, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 4, 2, 0, 0, }, +{e: 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:59, 4:24, 6:3, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:6, 2:6, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 6, 4, 0, 4, 4, 6, 6, 4, 4, 4, 6, 4, }, +{2: 16, 4, 6, 6, 2, 4, 6, 6, 0, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 0, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, 6, 0, 0, 4, }, +{8: 16, 6, 2, 0, 4, 2, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, }, +{3: 16, 4, 4, 2, 2, 8, 2, 0, 2, 0, 4, 0, 0, 0, 0, 4, }, +{5: 16, 0, 6, 0, 0, 2, 8, 0, 0, 2, 0, 4, 6, 0, 4, 0, }, +{6: 16, 4, 6, 4, 0, 0, 0, 10, 6, 0, 0, 4, 4, 6, 0, 4, }, +{9: 16, 4, 0, 0, 6, 2, 0, 6, 8, 0, 0, 0, 0, 2, 0, 4, }, +{a: 16, 6, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 6, 0, 0, 0, }, +{c: 16, 6, 0, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 4, 0, 4, }, +{7: 16, 4, 4, 0, 2, 0, 4, 4, 0, 2, 2, 8, 0, 0, 2, 0, }, +{b: 16, 4, 0, 6, 0, 0, 6, 4, 0, 6, 0, 0, 10, 4, 4, 4, }, +{d: 16, 4, 2, 0, 0, 0, 0, 6, 2, 0, 4, 0, 4, 10, 0, 0, }, +{e: 16, 6, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 4, 0, 10, 4, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:30, 4:54, 6:27, 8:6, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{b: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 12, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:6, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, -8, -8, 8, -16, 8, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, 0, 0, 8, -8, 8, -8, 8, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, -8, 0, 0, 8, 0, -8, 8, 8, 0, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, 0, 8, 0, 0, 8, -8, -8, -8, -8, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, -8, 0, 0, -8, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 8, 8, -16, -8, 0, 0, 0, 8, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 8, -8, 0, 0, 0, -8, -8, 8, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, -8, 8, -8, -8, 0, 0, 8, 0, }, +{c: 16, -8, 0, 0, 0, 0, 0, -8, -8, -8, 8, 0, 8, -8, 8, 0, }, +{7: 16, 8, -8, -8, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, -8, 0, 0, -8, 0, 0, -16, 8, 8, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, 8, -8, 0, 0, -8, 8, 8, 0, }, +{e: 16, -8, 0, -8, 0, 0, 8, 8, -8, 8, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 8, 8, 8, 0, -8, 8, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, , x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, , , x, , x, , , x, , , x, , , x, }, +{d: , , x, , , x, x, , , x, , , , x, , x, }, +{e: , x, , x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,1011,1,}, +{1001,0001,1,}, +{1010,0110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x09,0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +200 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x0a,0x06,0x07,0x03,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{4: 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, }, +{8: 0, 2, 2, 0, 4, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{3: 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 4, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, 2, 0, 4, }, +{a: 0, 2, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 6, 4, 0, 0, }, +{d: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 4, 2, 0, 0, }, +{e: 0, 2, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:59, 4:24, 6:3, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:6, 2:6, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 6, 4, 0, 4, 4, 6, 6, 4, 4, 4, 6, 4, }, +{2: 16, 4, 6, 6, 2, 4, 6, 6, 0, 0, 0, 4, 0, 2, 0, 0, }, +{4: 16, 0, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, 6, 0, 0, 4, }, +{8: 16, 6, 2, 0, 4, 2, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, }, +{3: 16, 4, 4, 2, 2, 8, 2, 0, 2, 0, 4, 0, 0, 0, 0, 4, }, +{5: 16, 0, 6, 0, 0, 2, 8, 0, 0, 2, 0, 4, 6, 0, 4, 0, }, +{6: 16, 4, 6, 4, 0, 0, 0, 10, 6, 0, 0, 4, 4, 6, 0, 4, }, +{9: 16, 4, 0, 0, 6, 2, 0, 6, 8, 0, 0, 0, 0, 2, 0, 4, }, +{a: 16, 6, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 6, 0, 0, 0, }, +{c: 16, 6, 0, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 4, 0, 4, }, +{7: 16, 4, 4, 0, 2, 0, 4, 4, 0, 2, 2, 8, 0, 0, 2, 0, }, +{b: 16, 4, 0, 6, 0, 0, 6, 4, 0, 6, 0, 0, 10, 4, 4, 4, }, +{d: 16, 4, 2, 0, 0, 0, 0, 6, 2, 0, 4, 0, 4, 10, 0, 0, }, +{e: 16, 6, 0, 0, 2, 0, 4, 0, 0, 0, 0, 2, 4, 0, 10, 4, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:102, 2:30, 4:54, 6:27, 8:6, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 8, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{b: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 12, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:6, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, -8, -8, 8, -16, 8, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, 0, 0, 8, -8, 8, -8, 8, -8, 0, 0, -8, 0, -8, -8, }, +{4: 16, 0, -8, 0, 0, 8, 0, -8, 8, 8, 0, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, -8, -8, }, +{3: 16, 0, 8, 0, 0, 8, -8, -8, -8, -8, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, -8, 0, 0, -8, 0, -8, -8, 8, 0, 8, 0, 8, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 8, 8, -16, -8, 0, 0, 0, 8, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 8, -8, 0, 0, 0, -8, -8, 8, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, -8, 8, -8, -8, 0, 0, 8, 0, }, +{c: 16, -8, 0, 0, 0, 0, 0, -8, -8, -8, 8, 0, 8, -8, 8, 0, }, +{7: 16, 8, -8, -8, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, -8, 0, 0, -8, 0, 0, -16, 8, 8, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, 8, -8, 0, 0, -8, 8, 8, 0, }, +{e: 16, -8, 0, -8, 0, 0, 8, 8, -8, 8, 0, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 8, 8, 8, 0, -8, 8, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, , x, , x, x, x, , x, , x, , , x, x, }, +{9: , x, x, , x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , , , x, , x, x, , , x, , x, , , , x, }, +{b: , x, , , x, , x, , , x, , , x, , , x, }, +{d: , , x, , , x, x, , , x, , , , x, , x, }, +{e: , x, , x, , x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0110,1011,1,}, +{1001,0001,1,}, +{1010,0110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x05,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x03,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x04,0x09,0x0d,}}, +{{0x03,0x08,}, {0x06,}}, +{{0x05,0x08,}, {0x0d,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x06,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x09,0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x0f,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_201.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_201.txt new file mode 100644 index 0000000..6c02cdf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_201.txt @@ -0,0 +1,426 @@ +201 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x08,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, }, +{4: 0, 2, 0, 6, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 2, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 2, 2, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 6, 4, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 4, 2, 2, 2, 2, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 4, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 0, 0, 4, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, }, +{e: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 6, 6, 4, 4, 0, 4, 0, 4, 0, 0, 6, 0, 0, }, +{2: 16, 4, 16, 4, 4, 4, 0, 4, 8, 4, 8, 0, 8, 4, 8, 4, }, +{4: 16, 6, 4, 6, 0, 4, 6, 4, 0, 0, 2, 6, 2, 0, 0, 0, }, +{8: 16, 6, 4, 0, 4, 0, 0, 0, 8, 0, 0, 2, 6, 2, 0, 0, }, +{3: 16, 4, 4, 4, 0, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 16, 4, 0, 6, 2, 0, 4, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{6: 16, 0, 4, 4, 0, 0, 2, 4, 2, 2, 0, 2, 0, 0, 2, 2, }, +{9: 16, 4, 8, 2, 10, 4, 2, 0, 6, 8, 0, 0, 4, 0, 0, 0, }, +{a: 16, 0, 4, 0, 0, 4, 2, 2, 10, 6, 0, 0, 4, 0, 0, 0, }, +{c: 16, 4, 8, 0, 0, 4, 2, 2, 0, 0, 6, 0, 0, 8, 4, 10, }, +{7: 16, 0, 0, 6, 0, 4, 0, 2, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 16, 0, 8, 0, 4, 0, 0, 2, 4, 6, 0, 2, 6, 0, 0, 0, }, +{d: 16, 6, 4, 0, 2, 0, 2, 0, 0, 0, 10, 0, 0, 4, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 6, 6, 4, }, +{f: 16, 0, 4, 0, 0, 4, 0, 2, 0, 0, 8, 2, 0, 0, 6, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:34, 4:51, 6:21, 8:12, 10:5, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 4, 4, 4, 0, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -16, 0, -8, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 8, 0, -8, 16, -8, -16, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 8, -8, -8, 0, 0, 0, -8, }, +{8: 16, -8, 8, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, }, +{3: 16, -8, -8, 8, 0, 0, 0, 0, -8, 8, 8, -8, 0, -16, 0, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, -8, 8, }, +{6: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{9: 16, 0, 8, 8, -8, -8, 0, 0, 0, 0, -16, -8, 8, 0, -8, 8, }, +{a: 16, -8, -8, 8, 0, 0, -8, -8, 0, 0, -8, 8, 0, 0, 0, 8, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, 0, -8, 8, 0, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, -8, 0, 8, 0, 8, -8, }, +{b: 16, 8, -8, 8, 0, 0, 8, 0, 0, -8, -8, 0, -8, 0, 0, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, 0, -8, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, 0, 8, 0, 8, 0, 8, -8, 0, 0, -8, -8, }, +{f: 16, 0, -8, -8, 0, 8, -8, 0, -8, -8, 8, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, , x, x, , , , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, , , x, x, , , x, x, }, +{9: , , x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, , x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, , , x, , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , , x, x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0010,1,}, +{0100,1100,1,}, +{1100,1001,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +201 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x08,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, }, +{4: 0, 2, 0, 6, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 0, }, +{8: 0, 2, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, 2, 0, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 2, 2, 6, 2, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 0, 4, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 4, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, }, +{f: 0, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 6, 6, 4, 4, 0, 4, 0, 4, 0, 0, 6, 0, 0, }, +{2: 16, 4, 16, 4, 4, 4, 0, 4, 8, 4, 8, 0, 8, 4, 8, 4, }, +{4: 16, 6, 4, 6, 0, 4, 6, 4, 2, 0, 0, 6, 0, 0, 2, 0, }, +{8: 16, 6, 4, 0, 4, 0, 2, 0, 10, 0, 0, 0, 4, 2, 0, 0, }, +{3: 16, 4, 4, 4, 0, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 16, 4, 0, 6, 0, 0, 4, 2, 2, 2, 2, 0, 0, 2, 0, 0, }, +{6: 16, 0, 4, 4, 0, 0, 2, 4, 0, 2, 2, 2, 2, 0, 0, 2, }, +{9: 16, 4, 8, 0, 8, 4, 2, 2, 6, 10, 0, 0, 4, 0, 0, 0, }, +{a: 16, 0, 4, 0, 0, 4, 0, 2, 8, 6, 0, 2, 6, 0, 0, 0, }, +{c: 16, 4, 8, 2, 0, 4, 2, 0, 0, 0, 6, 0, 0, 10, 4, 8, }, +{7: 16, 0, 0, 6, 2, 4, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 8, 2, 6, 0, 0, 0, 4, 4, 0, 2, 6, 0, 0, 0, }, +{d: 16, 6, 4, 0, 2, 0, 0, 0, 0, 0, 8, 2, 0, 4, 6, 0, }, +{e: 16, 0, 8, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 4, 6, 6, }, +{f: 16, 0, 4, 0, 0, 4, 2, 2, 0, 0, 10, 0, 0, 0, 4, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:34, 4:51, 6:21, 8:12, 10:5, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{5: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 8, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:5, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -16, 0, -8, }, +{2: 16, 8, -16, 8, 0, -8, 0, -8, 8, 0, 8, 0, -8, 16, -8, -16, }, +{4: 16, 0, 8, -8, 8, 0, -8, 0, 0, 8, -8, -8, 8, 0, -8, -8, }, +{8: 16, -8, 8, 8, -8, 0, 0, 0, 0, 0, -8, 8, -8, 0, 0, -8, }, +{3: 16, -8, -8, 8, 0, 0, 0, 0, -8, 8, 8, -8, 0, -16, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, -8, 0, -8, 0, 8, 8, }, +{9: 16, 0, 8, 8, -8, -8, 0, 8, 0, -8, -16, 0, 0, 0, -8, 8, }, +{a: 16, -8, -8, 8, 0, 0, -8, 0, 0, -8, -8, 0, 8, 0, 0, 8, }, +{c: 16, 0, 8, -16, -8, 8, 0, -8, 0, 0, 8, -8, -8, 0, 0, 8, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, 8, -8, 8, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 8, -8, }, +{e: 16, 0, -8, -8, 0, -8, 8, 0, 8, -8, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, 0, 0, -8, 0, -8, 0, 8, 8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, , , x, , , , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, x, , x, , x, x, }, +{c: , x, x, , x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, , , x, , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , x, , , x, x, x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0010,1,}, +{0100,1100,1,}, +{1100,1001,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x03,0x05,0x06,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_202.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_202.txt new file mode 100644 index 0000000..bfc33ff --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_202.txt @@ -0,0 +1,426 @@ +202 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x04,0x0e,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x06,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{8: 0, 0, 0, 2, 6, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{5: 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 2, 4, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 2, 2, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 6, 2, 0, }, +{7: 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 4, }, +{f: 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 16, 4, 8, 8, 0, 6, 4, 10, 0, 2, 0, 4, 0, 0, 0, 2, }, +{4: 16, 0, 4, 8, 4, 4, 0, 4, 6, 6, 6, 4, 4, 4, 4, 6, }, +{8: 16, 4, 0, 10, 6, 0, 4, 0, 8, 0, 4, 2, 2, 8, 0, 0, }, +{3: 16, 4, 4, 0, 0, 8, 4, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{5: 16, 0, 0, 0, 8, 8, 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, }, +{6: 16, 4, 4, 8, 0, 10, 4, 6, 2, 0, 2, 8, 0, 0, 0, 0, }, +{9: 16, 4, 0, 0, 10, 0, 4, 0, 6, 2, 0, 0, 2, 4, 0, 0, }, +{a: 16, 0, 2, 10, 2, 0, 0, 0, 0, 4, 0, 0, 4, 0, 6, 4, }, +{c: 16, 4, 0, 10, 8, 0, 4, 0, 4, 0, 8, 2, 0, 6, 2, 0, }, +{7: 16, 4, 0, 0, 0, 4, 4, 8, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 16, 4, 0, 0, 4, 0, 4, 0, 0, 0, 6, 0, 0, 10, 2, 2, }, +{e: 16, 0, 2, 10, 0, 0, 0, 0, 0, 4, 0, 0, 6, 2, 4, 4, }, +{f: 16, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:48, 6:12, 8:15, 10:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{a: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 12, 0, 4, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{d: 0, 0, 0, 0, 4, 0, 8, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 0, -8, -8, 0, 0, -8, 8, -16, -8, 8, 0, 0, }, +{2: 16, 0, -16, 8, 8, 0, 0, -8, 0, -8, 8, 0, 0, -8, -8, 8, }, +{4: 16, 8, 8, -8, 0, 8, -8, -8, 8, 8, -8, -16, 8, -8, -8, 0, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, 0, -8, -16, 0, 0, 0, -8, -8, }, +{3: 16, -8, -8, 8, 0, 0, -8, 0, -8, 8, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 0, -8, 8, 0, 0, -8, -8, 16, -8, -8, 0, 0, }, +{6: 16, 0, -8, -8, 8, 0, -8, 8, 0, -16, -8, 0, 0, 0, 8, 8, }, +{9: 16, -8, 8, 8, 0, -8, 0, 0, -8, 8, -8, 0, -8, 0, 0, 0, }, +{a: 16, 8, -8, 8, -8, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, 0, -8, 8, 0, 8, 0, 8, -8, }, +{7: 16, -8, -8, -8, 0, 0, 8, 0, -8, 8, -8, 0, 0, 8, 0, 0, }, +{b: 16, 0, -8, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{d: 16, -8, 8, -8, 0, -8, 0, 0, -8, 8, 8, 0, -8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, 8, 8, 8, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, , , x, x, x, , x, x, x, }, +{6: , x, , x, , , x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , x, , x, , , , x, x, , x, }, +{a: , x, , x, x, , x, , , x, , , x, , x, x, }, +{c: , x, x, , , , x, , , , x, , , x, x, x, }, +{7: , x, , x, , , x, , , x, x, x, , , x, x, }, +{b: , x, , x, x, , x, , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0010,1,}, +{0100,1100,1,}, +{0111,0001,1,}, +{0111,0100,1,}, +{0111,0101,0,}, +{1010,0110,1,}, +{1100,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,}}, +{{0x01,0x0a,0x04,}, {0x07,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x07,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,}}, +{{0x09,0x02,}, {0x02,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x07,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +202 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x08,0x0e,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x06,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + + + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 4, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 0, 0, 0, 8, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{8: 0, 0, 0, 0, 6, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 6, 0, 0, 4, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 4, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 4, 6, 0, 0, 0, 0, 2, 0, 0, 2, }, +{9: 0, 4, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 2, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{c: 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 2, 2, 0, 2, 0, }, +{d: 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 4, 2, }, +{f: 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 16, 4, 8, 4, 0, 4, 0, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 16, 0, 8, 8, 10, 0, 0, 8, 0, 10, 10, 0, 0, 0, 10, 0, }, +{8: 16, 4, 0, 4, 6, 0, 8, 0, 10, 2, 8, 0, 2, 4, 0, 0, }, +{3: 16, 4, 6, 4, 0, 8, 8, 10, 0, 0, 0, 4, 2, 0, 0, 2, }, +{5: 16, 0, 4, 0, 4, 4, 16, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 16, 4, 10, 4, 0, 4, 8, 6, 0, 0, 0, 8, 2, 0, 0, 2, }, +{9: 16, 4, 0, 6, 8, 0, 0, 2, 6, 0, 4, 0, 2, 0, 0, 0, }, +{a: 16, 0, 2, 6, 0, 2, 0, 0, 2, 4, 0, 2, 2, 0, 4, 0, }, +{c: 16, 4, 0, 6, 4, 0, 0, 2, 0, 0, 8, 0, 0, 6, 0, 2, }, +{7: 16, 4, 4, 4, 2, 0, 0, 8, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 0, 4, 2, 2, 0, 0, 2, 4, 0, 2, 2, 0, 6, 0, }, +{d: 16, 4, 0, 4, 8, 0, 8, 0, 4, 0, 6, 0, 0, 10, 2, 2, }, +{e: 16, 0, 0, 4, 0, 2, 0, 0, 0, 6, 2, 2, 0, 2, 4, 2, }, +{f: 16, 0, 2, 6, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:48, 6:12, 8:15, 10:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 8, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 12, 4, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 12, 0, 4, 4, 4, 4, }, +{7: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{b: 0, 8, 0, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 8, 0, }, +{e: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +{f: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 0, -8, -8, 0, 0, -8, 8, 0, 8, -8, 0, 0, }, +{2: 16, 0, -8, 8, 0, -8, 0, 0, 0, 8, 8, -8, -8, 0, 0, -8, }, +{4: 16, 16, 8, -8, 0, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, -8, 0, 8, 0, -8, 0, -16, 8, -8, 0, -8, 0, }, +{3: 16, 0, -16, 8, 8, 0, 0, -8, 8, -8, 8, 0, -8, 0, -8, 0, }, +{5: 16, -16, 8, -8, 0, -8, 8, 0, 0, -8, -8, 0, 8, 8, 0, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 0, 8, 0, -8, 8, -16, 0, 0, 8, }, +{9: 16, 0, 8, 8, 0, 0, -8, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{a: 16, 0, -8, 8, 0, 0, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, -8, -8, -8, 8, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, }, +{d: 16, 0, 8, -16, -8, 0, 0, -8, -8, 0, 8, 0, -8, 8, 0, 8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, -8, 0, 8, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , , x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , x, x, x, x, , x, x, }, +{5: , , x, x, x, , x, , , x, x, x, , x, x, x, }, +{6: , , x, x, x, , x, x, , x, x, x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , , x, x, x, , x, , , , x, , , x, x, x, }, +{7: , , , x, , , , , , x, x, x, , , x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , , x, x, x, , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0001,0001,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0010,0011,1,}, +{0100,1101,1,}, +{1011,0110,1,}, +{1100,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x0a,0x04,}, {0x01,}}, +{{0x04,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x02,0x08,}, {0x0c,}}, +{{0x06,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,}}, +{{0x02,0x0c,}, {0x07,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,}}, +{{0x0b,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,}}, +{{0x09,0x02,}, {0x0f,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x01,}}, +{{0x09,0x0a,}, {0x02,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x01,0x08,0x09,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_203.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_203.txt new file mode 100644 index 0000000..6d286e3 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_203.txt @@ -0,0 +1,426 @@ +203 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x04,0x0f,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 4, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{8: 0, 4, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{5: 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 4, 2, 2, 0, 2, }, +{9: 0, 0, 0, 0, 2, 0, 4, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 2, 2, 2, 2, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 6, 2, 2, }, +{7: 0, 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 2, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 2, 0, }, +{d: 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:2, 4:5, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 16, 4, 8, 4, 0, 6, 8, 4, 0, 0, 0, 10, 2, 0, 0, 2, }, +{4: 16, 0, 0, 8, 0, 8, 0, 0, 10, 10, 0, 8, 0, 10, 10, 0, }, +{8: 16, 4, 0, 6, 6, 0, 0, 0, 8, 0, 0, 2, 2, 4, 0, 0, }, +{3: 16, 4, 4, 4, 0, 8, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{5: 16, 0, 4, 0, 4, 4, 16, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 16, 4, 0, 4, 0, 4, 0, 4, 2, 0, 0, 8, 2, 2, 0, 2, }, +{9: 16, 4, 0, 4, 10, 0, 8, 0, 6, 2, 4, 0, 2, 8, 0, 0, }, +{a: 16, 0, 2, 6, 2, 2, 0, 2, 0, 4, 0, 0, 2, 0, 4, 0, }, +{c: 16, 4, 0, 4, 4, 0, 8, 0, 8, 0, 10, 0, 0, 6, 2, 2, }, +{7: 16, 4, 4, 4, 0, 10, 8, 8, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 0, 2, 4, 2, 0, 0, 2, 2, 4, 0, 0, 2, 0, 6, 0, }, +{d: 16, 4, 0, 6, 0, 0, 0, 0, 4, 0, 6, 2, 0, 8, 0, 2, }, +{e: 16, 0, 2, 4, 0, 0, 0, 2, 0, 6, 2, 0, 0, 2, 4, 2, }, +{f: 16, 0, 2, 6, 0, 2, 0, 2, 0, 4, 2, 0, 0, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:48, 6:12, 8:15, 10:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 8, 0, 4, 0, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{5: 0, 0, 0, 4, 8, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 12, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{e: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 8, 0, 0, 0, 0, -8, -8, 8, -8, -16, 0, 0, -8, }, +{2: 16, -8, -16, 8, 8, 8, 0, -8, 0, -8, 8, 0, 0, 0, -8, 0, }, +{4: 16, 8, 8, -8, 0, 0, -8, -8, 8, 8, -8, -8, 16, -8, -8, -8, }, +{8: 16, -8, 8, 8, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, -8, }, +{3: 16, -8, -8, 8, 0, 0, -8, 0, -8, 8, 8, 0, 0, -8, 0, 0, }, +{5: 16, 8, 8, -8, 0, 0, 0, 0, -8, -8, -8, 8, -16, 0, 0, 8, }, +{6: 16, -8, -8, -8, 0, 0, 0, 8, 8, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 0, 0, 0, -16, 0, 0, 8, -8, 8, }, +{a: 16, 8, -8, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, }, +{c: 16, -8, 8, -16, -8, -8, 8, -8, 0, 0, 8, 8, 0, 0, 0, 0, }, +{7: 16, -16, -8, -8, 8, 8, 8, 0, -8, 0, -8, 0, 0, 8, 0, 0, }, +{b: 16, 8, -8, 8, -8, -8, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, -8, 8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, -8, 8, -8, }, +{e: 16, 8, -8, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{f: 16, 8, -8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{6: , x, , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, , x, , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, x, x, x, , x, }, +{c: , x, x, , x, x, x, , x, x, x, x, x, x, , x, }, +{7: , , , x, , x, , , x, x, x, , x, x, x, x, }, +{b: , x, , x, x, , x, , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , x, , , x, x, , , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0001,0111,1,}, +{0010,0010,1,}, +{0100,1100,1,}, +{1011,0001,1,}, +{1011,0100,0,}, +{1011,0101,1,}, +{1100,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x01,0x0a,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0b,}}, +{{0x03,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x01,0x04,0x05,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x0b,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x0b,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +203 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x08,0x0f,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x06, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + + + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 4, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 0, 0, 0, 8, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{8: 0, 4, 0, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 6, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 4, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 2, 0, 2, 2, }, +{9: 0, 0, 0, 2, 4, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 0, 4, 0, 2, 0, }, +{c: 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{7: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 0, 0, }, +{b: 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 4, }, +{f: 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:2, 4:5, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 16, 4, 8, 0, 0, 4, 4, 0, 0, 2, 0, 4, 2, 0, 2, 2, }, +{4: 16, 0, 4, 8, 6, 4, 0, 4, 4, 6, 4, 4, 4, 6, 4, 6, }, +{8: 16, 4, 0, 0, 6, 0, 4, 0, 10, 2, 4, 0, 2, 0, 0, 0, }, +{3: 16, 4, 6, 8, 0, 8, 4, 4, 0, 2, 0, 10, 0, 0, 0, 2, }, +{5: 16, 0, 8, 0, 0, 0, 16, 0, 8, 0, 8, 8, 0, 0, 0, 0, }, +{6: 16, 4, 4, 0, 0, 0, 4, 4, 0, 2, 0, 8, 2, 0, 2, 2, }, +{9: 16, 4, 0, 10, 8, 0, 4, 2, 6, 0, 8, 0, 2, 4, 0, 0, }, +{a: 16, 0, 0, 10, 0, 2, 0, 0, 2, 4, 0, 0, 4, 0, 6, 4, }, +{c: 16, 4, 0, 0, 0, 0, 4, 0, 4, 0, 10, 0, 0, 6, 2, 2, }, +{7: 16, 4, 10, 8, 2, 4, 4, 8, 0, 0, 0, 6, 0, 2, 0, 0, }, +{b: 16, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, }, +{d: 16, 4, 0, 10, 4, 0, 4, 2, 8, 0, 6, 0, 0, 8, 2, 0, }, +{e: 16, 0, 0, 10, 0, 2, 0, 0, 0, 4, 2, 0, 6, 0, 4, 4, }, +{f: 16, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:48, 6:12, 8:15, 10:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 0, 0, 4, 12, 4, 4, 0, 0, 0, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 8, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 8, }, +{b: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:6, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, 0, 0, -8, -8, 8, 8, 0, -16, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, 0, 0, 0, 8, 8, -8, -8, 0, 0, -8, }, +{4: 16, 8, 8, -8, 0, 8, 0, -8, 8, 8, -8, -8, 8, -16, -8, -8, }, +{8: 16, -8, 8, 8, 0, -8, 0, 0, -8, 8, -8, 0, -8, 0, 0, 0, }, +{3: 16, 0, -16, 8, 8, 0, 8, -8, 0, -8, 8, -8, 0, 0, -8, 0, }, +{5: 16, -8, 8, -8, 0, 0, 0, 0, -8, -8, -8, -8, 0, 16, 0, 8, }, +{6: 16, 0, -8, -8, 0, -8, 0, 0, 0, 8, -8, 8, -8, 0, 0, 8, }, +{9: 16, 0, 8, 8, -8, 0, -8, 8, 8, -8, -16, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, 0, -8, -8, 0, 8, -8, 0, 8, 0, 0, 0, }, +{c: 16, -8, 8, -8, 0, -8, 0, 0, -8, 8, 8, 0, -8, 0, 0, 0, }, +{7: 16, 0, -8, -8, 8, 0, 8, 8, 0, -16, -8, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 8, 8, -16, -8, 0, -8, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{3: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , , x, x, x, x, x, x, , x, }, +{c: , x, x, x, x, x, x, , x, x, x, x, x, x, , x, }, +{7: , x, , x, , x, x, , x, x, x, , x, x, x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , x, x, x, , x, , , x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0011,1,}, +{0100,1101,1,}, +{1010,0111,1,}, +{1100,1001,1,}, +{1101,0001,1,}, +{1101,0100,1,}, +{1101,0101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x0a,0x04,}, {0x0d,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x0d,}}, +{{0x0a,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x04,}, {0x0d,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x04,0x09,0x0d,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x0d,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0d,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_204.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_204.txt new file mode 100644 index 0000000..c81919f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_204.txt @@ -0,0 +1,426 @@ +204 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0f,0x0e,0x0d, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 2, 2, 0, 2, 0, }, +{3: 0, 6, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, 4, 0, 0, }, +{a: 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, }, +{c: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 4, }, +{7: 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:5, 4:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 0, 4, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 0, 4, 10, 0, 0, 2, 6, 4, 0, 0, 2, 8, 4, 0, 8, }, +{8: 16, 0, 4, 0, 6, 2, 0, 0, 2, 4, 0, 2, 2, 0, 2, 0, }, +{3: 16, 6, 4, 0, 2, 8, 2, 0, 0, 0, 10, 0, 0, 4, 4, 8, }, +{5: 16, 2, 6, 0, 0, 0, 4, 2, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 0, 6, 4, 0, 2, 0, 10, 0, 0, 0, 2, 4, 4, 0, 0, }, +{9: 16, 0, 6, 0, 0, 2, 0, 4, 4, 2, 0, 0, 10, 4, 0, 0, }, +{a: 16, 2, 6, 0, 4, 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, 0, }, +{c: 16, 10, 4, 0, 2, 4, 2, 0, 0, 0, 6, 0, 0, 4, 8, 8, }, +{7: 16, 0, 4, 2, 0, 2, 6, 2, 0, 2, 0, 4, 0, 0, 2, 0, }, +{b: 16, 0, 4, 4, 2, 0, 0, 8, 10, 2, 0, 0, 6, 4, 0, 8, }, +{d: 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 16, 0, 0, }, +{e: 16, 4, 4, 0, 2, 0, 2, 0, 0, 2, 8, 2, 0, 4, 4, 0, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:38, 4:48, 6:16, 8:15, 10:6, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 12, 0, 0, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 8, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 0, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, -8, -16, 8, 0, 0, 8, 8, 0, -8, 0, -8, -8, 0, 8, }, +{8: 16, 0, -8, 8, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, }, +{3: 16, -8, 8, 8, 8, 0, -8, 0, -16, 0, 8, 0, -8, -8, 0, 0, }, +{5: 16, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, -8, 8, 0, 0, }, +{6: 16, 0, 0, -8, 8, 0, 0, -8, 8, -8, 0, 0, 8, -8, 0, -8, }, +{9: 16, -8, 0, 8, -8, -8, 0, -8, 8, -8, 0, 0, 8, 0, 0, 0, }, +{a: 16, 8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, -8, 0, 8, -8, -16, 0, 0, 8, }, +{7: 16, 0, -8, -8, 8, 0, 0, 0, -8, 0, -8, 0, 8, 0, 0, 0, }, +{b: 16, -8, -8, 8, -16, 8, 0, 0, 8, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, -8, -8, 8, -8, 0, 8, -8, 0, 16, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, -8, 0, 0, 8, 8, 0, 0, -8, }, +{f: 16, 0, 0, -8, -8, 0, -8, 8, 8, 8, 0, -8, 8, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, , x, x, x, x, , x, , x, x, x, x, x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, x, , x, x, x, , x, x, x, x, x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, , x, x, x, x, x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , x, , x, , , x, , x, , x, x, x, x, x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0100,0100,1,}, +{1000,1011,1,}, +{1001,0011,1,}, +{1011,1100,1,}, +{1110,0010,1,}, +{1110,1101,0,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x01,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x04,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x09,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x03,}}, +{{0x0d,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +204 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0f,0x0e,0x0d, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 6, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 2, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{6: 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 4, }, +{a: 0, 2, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 6, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, 0, }, +{e: 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:170, 2:56, 4:24, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:5, 4:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 6, 2, 0, 0, 2, 10, 0, 0, 8, 4, 4, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 0, 4, 0, }, +{4: 16, 2, 6, 10, 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 4, }, +{8: 16, 0, 6, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, }, +{3: 16, 4, 4, 0, 2, 8, 0, 2, 2, 0, 4, 2, 0, 0, 0, 4, }, +{5: 16, 0, 6, 2, 0, 2, 4, 0, 0, 0, 2, 6, 0, 0, 2, 0, }, +{6: 16, 0, 4, 6, 0, 0, 2, 10, 4, 0, 0, 2, 8, 8, 0, 4, }, +{9: 16, 2, 6, 4, 2, 0, 0, 0, 4, 0, 0, 0, 10, 0, 0, 4, }, +{a: 16, 2, 4, 0, 4, 0, 0, 0, 2, 6, 0, 2, 2, 0, 2, 0, }, +{c: 16, 4, 4, 0, 0, 10, 2, 0, 0, 2, 6, 0, 0, 8, 8, 4, }, +{7: 16, 2, 4, 2, 2, 0, 6, 2, 0, 0, 0, 4, 0, 0, 2, 0, }, +{b: 16, 0, 4, 8, 2, 0, 0, 4, 10, 2, 0, 0, 6, 8, 0, 4, }, +{d: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 16, 4, 0, }, +{e: 16, 0, 4, 0, 2, 4, 2, 0, 0, 2, 8, 2, 0, 0, 4, 4, }, +{f: 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:38, 4:48, 6:16, 8:15, 10:6, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, 4, 0, }, +{b: 0, 0, 0, 4, 4, 0, 4, 12, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +{f: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, -8, -16, 0, 8, 0, 0, -8, 0, 8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, -8, -8, 8, 0, 0, 8, 8, 0, 0, -8, -8, -8, 0, 0, }, +{8: 16, 8, -8, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, 8, -8, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, }, +{6: 16, 0, 8, -16, 8, 0, 0, -8, 8, 0, -8, 0, 8, -8, 0, -8, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, 0, 0, -8, -8, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, -16, -8, -8, 8, 0, 0, 0, 8, 8, }, +{7: 16, 0, 0, -8, 8, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, 0, 8, -16, 0, 0, -8, 8, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -16, -8, 8, 8, -8, 0, 8, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, 0, 8, 8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 16, -8, -8, 8, 8, 0, -8, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, x, x, x, x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , x, x, x, x, x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, x, x, x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, x, x, x, , , x, , x, , x, x, x, x, x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0011,0010,1,}, +{0011,1101,1,}, +{0011,1111,0,}, +{0100,0110,1,}, +{0110,1100,1,}, +{1000,1011,1,}, +{1001,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x09,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0e,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_205.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_205.txt new file mode 100644 index 0000000..fb98403 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_205.txt @@ -0,0 +1,426 @@ +205 Sbox: +LUT = { +0x0d,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{4: 0, 2, 0, 4, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 2, 2, 6, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, }, +{9: 0, 0, 0, 4, 2, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 2, 0, 2, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 0, 4, 0, 2, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 10, 4, 2, 4, 2, 8, 0, 4, 0, 0, 8, 0, 0, }, +{2: 16, 0, 8, 0, 0, 0, 10, 0, 8, 0, 10, 10, 8, 0, 10, 0, }, +{4: 16, 6, 4, 4, 2, 0, 8, 0, 0, 0, 0, 6, 0, 0, 2, 0, }, +{8: 16, 4, 4, 4, 4, 0, 0, 4, 10, 0, 0, 0, 6, 6, 0, 6, }, +{3: 16, 2, 0, 2, 0, 6, 4, 10, 8, 4, 4, 0, 0, 0, 0, 8, }, +{5: 16, 4, 4, 6, 2, 6, 6, 6, 0, 0, 2, 4, 0, 0, 0, 0, }, +{6: 16, 0, 6, 0, 0, 6, 8, 4, 0, 2, 0, 4, 2, 0, 0, 0, }, +{9: 16, 4, 4, 4, 6, 4, 0, 0, 10, 6, 0, 0, 6, 4, 0, 0, }, +{a: 16, 0, 4, 0, 0, 4, 2, 0, 8, 4, 0, 2, 4, 2, 0, 2, }, +{c: 16, 6, 4, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 6, 4, 6, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 2, 0, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 4, 8, 2, 2, 0, 4, 0, 2, 4, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 6, 0, 2, 6, 0, 0, 2, 0, 8, 0, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:34, 4:42, 6:26, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 8, 4, 0, 0, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, 0, 0, 8, 0, 0, -16, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 0, -8, 8, -8, -8, 16, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, 0, -8, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, -8, 8, 8, -16, 0, 0, 8, 8, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, -8, 0, 8, 8, -8, 0, 0, 0, 8, 0, 0, -16, -8, 8, }, +{5: 16, 0, 8, -8, 8, 0, 0, -8, -8, 0, -8, 8, -8, 0, -8, 8, }, +{6: 16, 0, -16, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, 0, -8, 0, 8, 0, -16, -8, 8, 0, -8, 0, }, +{a: 16, -8, -8, 0, -8, 0, 8, -8, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, -8, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 8, -8, 0, -8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, 8, 0, 0, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, , x, x, x, , x, , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , , x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, , x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, , x, , x, , , x, x, x, }, +{7: , x, , , x, , x, , x, , x, x, , x, , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0110,1,}, +{1000,1000,1,}, +{1100,1001,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x04,0x09,0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x0d,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +205 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x00,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{4: 0, 2, 0, 4, 0, 2, 2, 0, 4, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 4, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 2, 4, 0, 0, }, +{7: 0, 0, 2, 2, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 4, 2, 4, 0, 4, 0, 6, 2, 0, 6, 0, 0, }, +{2: 16, 0, 8, 4, 4, 0, 4, 6, 4, 4, 4, 6, 4, 4, 6, 6, }, +{4: 16, 10, 0, 4, 4, 2, 6, 0, 4, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 4, 0, 2, 4, 0, 2, 0, 6, 0, 2, 0, 2, 0, 0, 2, }, +{3: 16, 2, 0, 0, 0, 6, 6, 6, 4, 4, 4, 0, 0, 0, 2, 6, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{6: 16, 2, 0, 0, 4, 10, 6, 4, 0, 0, 0, 2, 4, 0, 0, 0, }, +{9: 16, 8, 8, 0, 10, 8, 0, 0, 10, 8, 0, 0, 8, 0, 2, 2, }, +{a: 16, 0, 0, 0, 0, 4, 0, 2, 6, 4, 0, 2, 2, 2, 2, 0, }, +{c: 16, 4, 10, 0, 0, 4, 2, 0, 0, 0, 6, 0, 2, 8, 4, 8, }, +{7: 16, 0, 10, 6, 0, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 2, 6, 4, 0, 2, 4, 0, 0, 0, }, +{d: 16, 8, 0, 0, 6, 0, 0, 0, 4, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 10, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 6, 4, 4, }, +{f: 16, 0, 0, 0, 6, 8, 0, 0, 0, 2, 6, 0, 4, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:34, 4:42, 6:26, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 12, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:4, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, -8, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, -8, 8, 0, 8, 0, -8, 0, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, -8, -8, 0, 8, 0, -8, 0, 0, 0, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 8, 8, -16, 0, 0, 16, 0, -8, -8, 0, 0, 0, -16, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -16, 0, -8, 8, 0, -8, 8, 8, 0, }, +{7: 16, 8, -8, -8, 8, 0, 0, 0, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, 8, 8, 8, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 8, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, , , x, , x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0010,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,1001,1,}, +{1100,1011,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x09,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x03,0x0c,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_206.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_206.txt new file mode 100644 index 0000000..89e3f9a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_206.txt @@ -0,0 +1,426 @@ +206 Sbox: +LUT = { +0x0e,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 8, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 4, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, }, +{a: 0, 0, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 6, 0, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 4, 0, 0, }, +{7: 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 6, 0, 4, 4, 6, 4, 6, 2, 0, }, +{2: 16, 0, 8, 6, 4, 0, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, }, +{4: 16, 0, 10, 4, 2, 0, 4, 4, 0, 0, 0, 6, 0, 2, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 2, 0, 2, 0, 6, 6, 4, 4, 4, 6, 0, 0, 0, 0, 6, }, +{5: 16, 0, 0, 2, 4, 8, 4, 6, 2, 0, 0, 0, 6, 0, 0, 0, }, +{6: 16, 4, 10, 4, 2, 4, 8, 6, 0, 0, 2, 8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 2, 2, 4, 0, 0, 4, 6, 0, 2, 0, 0, 2, 2, }, +{a: 16, 8, 8, 2, 8, 8, 2, 0, 8, 10, 0, 0, 10, 0, 0, 0, }, +{c: 16, 4, 10, 0, 0, 4, 0, 0, 2, 0, 6, 2, 0, 8, 4, 8, }, +{7: 16, 8, 0, 2, 0, 0, 0, 6, 2, 4, 0, 4, 6, 0, 0, 0, }, +{b: 16, 4, 0, 0, 2, 0, 2, 2, 0, 6, 2, 0, 4, 2, 0, 0, }, +{d: 16, 10, 0, 0, 0, 2, 0, 0, 0, 4, 6, 0, 4, 4, 2, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 0, 0, 4, 10, 0, 0, 0, 0, 6, 0, 4, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:34, 4:42, 6:26, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 4, 0, 12, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 12, 0, }, +{f: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, 0, 8, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, -8, 0, 0, 8, 0, -8, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 8, 0, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -16, 0, 16, -16, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, 0, -16, 8, -8, 0, 8, 8, 0, }, +{7: 16, -8, 0, 0, 8, 0, -8, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, -8, 0, 8, 0, 8, -8, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 8, -8, 0, 8, 0, -8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , , x, , x, x, , x, , x, x, x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, , x, , x, , x, x, , , x, x, x, }, +{7: , , x, , x, , , x, , x, x, x, , , x, x, }, +{b: , x, , , , x, , x, , x, x, , x, , x, x, }, +{d: , , , x, , x, , x, , x, x, , , x, x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0110,1010,1,}, +{1000,1000,1,}, +{1010,0110,1,}, +{1010,1010,0,}, +{1010,1100,1,}, +{1100,1010,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x0a,}}, +{{0x09,0x0a,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0b,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x03,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +206 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x0e,0x09,0x0a,0x0b,0x0c,0x0d,0x00,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, }, +{2: 0, 0, 8, 2, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 4, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{3: 0, 2, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 2, 4, 0, 2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 6, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, }, +{e: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 4, 0, 8, 4, 8, 4, 10, 0, 2, }, +{2: 16, 0, 8, 10, 8, 0, 0, 10, 0, 8, 10, 0, 0, 0, 10, 0, }, +{4: 16, 0, 6, 4, 0, 2, 2, 4, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{3: 16, 2, 0, 0, 0, 6, 8, 4, 4, 8, 4, 0, 0, 2, 0, 10, }, +{5: 16, 0, 6, 4, 0, 6, 4, 8, 0, 2, 0, 0, 2, 0, 0, 0, }, +{6: 16, 6, 4, 4, 0, 4, 6, 6, 0, 0, 0, 6, 2, 0, 2, 0, }, +{9: 16, 0, 4, 0, 4, 4, 2, 0, 4, 8, 2, 2, 0, 0, 2, 0, }, +{a: 16, 4, 4, 0, 6, 4, 0, 0, 6, 10, 0, 4, 6, 4, 0, 0, }, +{c: 16, 4, 4, 0, 0, 6, 0, 2, 0, 0, 6, 0, 2, 6, 4, 6, }, +{7: 16, 6, 4, 6, 0, 0, 0, 8, 2, 0, 2, 4, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 0, 6, 0, 0, 10, 0, 6, 4, 4, 0, 4, }, +{d: 16, 6, 4, 2, 0, 0, 0, 0, 0, 0, 8, 0, 2, 4, 6, 0, }, +{e: 16, 2, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 6, 0, 2, 6, 0, 0, 2, 0, 8, 0, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:34, 4:42, 6:26, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 8, 0, 0, 8, -8, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 16, -8, 0, 8, -8, 0, -8, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 8, 0, 0, -8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 8, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -16, 0, 0, 8, 0, 0, -8, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, -8, 8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, -8, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, -16, -8, 8, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, 0, -8, 8, 0, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, 8, 0, -8, 8, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 8, -8, -8, 8, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, 8, -8, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 8, 0, 0, 8, 0, 0, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, x, , x, x, x, x, }, +{a: , , x, x, , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , x, , , , , x, , x, x, , x, , x, x, }, +{d: , , , , x, , , x, , x, x, , , x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1000,1010,1,}, +{1100,1011,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_207.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_207.txt new file mode 100644 index 0000000..a26bc86 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_207.txt @@ -0,0 +1,426 @@ +207 Sbox: +LUT = { +0x08,0x0d,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x00,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 4, }, +{4: 0, 0, 0, 4, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 4, 0, 4, 0, 2, 2, 0, 2, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 8, 2, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 0, }, +{f: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:1, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 4, 2, 6, 2, 4, 0, 6, 0, 0, 6, 0, 0, }, +{2: 16, 0, 10, 0, 0, 0, 6, 0, 6, 0, 4, 4, 4, 4, 6, 4, }, +{4: 16, 8, 0, 4, 4, 0, 6, 0, 6, 0, 0, 2, 2, 0, 0, 0, }, +{8: 16, 4, 0, 2, 4, 0, 2, 0, 6, 0, 2, 0, 2, 0, 0, 2, }, +{3: 16, 0, 0, 2, 0, 6, 4, 4, 4, 6, 6, 0, 0, 0, 2, 6, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 0, 0, 0, 4, 0, 2, 2, 0, }, +{6: 16, 0, 2, 0, 0, 8, 4, 4, 4, 4, 0, 2, 2, 0, 2, 0, }, +{9: 16, 10, 8, 0, 10, 10, 0, 0, 8, 10, 0, 0, 8, 0, 0, 0, }, +{a: 16, 0, 2, 0, 0, 4, 2, 2, 4, 4, 0, 2, 2, 2, 0, 0, }, +{c: 16, 4, 8, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 8, 4, 10, }, +{7: 16, 2, 8, 2, 0, 0, 4, 0, 4, 2, 0, 4, 4, 0, 0, 2, }, +{b: 16, 0, 8, 4, 2, 2, 0, 4, 4, 0, 2, 2, 4, 0, 0, 0, }, +{d: 16, 8, 0, 0, 6, 0, 0, 0, 4, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 10, 4, 0, 0, 0, 6, 6, 0, 4, 0, 4, 6, 4, 4, }, +{f: 16, 2, 0, 0, 2, 8, 0, 0, 4, 4, 4, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:97, 2:39, 4:47, 6:21, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 4, 0, 4, 4, 8, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{6: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, -8, 0, 8, 0, -8, -8, 8, 0, }, +{2: 16, 0, -8, 0, 0, -8, 8, 0, 8, 0, 8, -8, -8, 8, -16, 0, }, +{4: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, -8, 0, 0, 8, -8, -8, -8, 0, 8, 0, 8, -8, -8, 8, }, +{5: 16, 0, 8, -16, 8, -8, 0, -8, 0, 8, -8, 8, 0, 0, -8, 0, }, +{6: 16, 8, -16, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, }, +{9: 16, -8, 8, 16, -8, -8, -8, 8, 0, -8, -8, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 0, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -16, -8, 8, 0, -8, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, 0, 0, 8, 0, 0, 0, 8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 8, -8, 0, 0, -8, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{e: 16, 8, -8, 0, 0, -16, 0, 0, 8, -8, 8, 0, 0, 8, -8, -8, }, +{f: 16, -8, -8, 0, 0, 8, 0, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, , , x, x, , x, , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , x, , , , , x, , x, , x, x, , x, , x, }, +{b: , , x, , x, x, x, , x, , x, , x, x, , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0110,1,}, +{0011,1110,1,}, +{0100,0101,1,}, +{0100,1001,0,}, +{0100,1100,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x09,0x02,0x0c,}, {0x04,}}, +{{0x09,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,}}, +{{0x0d,0x0e,}, {0x03,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +207 Inverse Sbox: +LUT = { +0x0d,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, }, +{2: 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 6, 0, }, +{4: 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, }, +{5: 0, 2, 2, 2, 2, 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 0, 2, 0, 0, 4, 0, 2, 0, }, +{9: 0, 0, 2, 2, 2, 0, 0, 0, 8, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, }, +{c: 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 6, 0, 2, 2, 0, 0, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:1, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 4, 0, 4, 0, 10, 0, 4, 2, 0, 8, 0, 2, }, +{2: 16, 0, 10, 0, 0, 0, 8, 2, 8, 2, 8, 8, 8, 0, 10, 0, }, +{4: 16, 4, 0, 4, 2, 2, 8, 0, 0, 0, 2, 2, 4, 0, 4, 0, }, +{8: 16, 4, 0, 4, 4, 0, 0, 0, 10, 0, 0, 0, 2, 6, 0, 2, }, +{3: 16, 2, 0, 0, 0, 6, 4, 8, 10, 4, 4, 0, 2, 0, 0, 8, }, +{5: 16, 6, 6, 6, 2, 4, 6, 4, 0, 2, 0, 4, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 10, 4, 0, 2, 0, 0, 4, 0, 6, 0, }, +{9: 16, 4, 6, 6, 6, 4, 0, 4, 8, 4, 0, 4, 4, 4, 6, 4, }, +{a: 16, 0, 0, 0, 0, 6, 0, 4, 10, 4, 0, 2, 0, 2, 0, 4, }, +{c: 16, 6, 4, 0, 2, 6, 0, 0, 0, 0, 6, 0, 2, 6, 4, 4, }, +{7: 16, 0, 4, 2, 0, 0, 4, 2, 0, 2, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 4, 2, 2, 0, 0, 2, 8, 2, 0, 4, 4, 0, 4, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:97, 2:39, 4:47, 6:21, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{3: 0, 0, 4, 4, 4, 12, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 16, -16, 0, 0, -16, 0, 0, 0, 0, 8, 0, 0, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, -8, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 8, 0, -8, 0, 0, -8, -8, -8, }, +{3: 16, -16, -8, 8, 0, 8, -8, 0, 0, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, 0, 8, 0, 8, -8, 8, -8, -8, 8, -8, 0, -8, 0, -8, 0, }, +{6: 16, 0, -8, 0, 0, -8, -8, 0, 0, 8, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, -8, -8, 8, 8, -8, -8, -8, 8, 8, -16, 0, }, +{a: 16, 0, -8, 0, 0, -8, 0, 0, 0, -8, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 8, 0, -8, 8, -8, -8, -8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 0, 0, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, -8, 0, 0, 8, 8, 0, 0, -8, 8, -8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, , , x, , x, , x, x, , x, , x, }, +{6: , , , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, x, , , x, , x, , x, , x, x, , x, }, +{a: , , , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , x, x, x, }, +{7: , , , x, , , x, , x, , x, x, , x, , x, }, +{b: , , , , , , x, , x, , x, , x, x, , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , , x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{1100,1011,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x05,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_208.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_208.txt new file mode 100644 index 0000000..2e89ac3 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_208.txt @@ -0,0 +1,426 @@ +208 Sbox: +LUT = { +0x08,0x00,0x0c,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x01,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, }, +{2: 0, 0, 8, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 0, 6, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 2, 0, 6, 0, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 2, 2, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{9: 0, 2, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 6:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 6, 0, 4, 2, 4, 0, 6, 0, 0, 6, 2, 0, }, +{2: 16, 0, 8, 6, 4, 0, 6, 4, 4, 4, 4, 4, 4, 4, 6, 6, }, +{4: 16, 8, 8, 10, 0, 8, 10, 8, 0, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 4, 10, 0, 6, 4, 0, 2, 8, 4, 2, 0, 8, 0, 0, 0, }, +{3: 16, 0, 0, 6, 4, 6, 0, 0, 0, 2, 6, 4, 4, 0, 2, 6, }, +{5: 16, 4, 0, 6, 2, 2, 4, 0, 2, 0, 0, 0, 2, 2, 0, 0, }, +{6: 16, 0, 8, 4, 0, 0, 4, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{9: 16, 10, 0, 4, 6, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 0, }, +{a: 16, 0, 10, 0, 6, 0, 0, 0, 4, 4, 0, 2, 4, 2, 0, 0, }, +{c: 16, 4, 10, 0, 0, 4, 0, 0, 2, 0, 6, 2, 0, 8, 4, 8, }, +{7: 16, 2, 0, 4, 0, 4, 0, 2, 2, 2, 0, 4, 2, 0, 0, 2, }, +{b: 16, 0, 0, 0, 4, 10, 6, 4, 0, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 8, 0, 4, 0, 2, 6, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 0, 0, 2, 8, 4, 4, 0, 0, 4, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:97, 2:39, 4:47, 6:21, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 12, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{4: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{5: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 12, 4, }, +{f: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:6, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, -8, 8, -8, 0, 8, 0, -8, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, 0, 8, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 0, 16, -16, 0, 0, 0, -8, 0, }, +{8: 16, 8, 8, 8, -8, 0, 0, 8, 0, -16, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, -8, 0, 0, 8, -8, -8, -8, 0, 8, 0, 8, -8, -8, 8, }, +{5: 16, -8, 8, 0, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, -8, 0, }, +{6: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 0, 0, 0, -8, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{a: 16, 0, -8, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, 0, -16, 8, -8, 0, 8, 8, 0, }, +{7: 16, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, -8, 0, 0, 8, 0, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, , , , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , x, , x, x, , x, }, +{a: , , x, , x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, , , , , , , , , x, x, , , , x, }, +{b: , , x, , x, x, , , , , x, , x, , , x, }, +{d: , x, x, x, x, x, , , , , x, , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0110,1,}, +{0110,0100,1,}, +{1010,0100,0,}, +{1010,1000,1,}, +{1010,1100,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x04,0x08,}, {0x0a,}}, +{{0x03,0x04,0x08,}, {0x0a,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x03,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x03,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x08,}, {0x0a,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x01,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +208 Inverse Sbox: +LUT = { +0x01,0x0c,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x02,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 4, 0, 2, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 6, 0, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 6, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, }, +{5: 0, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, 4, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 0, 4, 0, 2, 2, 0, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 6, 0, 2, 2, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 6:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 8, 4, 0, 4, 0, 10, 0, 4, 2, 0, 8, 0, 2, }, +{2: 16, 0, 8, 8, 10, 0, 0, 8, 0, 10, 10, 0, 0, 0, 10, 0, }, +{4: 16, 4, 6, 10, 0, 6, 6, 4, 4, 0, 0, 4, 0, 4, 0, 0, }, +{8: 16, 6, 4, 0, 6, 4, 2, 0, 6, 6, 0, 0, 4, 0, 0, 2, }, +{3: 16, 0, 0, 8, 4, 6, 2, 0, 0, 0, 4, 4, 10, 2, 0, 8, }, +{5: 16, 4, 6, 10, 0, 0, 4, 4, 4, 0, 0, 0, 6, 6, 0, 4, }, +{6: 16, 2, 4, 8, 2, 0, 0, 4, 0, 0, 0, 2, 4, 0, 2, 4, }, +{9: 16, 4, 4, 0, 8, 0, 2, 0, 4, 4, 2, 2, 0, 0, 2, 0, }, +{a: 16, 0, 4, 2, 4, 2, 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, }, +{c: 16, 6, 4, 0, 2, 6, 0, 0, 0, 0, 6, 0, 2, 6, 4, 4, }, +{7: 16, 0, 4, 8, 0, 4, 0, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 2, 8, 4, 2, 2, 0, 4, 0, 2, 4, 0, 0, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 2, 6, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, }, +{f: 16, 0, 6, 0, 0, 6, 0, 2, 0, 0, 8, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:97, 2:39, 4:47, 6:21, 8:13, 10:8, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:6, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 0, -8, 0, 8, 0, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 16, -8, 8, 0, -8, 8, -8, 0, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 8, 0, 8, 0, -8, -8, 8, 0, -8, -8, 8, 0, -16, 0, }, +{8: 16, 0, 8, 8, -8, 0, 8, 8, -8, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -16, -8, 0, 0, 8, 0, -8, 0, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 8, 0, 0, -16, 8, 8, -8, 0, 0, 0, -8, -8, }, +{6: 16, 0, -8, 0, 0, 0, -8, 8, 0, 0, -8, 8, -8, 0, 8, -8, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, -8, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 0, 0, 0, 0, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 8, 0, -8, 8, -8, -8, -8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, -8, -8, 0, 0, 8, 8, }, +{b: 16, 0, -8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , , , x, x, x, , , x, }, +{5: , , x, x, , , x, , , , x, x, , x, , x, }, +{6: , , x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , , x, x, , , , , x, , x, , x, x, , x, }, +{a: , , x, , x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , , x, x, , , , , , , x, x, , , , x, }, +{b: , , x, , , , , , , , x, , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,1111,1,}, +{0110,0101,1,}, +{1100,1011,1,}, +{1110,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x05,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x02,0x03,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,0x02,0x03,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_209.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_209.txt new file mode 100644 index 0000000..61baefc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_209.txt @@ -0,0 +1,426 @@ +209 Sbox: +LUT = { +0x04,0x00,0x01,0x0c,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{3: 0, 2, 0, 0, 4, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 4, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 4, 0, }, +{c: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, 4, 0, 0, 2, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 6, }, +{d: 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, 0, }, +{e: 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 6, 4, 0, 6, 0, 4, 2, 4, 2, 0, 6, 0, 0, }, +{2: 16, 0, 6, 6, 4, 0, 2, 6, 2, 4, 6, 0, 0, 0, 4, 0, }, +{4: 16, 4, 4, 10, 0, 4, 6, 6, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 4, 4, 0, 10, 4, 0, 0, 6, 6, 0, 4, 6, 0, 0, 4, }, +{3: 16, 2, 0, 4, 8, 6, 2, 0, 0, 0, 4, 10, 4, 0, 0, 8, }, +{5: 16, 8, 2, 4, 0, 0, 4, 2, 0, 2, 4, 0, 0, 4, 2, 0, }, +{6: 16, 0, 8, 4, 0, 2, 0, 4, 2, 0, 4, 2, 0, 2, 4, 0, }, +{9: 16, 8, 0, 0, 4, 2, 0, 2, 4, 2, 4, 0, 0, 4, 0, 2, }, +{a: 16, 0, 10, 0, 4, 0, 2, 0, 0, 4, 6, 0, 2, 0, 4, 0, }, +{c: 16, 10, 8, 0, 0, 10, 0, 0, 0, 0, 8, 0, 0, 10, 8, 10, }, +{7: 16, 0, 0, 6, 0, 8, 0, 2, 0, 0, 6, 4, 0, 0, 2, 4, }, +{b: 16, 0, 0, 4, 10, 8, 0, 0, 0, 2, 4, 4, 8, 2, 0, 6, }, +{d: 16, 4, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 4, 2, 0, }, +{e: 16, 2, 4, 0, 2, 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:38, 4:47, 6:21, 8:12, 10:9, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 4, 4, 4, 12, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 8, 4, 0, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:9, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, 0, 0, -8, 8, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 8, -8, 0, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 8, -8, -8, 8, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 8, -8, 8, 8, 8, -8, -8, -16, 0, 0, 0, 0, -8, }, +{3: 16, -8, 0, 8, 8, 8, 0, 0, -16, -8, 0, 8, 0, -8, -8, 0, }, +{5: 16, 0, 0, 0, 8, -16, 0, 0, -8, 8, 0, 0, -8, 0, 0, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 8, -16, 0, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 0, -8, -8, 0, 0, 8, -8, 0, 0, 8, -8, 0, 8, }, +{a: 16, 8, -8, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 8, 0, 0, }, +{c: 16, 0, 8, -8, -8, 8, -8, -8, -8, -8, 16, -8, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 8, 8, -8, 0, -8, -8, 0, 0, 8, 0, 0, 0, }, +{b: 16, -8, -8, 0, -16, 8, 8, 0, 8, 8, 0, 0, -8, -8, 0, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, -8, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, x, , , x, , x, , x, x, , x, }, +{a: , , x, x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, x, x, , , , , x, x, , , , x, }, +{b: , , x, , , , , , , , x, , x, , , x, }, +{d: , , , x, x, x, , , , , x, , , x, , x, }, +{e: , , x, x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0011,0101,1,}, +{1000,1011,1,}, +{1001,0011,1,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1100,1000,1,}, +{1100,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +209 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 4, 0, 2, 0, 0, 0, 2, 0, 0, }, +{4: 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 6, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, 2, 4, 0, 0, 0, 0, }, +{5: 0, 2, 2, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 2, 2, 2, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 0, 0, 2, }, +{7: 0, 2, 0, 2, 4, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, 2, 0, 2, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 6, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:2, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 4, 2, 8, 0, 8, 0, 10, 0, 0, 4, 2, 0, }, +{2: 16, 0, 6, 4, 4, 0, 2, 8, 0, 10, 8, 0, 0, 2, 4, 0, }, +{4: 16, 6, 6, 10, 0, 4, 4, 4, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 4, 4, 0, 10, 8, 0, 0, 4, 4, 0, 0, 10, 2, 2, 0, }, +{3: 16, 0, 0, 4, 4, 6, 0, 2, 2, 0, 10, 8, 8, 0, 0, 4, }, +{5: 16, 6, 2, 6, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{6: 16, 0, 6, 6, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 16, 4, 2, 0, 6, 0, 0, 2, 4, 0, 0, 0, 0, 2, 2, 2, }, +{a: 16, 2, 4, 0, 6, 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, }, +{c: 16, 4, 6, 0, 0, 4, 4, 4, 4, 6, 8, 6, 4, 4, 4, 6, }, +{7: 16, 2, 0, 6, 4, 10, 0, 2, 0, 0, 0, 4, 4, 0, 0, 0, }, +{b: 16, 0, 0, 4, 6, 4, 0, 0, 0, 2, 0, 0, 8, 2, 0, 6, }, +{d: 16, 6, 0, 0, 0, 0, 4, 2, 4, 0, 10, 0, 2, 4, 0, 0, }, +{e: 16, 0, 4, 0, 0, 0, 2, 4, 0, 4, 8, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 4, 4, 8, 0, 0, 2, 0, 10, 4, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:38, 4:47, 6:21, 8:12, 10:9, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:3, 4:9, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, -16, 8, 8, 0, -8, 0, 0, 0, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, 0, 8, 8, 0, -16, 0, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 8, 0, 0, -8, -8, 0, 16, 0, -8, -8, -8, }, +{3: 16, -8, -8, 0, 8, 8, -8, 0, -8, -16, 0, 0, 8, 0, 0, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, -8, 8, 0, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 8, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 0, 0, -8, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 0, -8, -8, 8, 0, -8, -8, -8, 8, -16, -8, 8, 8, 8, }, +{7: 16, 0, 0, 0, 8, 8, 0, 8, -8, -8, -8, 0, 0, -8, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 8, 8, -8, 0, 0, -8, 0, -8, }, +{d: 16, -8, 8, 0, -8, -8, -8, 0, 8, -8, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, -8, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, -8, -8, 0, -16, 8, -8, 0, 8, 8, 0, 0, -8, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , x, , x, x, , x, }, +{a: , x, x, , x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, x, , x, x, , , , , x, , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0011,0010,1,}, +{0111,0100,1,}, +{0111,1000,0,}, +{0111,1100,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1010,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x07,}}, +{{0x01,0x04,0x08,}, {0x07,}}, +{{0x03,0x04,0x08,}, {0x07,}}, +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x0c,}, {0x07,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x09,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_210.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_210.txt new file mode 100644 index 0000000..351062f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_210.txt @@ -0,0 +1,426 @@ +210 Sbox: +LUT = { +0x04,0x00,0x01,0x0e,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, }, +{2: 0, 0, 6, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, }, +{3: 0, 2, 0, 0, 2, 6, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 0, 2, 4, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 2, 0, 0, 4, 2, 0, 0, 0, 2, 0, 4, }, +{a: 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 0, 2, 2, 0, 2, 0, }, +{c: 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 2, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 4, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 6, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 2, 0, 0, 0, 4, 0, 10, 4, 8, 4, 8, 0, 2, }, +{2: 16, 0, 6, 8, 4, 0, 2, 4, 2, 8, 4, 0, 0, 0, 10, 0, }, +{4: 16, 0, 6, 4, 0, 0, 2, 6, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 16, 0, 4, 4, 4, 0, 2, 0, 2, 8, 0, 2, 2, 0, 4, 0, }, +{3: 16, 2, 0, 0, 2, 6, 8, 4, 4, 10, 4, 0, 0, 0, 0, 8, }, +{5: 16, 2, 2, 0, 2, 6, 4, 6, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 16, 4, 6, 4, 0, 6, 4, 10, 0, 0, 0, 6, 4, 4, 0, 0, }, +{9: 16, 0, 0, 2, 0, 6, 4, 0, 4, 10, 0, 0, 0, 2, 0, 4, }, +{a: 16, 4, 6, 4, 4, 4, 4, 0, 4, 8, 0, 6, 6, 4, 6, 4, }, +{c: 16, 8, 4, 0, 2, 4, 0, 0, 2, 0, 10, 0, 0, 10, 4, 4, }, +{7: 16, 10, 0, 2, 0, 2, 0, 6, 0, 0, 4, 4, 0, 4, 0, 0, }, +{b: 16, 8, 0, 0, 2, 0, 0, 4, 0, 10, 4, 4, 8, 6, 0, 2, }, +{d: 16, 4, 0, 0, 0, 0, 0, 4, 2, 0, 6, 0, 6, 8, 2, 0, }, +{e: 16, 0, 4, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 2, 2, 2, 4, 0, 0, 2, 0, 6, 0, 2, 0, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:38, 4:47, 6:21, 8:12, 10:9, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, 0, 8, -8, 8, 0, -16, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 8, -8, 0, -8, 8, 0, 0, -8, 0, 8, -16, -8, }, +{4: 16, 0, 0, -8, 8, 0, 0, 0, 8, 0, -8, -8, 0, 0, -8, 0, }, +{8: 16, 0, 0, 0, -8, 0, 0, 8, -8, 0, -8, 8, 0, 8, -8, -8, }, +{3: 16, -8, 0, 8, 8, 0, 0, -8, -16, 0, 0, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, 0, -8, 0, 0, 8, -8, 0, -8, 0, }, +{6: 16, 0, -16, 0, 8, 0, -8, 0, 8, -8, -8, 8, -8, 0, 8, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 8, -8, -8, 8, }, +{a: 16, 8, -16, 8, -8, -8, 8, -8, -8, 8, -8, -8, 8, 0, 8, 0, }, +{c: 16, 0, 16, 0, -8, 0, -8, 0, -8, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, -8, 0, -8, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, -8, 0, 0, -16, 0, 8, -8, 8, 0, 0, 8, 0, -8, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, -8, 0, 8, -8, 0, 8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 0, -8, 0, 8, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, , x, x, x, , x, , x, x, x, , , x, x, }, +{9: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , , , x, x, x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, x, x, , x, , x, x, , , x, , x, }, +{7: , x, , x, x, x, , x, , x, x, x, , , x, x, }, +{b: , , , , , , , x, , x, x, , x, , x, x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , , x, x, x, , x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0110,1,}, +{0010,1010,1,}, +{0010,1100,0,}, +{0111,0001,1,}, +{1000,1011,1,}, +{1001,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x0a,0x0c,}, {0x02,}}, +{{0x09,0x0a,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x02,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x07,}}, +{{0x03,0x04,}, {0x09,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x09,0x0b,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +210 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x0e,0x09,0x0a,0x0b,0x0c,0x0d,0x03,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{4: 0, 2, 4, 4, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +{3: 0, 0, 0, 0, 0, 6, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, }, +{5: 0, 0, 2, 2, 2, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, 2, 2, 2, }, +{7: 0, 4, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 6, 4, 2, 0, }, +{e: 0, 0, 2, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, }, +{f: 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 2, 4, 0, 4, 8, 10, 8, 4, 0, 0, }, +{2: 16, 0, 6, 6, 4, 0, 2, 6, 0, 6, 4, 0, 0, 0, 4, 2, }, +{4: 16, 2, 8, 4, 4, 0, 0, 4, 2, 4, 0, 2, 0, 0, 0, 2, }, +{8: 16, 0, 4, 0, 4, 2, 2, 0, 0, 4, 2, 0, 2, 0, 2, 2, }, +{3: 16, 0, 0, 0, 0, 6, 6, 6, 6, 4, 4, 2, 0, 0, 2, 4, }, +{5: 16, 0, 2, 2, 2, 8, 4, 4, 4, 4, 0, 0, 0, 0, 2, 0, }, +{6: 16, 4, 4, 6, 0, 4, 6, 10, 0, 0, 0, 6, 4, 4, 0, 0, }, +{9: 16, 0, 2, 2, 2, 4, 0, 0, 4, 4, 2, 0, 0, 2, 0, 2, }, +{a: 16, 10, 8, 0, 8, 10, 0, 0, 10, 8, 0, 0, 10, 0, 0, 0, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 8, 0, 2, 2, 0, 0, 6, 0, 6, 0, 4, 4, 0, 0, 0, }, +{b: 16, 4, 0, 0, 2, 0, 0, 4, 0, 6, 0, 0, 8, 6, 0, 2, }, +{d: 16, 8, 0, 0, 0, 0, 0, 4, 2, 4, 10, 4, 6, 8, 2, 0, }, +{e: 16, 0, 10, 0, 4, 0, 2, 0, 0, 6, 4, 0, 0, 2, 4, 0, }, +{f: 16, 2, 0, 2, 0, 8, 0, 0, 4, 4, 4, 0, 2, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:98, 2:38, 4:47, 6:21, 8:12, 10:9, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 4, 8, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, -8, 0, -16, 0, 8, -8, -8, 0, 8, 0, }, +{2: 16, 8, -8, 0, 8, -8, 8, -8, 8, 0, 0, -8, -8, 0, -8, 0, }, +{4: 16, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, -16, 0, 0, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 0, -8, 0, 0, 8, -8, 0, -8, 0, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, -8, -8, 0, 8, 8, 0, -8, 8, }, +{5: 16, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 8, 0, 0, -16, 0, }, +{6: 16, 0, 0, -16, 8, -8, 0, 0, 8, -8, -8, 8, 0, -8, 8, 0, }, +{9: 16, 0, 8, 0, -8, 0, 0, 0, 8, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 16, -8, -8, 0, -8, -8, 8, -8, -8, 8, -8, 8, 8, }, +{c: 16, 0, 0, -16, -8, 8, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, }, +{7: 16, 0, 0, 0, 8, 0, 0, 8, -8, 0, -8, -8, 0, -8, 8, -8, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, 8, 0, -8, 8, -8, -8, 8, 0, }, +{d: 16, -8, 0, 0, -16, 0, -8, -8, 8, 0, 0, 8, 0, 8, 8, -8, }, +{e: 16, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 8, 0, 0, -8, -8, }, +{f: 16, -8, 0, 0, -8, 0, -8, 8, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, , x, x, x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , , x, x, , x, , x, x, , x, , x, x, }, +{c: , x, x, , x, x, , x, , x, x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , x, , , x, x, , x, , x, x, , x, , x, x, }, +{d: , , , , , , , x, , x, x, , , x, x, x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0100,0110,1,}, +{0100,1010,0,}, +{0100,1100,1,}, +{0111,0100,1,}, +{1000,1101,1,}, +{1001,0001,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,}}, +{{0x01,0x0a,0x0c,}, {0x04,}}, +{{0x09,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x03,0x04,0x07,}}, +{{0x02,0x0c,}, {0x01,0x04,0x05,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x07,}}, +{{0x09,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x02,0x09,0x0b,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x09,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_211.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_211.txt new file mode 100644 index 0000000..a0e86dc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_211.txt @@ -0,0 +1,426 @@ +211 Sbox: +LUT = { +0x08,0x00,0x01,0x03,0x02,0x0f,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, }, +{2: 0, 0, 4, 2, 4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, }, +{8: 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 4, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 4, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 4, 6, 0, 0, }, +{e: 0, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:4, 4:4, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 2, 0, 2, 0, 0, 8, 0, 4, 4, 4, 10, 8, 0, 0, }, +{2: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{4: 16, 0, 0, 6, 2, 4, 0, 0, 4, 6, 0, 6, 0, 4, 6, 2, }, +{8: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{3: 16, 2, 0, 4, 0, 8, 2, 0, 4, 4, 0, 4, 2, 0, 0, 2, }, +{5: 16, 0, 6, 0, 4, 0, 6, 2, 2, 4, 0, 6, 0, 4, 0, 6, }, +{6: 16, 4, 0, 0, 0, 2, 0, 8, 0, 6, 4, 6, 0, 0, 2, 0, }, +{9: 16, 2, 0, 6, 0, 4, 0, 0, 8, 6, 0, 0, 0, 4, 0, 2, }, +{a: 16, 4, 6, 4, 4, 4, 6, 4, 4, 8, 6, 0, 6, 0, 4, 4, }, +{c: 16, 8, 0, 2, 0, 0, 0, 6, 0, 4, 8, 4, 4, 10, 0, 2, }, +{7: 16, 8, 4, 4, 0, 4, 4, 10, 0, 0, 0, 10, 0, 0, 2, 2, }, +{b: 16, 10, 0, 0, 2, 2, 0, 4, 0, 6, 0, 4, 4, 0, 0, 0, }, +{d: 16, 4, 0, 6, 4, 0, 6, 4, 4, 0, 6, 0, 4, 10, 0, 0, }, +{e: 16, 0, 2, 6, 2, 0, 2, 2, 0, 4, 0, 0, 0, 2, 4, 0, }, +{f: 16, 0, 0, 0, 0, 2, 6, 0, 2, 4, 2, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:38, 4:52, 6:24, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, 0, 0, 0, 0, 8, 0, -8, -8, 8, -16, }, +{2: 16, 8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, -8, }, +{4: 16, 8, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 8, 0, 8, -8, 0, 0, 0, 0, -8, 0, 0, -8, 8, -8, -8, }, +{3: 16, -16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, -8, 0, -8, 8, -8, 8, 0, 0, 0, -8, 0, -8, 8, -8, 8, }, +{6: 16, 8, -8, -8, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 8, }, +{9: 16, -8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, 8, -8, -8, 8, }, +{a: 16, 8, -8, 8, -8, -8, 8, -16, -8, 8, -8, -8, 0, 0, 8, 8, }, +{c: 16, 8, 0, -16, 0, 0, -8, 0, 8, -8, 0, 0, -8, -8, 8, 8, }, +{7: 16, -8, -8, -8, 8, 0, 0, 16, -8, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, 0, 8, 0, 0, -8, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, -8, 8, -8, -8, 0, 0, -16, 8, 0, 0, 8, 0, 0, 8, -8, }, +{e: 16, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, -8, -8, }, +{f: 16, -8, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, x, , x, , x, x, x, x, , x, x, x, x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, , , x, x, , x, x, x, x, x, x, , x, x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0001,0011,1,}, +{0100,1100,1,}, +{0110,0111,0,}, +{0110,1010,1,}, +{0110,1101,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x09,0x0a,0x04,}, {0x06,}}, +{{0x01,0x0a,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x0b,0x04,}, {0x03,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x06,0x09,0x0f,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x06,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x01,0x06,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +211 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x08,0x0f,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x05, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{2: 0, 2, 4, 0, 4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, }, +{8: 0, 2, 4, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 0, 0, 2, 0, 0, 0, 2, 2, 2, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 6, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 8, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 6, 4, 0, 0, 0, }, +{b: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, }, +{f: 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:62, 4:18, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:4, 4:4, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 4, 2, 4, 8, 8, 10, 4, 0, 0, }, +{2: 16, 2, 8, 0, 4, 0, 6, 0, 0, 6, 0, 4, 0, 0, 2, 0, }, +{4: 16, 0, 2, 6, 0, 4, 0, 0, 6, 4, 2, 4, 0, 6, 6, 0, }, +{8: 16, 2, 4, 2, 8, 0, 4, 0, 0, 4, 0, 0, 2, 4, 2, 0, }, +{3: 16, 0, 2, 4, 0, 8, 0, 2, 4, 4, 0, 4, 2, 0, 0, 2, }, +{5: 16, 0, 4, 0, 4, 2, 6, 0, 0, 6, 0, 4, 0, 6, 2, 6, }, +{6: 16, 8, 0, 0, 0, 0, 2, 8, 0, 4, 6, 10, 4, 4, 2, 0, }, +{9: 16, 0, 2, 4, 2, 4, 2, 0, 8, 4, 0, 0, 0, 4, 0, 2, }, +{a: 16, 4, 4, 6, 4, 4, 4, 6, 6, 8, 4, 0, 6, 0, 4, 4, }, +{c: 16, 4, 0, 0, 2, 0, 0, 4, 0, 6, 8, 0, 0, 6, 0, 2, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 10, 0, 0, 2, 2, 0, 0, 0, 6, 4, 0, 4, 4, 0, 0, }, +{d: 16, 8, 0, 4, 4, 0, 4, 0, 4, 0, 10, 0, 0, 10, 2, 2, }, +{e: 16, 0, 2, 6, 2, 0, 0, 2, 0, 4, 0, 2, 0, 0, 4, 2, }, +{f: 16, 0, 0, 2, 0, 2, 6, 0, 2, 4, 2, 2, 0, 0, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:38, 4:52, 6:24, 8:11, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 0, 8, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, }, +{9: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 8, -8, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 8, 0, 8, 0, -8, 8, 0, -8, 0, 0, 0, -8, 0, -8, -8, }, +{4: 16, 8, 8, -8, 0, 0, -8, -8, 8, 0, 0, -8, 8, 0, -8, -8, }, +{8: 16, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, -8, -16, }, +{3: 16, -8, -8, 8, 0, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, 8, }, +{5: 16, -8, 0, -8, 0, -8, 8, -8, -8, 8, 0, 8, 0, 0, -8, 8, }, +{6: 16, 8, 0, -16, 0, 0, -8, 0, -8, -8, 0, 0, -8, 8, 8, 8, }, +{9: 16, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, 8, }, +{a: 16, 8, -8, 8, -8, -8, 0, -8, 0, 8, -16, -8, 8, -8, 8, 8, }, +{c: 16, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 0, -8, -8, 8, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{b: 16, -8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, -8, 8, -8, }, +{d: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, -8, 8, -8, }, +{e: 16, 8, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, -8, -8, }, +{f: 16, -8, 0, -8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{3: , , x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{5: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{9: , , x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, x, , , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, x, x, x, x, x, , x, x, }, +{7: , , x, , , x, , x, x, x, x, , x, x, x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , x, x, x, , x, x, x, x, x, x, , x, x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0001,0001,1,}, +{0100,0110,1,}, +{1100,0111,1,}, +{1100,1010,1,}, +{1100,1101,0,}, +{1110,1001,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x04,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x0f,}}, +{{0x05,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x01,}}, +{{0x05,0x02,}, {0x05,0x09,0x0c,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x04,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_212.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_212.txt new file mode 100644 index 0000000..00c76c8 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_212.txt @@ -0,0 +1,414 @@ +212 Sbox: +LUT = { +0x08,0x06,0x01,0x02,0x03,0x05,0x00,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 8, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +{3: 0, 0, 0, 2, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 8, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 2, 0, 2, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 0, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:163, 2:73, 4:12, 6:5, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{2: 16, 4, 8, 6, 4, 6, 4, 4, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 6, 4, 6, 2, 6, 6, 4, 0, 0, 0, 4, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{3: 16, 4, 4, 6, 0, 6, 6, 4, 0, 2, 0, 6, 0, 0, 0, 2, }, +{5: 16, 4, 6, 4, 4, 4, 8, 6, 6, 4, 4, 4, 0, 6, 0, 4, }, +{6: 16, 6, 6, 4, 2, 4, 4, 6, 0, 2, 0, 6, 0, 0, 0, 0, }, +{9: 16, 2, 6, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 0, 2, 2, }, +{a: 16, 0, 6, 0, 8, 0, 6, 0, 0, 4, 2, 0, 2, 4, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 0, 4, 0, 2, 2, 4, 2, 8, 0, 4, 0, 4, 2, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, 2, 2, 4, }, +{e: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 4, 2, 4, 0, 2, 0, 2, 2, 0, 4, 2, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:86, 2:46, 4:55, 6:32, 8:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -8, 0, -8, 8, -8, 8, -8, 0, 8, -16, -8, }, +{4: 16, 0, 8, 0, 8, 8, -8, -8, 0, 8, -8, 0, 0, -8, -8, -8, }, +{8: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 0, 8, 8, 0, -8, -8, 0, 0, 0, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 8, -16, 8, -8, 0, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, -8, -8, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, 0, 8, 0, 0, 0, -8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, -8, 8, -16, 0, 0, 0, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, -8, 8, -8, -8, 0, -8, 0, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 8, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , , , x, x, , , x, }, +{5: , , , x, x, x, x, x, , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, , , , x, , x, , , , , x, , , x, }, +{d: , , , x, , x, , x, , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0101,1,}, +{0110,1010,1,}, +{1000,1000,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +212 Inverse Sbox: +LUT = { +0x06,0x02,0x03,0x04,0x08,0x05,0x01,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{3: 0, 2, 2, 2, 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 8, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 0, 0, 4, 2, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, 2, 0, 0, 4, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{7: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:163, 2:73, 4:12, 6:5, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 6, 0, 4, 4, 6, 2, 0, 0, 6, 0, 2, 0, 0, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 0, 4, 0, }, +{4: 16, 4, 6, 6, 0, 6, 4, 4, 0, 0, 2, 6, 0, 0, 2, 0, }, +{8: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{3: 16, 6, 6, 6, 0, 6, 4, 4, 0, 0, 0, 4, 2, 0, 0, 2, }, +{5: 16, 4, 4, 6, 4, 6, 8, 4, 0, 6, 0, 4, 4, 6, 4, 4, }, +{6: 16, 6, 4, 4, 0, 4, 6, 6, 0, 0, 0, 6, 2, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 6, 0, 4, 0, 0, 0, 8, 0, 4, 2, }, +{a: 16, 0, 4, 0, 8, 2, 4, 2, 2, 4, 2, 0, 0, 4, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{7: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 0, 4, 2, 2, 0, 0, 0, 4, 2, 2, 2, 4, 2, 0, 0, }, +{d: 16, 2, 0, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, 2, 2, 4, }, +{e: 16, 2, 6, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 4, 2, 4, 0, 2, 0, 2, 2, 0, 4, 2, 2, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:86, 2:46, 4:55, 6:32, 8:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 0, 0, 4, 4, 4, 4, 8, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:113, 4:116, 8:22, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 8, 0, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 8, 0, -8, 8, 8, -8, -8, 0, 0, 0, -8, 8, 0, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 8, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 8, 8, -8, -8, 0, 0, 8, 0, 0, -8, -8, 0, }, +{5: 16, -8, 8, -8, 8, -8, 8, -16, -8, 8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 0, -8, -8, 8, -8, -8, 8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, -8, 0, 0, 8, -8, 8, 8, }, +{c: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, -8, -8, 0, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -8, -8, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 0, -8, -8, }, +{f: 16, 0, 0, 0, -8, 8, 0, 8, -8, -8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , x, x, , x, , , , x, x, , , x, }, +{5: , x, , , x, , x, x, , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, , , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, x, , x, , , x, , , , , x, , , x, }, +{d: , x, , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 4 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1000,1100,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_213.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_213.txt new file mode 100644 index 0000000..4b61853 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_213.txt @@ -0,0 +1,426 @@ +213 Sbox: +LUT = { +0x08,0x00,0x01,0x0a,0x02,0x05,0x06,0x07,0x04,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, }, +{2: 0, 0, 8, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 0, 4, 0, 0, }, +{8: 0, 2, 2, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, }, +{3: 0, 2, 2, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 4, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 2, 4, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 2, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 6, 2, 2, 0, }, +{d: 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:67, 4:15, 6:5, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 8, 8, 0, 0, 4, 4, 0, 2, 10, 2, 0, 0, }, +{2: 16, 4, 8, 6, 4, 4, 4, 4, 6, 6, 4, 6, 4, 0, 4, 0, }, +{4: 16, 0, 4, 8, 2, 0, 2, 4, 4, 2, 0, 2, 0, 4, 0, 0, }, +{8: 16, 6, 6, 0, 6, 4, 0, 0, 6, 4, 2, 0, 4, 0, 2, 0, }, +{3: 16, 6, 6, 0, 4, 6, 2, 0, 4, 6, 0, 0, 4, 0, 0, 2, }, +{5: 16, 0, 6, 0, 0, 0, 8, 2, 6, 0, 4, 4, 0, 2, 0, 0, }, +{6: 16, 0, 4, 4, 0, 2, 0, 8, 4, 2, 0, 2, 0, 0, 2, 4, }, +{9: 16, 6, 4, 6, 4, 4, 4, 4, 8, 6, 4, 0, 4, 4, 0, 6, }, +{a: 16, 4, 4, 0, 8, 10, 2, 0, 4, 6, 2, 0, 8, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 0, 0, 4, 2, 0, 2, 2, }, +{b: 16, 4, 4, 0, 10, 8, 0, 0, 4, 4, 0, 0, 10, 2, 2, 0, }, +{d: 16, 2, 0, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, 6, 2, 0, }, +{e: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 2, 0, 4, 6, 0, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:44, 4:54, 6:24, 8:11, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{c: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -8, 8, -16, }, +{2: 16, 8, -8, 8, 8, -8, 8, -8, 8, -8, 0, -16, 0, 8, -8, -8, }, +{4: 16, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, 0, 8, -8, 0, -8, }, +{8: 16, 8, 8, 8, -8, 0, 0, 8, -8, -8, 0, 0, -8, 0, -8, -8, }, +{3: 16, -8, -8, 8, 8, 0, 0, -8, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, 0, 8, }, +{6: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, -8, 0, 8, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 8, 0, -8, -16, 8, 0, -8, 8, }, +{a: 16, 0, -8, 8, -8, 0, 0, -16, -8, 8, -8, 0, 0, 0, 8, 8, }, +{c: 16, 0, 8, -16, 0, 0, 0, -8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, -8, -8, 0, 0, 0, 16, 0, 0, 0, -8, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, , x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, , , , , x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , x, x, , , x, x, x, }, +{7: , x, , x, , x, , , , x, , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0110,1,}, +{0100,1100,1,}, +{0110,1010,1,}, +{0111,0010,1,}, +{0111,1001,1,}, +{0111,1011,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x07,}}, +{{0x09,0x02,0x04,}, {0x07,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x0f,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x07,0x09,0x0e,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x02,}, {0x07,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +213 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0a,0x08,0x05,0x06,0x07,0x00,0x09,0x03,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 0, 8, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, }, +{8: 0, 4, 0, 2, 6, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 2, 4, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 2, 0, 2, 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 6, 2, 0, 0, }, +{d: 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:67, 4:15, 6:5, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 0, 6, 6, 0, 0, 6, 4, 0, 0, 4, 2, 2, 0, }, +{2: 16, 4, 8, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 0, 6, 8, 0, 0, 0, 4, 6, 0, 2, 2, 0, 4, 0, 0, }, +{8: 16, 8, 4, 2, 6, 4, 0, 0, 4, 8, 0, 2, 10, 0, 0, 0, }, +{3: 16, 8, 4, 0, 4, 6, 0, 2, 4, 10, 0, 0, 8, 0, 0, 2, }, +{5: 16, 0, 4, 2, 0, 2, 8, 0, 4, 2, 4, 4, 0, 2, 0, 0, }, +{6: 16, 0, 4, 4, 0, 0, 2, 8, 4, 0, 2, 2, 0, 0, 2, 4, }, +{9: 16, 4, 6, 4, 6, 4, 6, 4, 8, 4, 4, 0, 4, 4, 0, 6, }, +{a: 16, 4, 6, 2, 4, 6, 0, 2, 6, 6, 0, 0, 4, 0, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{7: 16, 2, 6, 2, 0, 0, 4, 2, 0, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 10, 4, 0, 4, 4, 0, 0, 4, 8, 0, 2, 10, 2, 0, 0, }, +{d: 16, 2, 0, 4, 0, 0, 2, 0, 4, 0, 2, 0, 2, 6, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 2, 0, 4, 6, 0, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:44, 4:54, 6:24, 8:11, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 8, 0, 4, 0, 4, }, +{7: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 0, -8, -8, 8, -8, 0, 8, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 8, -8, 8, -8, 0, -8, 8, 0, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 0, 0, 0, -8, 8, -8, 0, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 8, 0, 8, 0, 8, -8, 0, -8, 0, -8, -8, 0, -16, }, +{3: 16, -8, -16, 8, 0, 8, -8, -8, 0, 0, 0, 8, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, -16, 0, 0, 0, 8, 0, 0, 0, 0, -8, 0, 0, 8, }, +{9: 16, -8, 8, 8, -8, -8, 0, 8, 8, -8, -8, -8, 0, 8, -16, 8, }, +{a: 16, 8, -8, 8, 0, -8, 0, -8, 0, 0, -8, -8, 8, -8, 0, 8, }, +{c: 16, 0, 8, -8, -8, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, 8, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 0, 0, -8, 0, 8, -8, 0, 0, 0, 16, -8, }, +{d: 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, 0, 0, -8, 8, 0, -8, 0, 0, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, , x, x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , x, , , , x, , , , x, , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0011,1,}, +{0100,0110,1,}, +{0110,0101,1,}, +{1110,0010,1,}, +{1110,1001,1,}, +{1110,1011,0,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x04,}, {0x0e,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x02,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x0e,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x04,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x05,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_214.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_214.txt new file mode 100644 index 0000000..d00925a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_214.txt @@ -0,0 +1,426 @@ +214 Sbox: +LUT = { +0x08,0x00,0x01,0x06,0x02,0x05,0x03,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, }, +{2: 0, 2, 8, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 2, 6, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 2, 0, 0, 0, 8, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 6, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 0, 0, 4, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, }, +{d: 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:67, 4:15, 6:5, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:6, 2:6, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 10, 2, 8, 4, 4, 0, 0, 0, 8, 0, 2, 0, 0, }, +{2: 16, 6, 8, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 6, 6, 6, 2, 4, 6, 4, 0, 2, 0, 4, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{3: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 0, 4, 0, 0, 2, 2, }, +{5: 16, 4, 6, 4, 4, 4, 8, 6, 6, 4, 4, 4, 0, 6, 0, 4, }, +{6: 16, 4, 4, 8, 0, 8, 4, 6, 0, 2, 0, 10, 2, 0, 0, 0, }, +{9: 16, 2, 4, 2, 0, 0, 4, 0, 8, 2, 4, 0, 4, 0, 0, 2, }, +{a: 16, 0, 6, 0, 4, 0, 6, 0, 0, 8, 2, 0, 2, 0, 0, 4, }, +{c: 16, 0, 4, 2, 0, 0, 4, 2, 4, 0, 8, 0, 0, 2, 4, 2, }, +{7: 16, 4, 4, 8, 0, 10, 4, 4, 0, 0, 0, 10, 2, 0, 0, 2, }, +{b: 16, 0, 6, 0, 2, 2, 0, 0, 4, 2, 0, 0, 4, 2, 2, 0, }, +{d: 16, 2, 0, 0, 4, 0, 6, 0, 0, 0, 2, 0, 2, 6, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 0, 2, 0, 0, 4, 2, 2, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:44, 4:54, 6:24, 8:11, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{9: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 4, 0, 4, 8, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 0, -8, 8, -16, }, +{2: 16, 8, -8, 8, 8, -16, 0, 0, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 8, 8, 0, 8, 0, 0, -8, 0, 8, -8, -8, 0, -8, -8, -8, }, +{8: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, -8, 8, -8, 8, -16, 8, -8, 0, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 0, -16, 0, 8, 0, -8, 0, 0, -8, -8, 8, 0, -8, 8, 8, }, +{9: 16, 0, 8, 0, -8, 0, -8, 0, 0, 0, 0, -16, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, 0, 8, }, +{c: 16, 0, 8, -8, -8, 0, -8, 0, 8, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 8, 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , , x, x, , , x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0011,0101,1,}, +{0011,0111,0,}, +{0111,1001,1,}, +{1000,1000,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x03,}}, +{{0x01,0x02,0x04,}, {0x03,}}, +{{0x09,0x02,0x0c,}, {0x03,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0f,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x07,}}, +{{0x0d,0x0a,}, {0x03,}}, +{{0x01,0x0e,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +214 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x08,0x05,0x03,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{4: 0, 2, 0, 6, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 8, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 4, 0, 4, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 0, 0, 4, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 4, 2, 2, 0, }, +{d: 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, 0, 0, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:166, 2:67, 4:15, 6:5, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:6, 2:6, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 6, 6, 0, 6, 4, 4, 2, 0, 0, 4, 0, 2, 0, 0, }, +{2: 16, 4, 8, 6, 4, 4, 6, 4, 4, 6, 4, 4, 6, 0, 4, 0, }, +{4: 16, 10, 4, 6, 0, 4, 4, 8, 2, 0, 2, 8, 0, 0, 0, 0, }, +{8: 16, 2, 4, 2, 8, 0, 4, 0, 0, 4, 0, 0, 2, 4, 2, 0, }, +{3: 16, 8, 4, 4, 0, 6, 4, 8, 0, 0, 0, 10, 2, 0, 0, 2, }, +{5: 16, 4, 4, 6, 4, 6, 8, 4, 4, 6, 4, 4, 0, 6, 0, 4, }, +{6: 16, 4, 6, 4, 0, 6, 6, 6, 0, 0, 2, 4, 0, 0, 2, 0, }, +{9: 16, 0, 6, 0, 2, 0, 6, 0, 8, 0, 4, 0, 4, 0, 0, 2, }, +{a: 16, 0, 4, 2, 4, 0, 4, 2, 2, 8, 0, 0, 2, 0, 0, 4, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{7: 16, 8, 4, 4, 0, 4, 4, 10, 0, 0, 0, 10, 0, 0, 2, 2, }, +{b: 16, 0, 4, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 2, 2, 0, }, +{d: 16, 2, 0, 0, 4, 0, 6, 0, 0, 0, 2, 0, 2, 6, 2, 0, }, +{e: 16, 0, 6, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:44, 4:54, 6:24, 8:11, 10:4, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 0, 0, 8, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 12, 0, 0, 4, 0, }, +{b: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:108, 8:24, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 0, 0, 0, 8, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 8, -8, 8, -16, 8, 0, 0, -8, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, 0, 0, 0, -8, -16, 8, 0, 0, -8, }, +{8: 16, 0, 8, 0, -8, 0, 0, 0, 0, 0, 0, 8, 0, -8, 0, -16, }, +{3: 16, -8, -16, 0, 8, 8, -8, 0, 0, -8, 0, 8, 0, -8, 0, 8, }, +{5: 16, -8, 8, -8, 8, -8, 8, -16, -8, 8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, -8, 0, 0, -8, 0, 8, -8, 0, 0, 8, }, +{9: 16, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, -8, -8, 8, -8, 8, }, +{a: 16, 0, -8, 0, -8, 0, 0, 0, 8, 8, -8, -8, 0, -8, 0, 8, }, +{c: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 8, 0, 0, 16, -8, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, -8, 0, 0, -8, }, +{e: 16, 0, -8, 0, -8, 0, 0, 0, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, 0, -8, 0, -8, 0, 0, 0, -8, 0, 0, -8, 8, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , , x, x, , x, , , , x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, , , x, x, , x, , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0010,0011,1,}, +{0110,0010,1,}, +{0110,0101,1,}, +{0110,0111,0,}, +{0111,0100,1,}, +{1000,1100,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x05,0x02,0x08,}, {0x06,}}, +{{0x01,0x02,0x04,}, {0x06,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x08,}, {0x06,0x09,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x06,0x09,0x0f,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,}}, +{{0x01,0x06,}, {0x03,0x05,0x06,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x02,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0c,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_215.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_215.txt new file mode 100644 index 0000000..0044908 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_215.txt @@ -0,0 +1,446 @@ +215 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x0c,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x03,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 8, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{9: 0, 4, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 0, 0, 0, 4, 2, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:174, 2:48, 4:30, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 2, 4, 8, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 16, 0, 8, 4, 6, 0, 4, 4, 6, 4, 6, 4, 4, 6, 4, 4, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 4, 0, 8, 0, 4, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{5: 16, 4, 0, 4, 0, 4, 8, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{6: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{9: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{a: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 6, 6, }, +{7: 16, 4, 0, 8, 2, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{b: 16, 4, 0, 8, 2, 4, 4, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{d: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 4, 0, 8, 0, 4, 4, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:40, 4:64, 6:8, 8:12, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{f: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 12, 4, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:2, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{2: 16, 8, 0, 8, 0, -8, 8, -8, 8, -16, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{5: 16, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, 0, -16, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 8, 0, -8, -8, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{a: 16, 0, -16, 8, 0, 0, 8, -8, 0, 0, -8, -8, 0, 8, 8, -8, }, +{c: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, 0, 0, -8, 0, 8, 0, 8, 0, 0, -8, -8, 8, 0, -8, -8, }, +{b: 16, 0, 0, 8, 0, 8, -8, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, -8, -8, 0, 8, 8, 0, 0, -8, 8, }, +{e: 16, 8, -16, -8, 0, -8, 0, 8, 8, 0, 8, 0, -8, 0, -8, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, -8, 0, 8, -8, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, , x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , x, , , , x, x, x, , , x, x, , x, , x, }, +{6: , x, , , , x, , x, , , x, x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , x, , , , x, , x, , , x, x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0010,0100,0,}, +{0010,1010,1,}, +{0010,1110,1,}, +{0100,0100,1,}, +{0110,0100,1,}, +{1000,0100,0,}, +{1000,1000,1,}, +{1000,1100,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1110,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 9, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x0a,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x0a,0x04,}, {0x02,}}, +{{0x09,0x0a,0x04,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x0a,}}, +{{0x05,0x02,}, {0x0a,}}, +{{0x09,0x02,}, {0x0a,}}, +{{0x0d,0x02,}, {0x0a,}}, +{{0x01,0x06,}, {0x0a,}}, +{{0x05,0x06,}, {0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x02,}}, +{{0x05,0x0a,}, {0x02,}}, +{{0x09,0x0a,}, {0x02,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +215 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x0c,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x04,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, }, +{8: 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 4, 0, }, +{9: 0, 2, 2, 0, 4, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 2, 4, 2, 0, 2, 0, 0, 0, }, +{d: 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 0, 2, }, +{e: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:174, 2:48, 4:30, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 0, 8, 16, 8, 0, 0, 8, 0, 16, 8, 0, 0, 0, 16, 0, }, +{4: 16, 4, 4, 16, 0, 8, 4, 4, 4, 4, 0, 8, 8, 4, 4, 8, }, +{8: 16, 2, 6, 0, 4, 0, 0, 2, 2, 4, 0, 2, 2, 0, 0, 0, }, +{3: 16, 4, 0, 16, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 8, 4, 16, 0, 4, 8, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{6: 16, 4, 4, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 16, 2, 6, 0, 4, 0, 0, 2, 2, 4, 0, 2, 2, 0, 0, 0, }, +{a: 16, 0, 4, 0, 6, 2, 2, 0, 2, 4, 2, 0, 2, 0, 0, 0, }, +{c: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{7: 16, 0, 4, 16, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 16, 0, 4, 0, 6, 2, 2, 0, 2, 4, 2, 0, 2, 0, 0, 0, }, +{d: 16, 0, 6, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 2, 4, 2, }, +{e: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:40, 4:64, 6:8, 8:12, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 8, 0, 8, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 12, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:2, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 8, -8, 0, -8, -8, 8, }, +{2: 16, 16, -16, 8, 0, -16, 8, -8, 0, 0, 8, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 16, -8, -8, 8, 8, -16, -8, 8, 0, 0, -16, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, -8, }, +{3: 16, -16, 0, 8, 0, 0, -8, -8, 0, 0, 8, 8, 0, -8, 8, -8, }, +{5: 16, 0, 16, -16, 8, 0, 0, -16, 8, 8, -8, 0, 8, -8, -8, -8, }, +{6: 16, 0, 0, -8, 0, -16, -8, 8, 0, 0, -8, 8, 0, 8, -8, 8, }, +{9: 16, 0, 0, 8, 0, 0, 0, 8, 0, -8, -8, 0, -8, 0, 0, -8, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 8, }, +{7: 16, 0, -16, -8, 0, 0, 8, 8, 0, 0, -8, -8, 0, -8, 8, 8, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, -8, 0, 0, 0, 0, 8, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, 0, -8, 0, 0, 8, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , x, x, x, , , x, }, +{5: , , , , , , x, x, , , x, x, , x, , x, }, +{6: , , , x, x, x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , x, x, , , , x, }, +{b: , , , x, , , , , , , x, , x, , , x, }, +{d: , , , , , , , x, , , x, , , x, , x, }, +{e: , , , x, x, x, , , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1100,0100,1,}, +{1111,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_216.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_216.txt new file mode 100644 index 0000000..84a7e64 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_216.txt @@ -0,0 +1,446 @@ +216 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x0d,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x03,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, }, +{b: 0, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 2, 2, }, +{e: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:174, 2:48, 4:30, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 4, 4, 16, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{2: 16, 0, 8, 0, 0, 0, 16, 0, 16, 0, 16, 8, 8, 0, 8, 0, }, +{4: 16, 8, 4, 8, 4, 4, 16, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{8: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{3: 16, 4, 0, 4, 4, 4, 16, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{5: 16, 4, 4, 4, 8, 8, 16, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 16, 0, 4, 0, 4, 4, 16, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 0, 6, 2, 2, 2, 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, }, +{c: 16, 0, 4, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 6, 2, }, +{7: 16, 4, 4, 4, 0, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 16, 0, 6, 2, 2, 2, 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, }, +{d: 16, 0, 4, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 2, 6, 2, }, +{e: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +{f: 16, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:40, 4:64, 6:8, 8:12, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{c: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 0, 4, 0, 4, 0, }, +{7: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:4, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 8, 0, 8, -8, 0, 8, 0, -8, -16, -8, 0, }, +{2: 16, 8, 0, 8, 0, -8, 0, -8, 8, -16, 8, -16, -8, 16, -8, 0, }, +{4: 16, 0, 8, -8, 8, -8, 8, -16, -8, 16, -16, 0, 0, 0, -8, 8, }, +{8: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 8, 0, -8, 0, -8, -8, 0, 8, 0, 8, -16, 8, 0, }, +{5: 16, -8, 8, -16, 8, -16, 8, -8, 0, 0, -8, 16, -8, 0, 0, 8, }, +{6: 16, 8, 0, -8, 0, 8, 0, 8, -8, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 8, 0, -8, -16, 8, 0, -8, 0, }, +{b: 16, 0, -8, 8, 0, 8, 0, -8, 0, 0, -8, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 8, -8, -8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +{f: 16, 0, -8, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{5: , , , , , x, x, x, x, , x, x, , x, , x, }, +{6: , , x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , x, x, x, }, +{7: , , , , , x, x, x, x, , x, x, , x, , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , x, x, x, , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0011,0101,1,}, +{0100,0101,1,}, +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 5, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x07,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +216 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x0d,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x04,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{4: 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 0, 4, 0, 0, 2, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, }, +{a: 0, 0, 0, 4, 2, 4, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:174, 2:48, 4:30, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 8, 2, 4, 4, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{2: 16, 0, 8, 4, 4, 0, 4, 4, 4, 6, 4, 4, 6, 4, 6, 6, }, +{4: 16, 4, 0, 8, 0, 4, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{8: 16, 4, 0, 4, 2, 4, 8, 4, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 16, 4, 0, 4, 0, 4, 8, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 4, 0, 4, 2, 4, 8, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{9: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{a: 16, 4, 0, 8, 2, 4, 4, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{c: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 0, 8, 4, 0, 0, 4, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 4, 0, 4, 0, 4, 8, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 4, 0, 8, 0, 4, 4, 0, 0, 0, 2, 4, 0, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:40, 4:64, 6:8, 8:12, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{3: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{5: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{f: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:4, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{2: 16, 8, -16, 8, 0, -8, 8, -8, 8, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, -8, 0, 0, -8, -8, 8, 0, 8, -8, }, +{8: 16, 0, 0, 8, 0, -8, -8, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{3: 16, -8, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{5: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, -8, 8, -8, 0, -8, 8, }, +{9: 16, 0, 0, 8, 0, 0, 8, 8, 0, -16, -8, -8, 0, 8, -8, -8, }, +{a: 16, 0, 0, 8, 0, 8, -8, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{c: 16, 8, 0, -8, 0, -8, 0, -8, 8, -16, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, -8, 0, -8, 0, 0, 0, -8, -8, 0, 8, 8, 0, 0, -8, 8, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, -8, 0, -8, 0, 0, 0, 8, -8, 0, 8, -8, 0, 0, 8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, , , , , x, x, x, , x, x, , x, , x, }, +{6: , x, , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, , x, , , , x, x, }, +{7: , x, , , , , x, , x, , x, x, , x, , x, }, +{b: , x, , x, , , x, , x, , x, , x, x, , x, }, +{d: , x, , , , , x, x, x, , x, , , , , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1000,0101,0,}, +{1000,1011,1,}, +{1000,1110,1,}, +{1010,0101,0,}, +{1010,1001,1,}, +{1010,1100,1,}, +{1100,0101,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 9, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0a,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x02,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x0a,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x02,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x02,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x0a,}}, +{{0x03,0x0c,}, {0x0a,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x0a,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x02,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x0a,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_217.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_217.txt new file mode 100644 index 0000000..038bd4d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_217.txt @@ -0,0 +1,416 @@ +217 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x0e,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, }, +{8: 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 2, 0, 6, 2, 2, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 2, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 4, 2, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 8, 2, 0, 2, 2, 0, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:56, 4:21, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 0, 4, 0, 6, 0, 6, 4, 4, 4, 6, 0, 0, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 0, 4, 6, 6, 0, 0, 4, 0, 6, 4, 2, 0, 0, 6, 2, }, +{8: 16, 0, 0, 6, 8, 4, 0, 2, 2, 0, 4, 0, 6, 0, 0, 0, }, +{3: 16, 4, 4, 0, 4, 16, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{5: 16, 0, 0, 0, 2, 4, 6, 6, 6, 4, 6, 0, 0, 0, 2, 4, }, +{6: 16, 6, 4, 6, 0, 4, 4, 6, 2, 0, 0, 6, 0, 2, 0, 0, }, +{9: 16, 0, 4, 2, 0, 0, 6, 0, 8, 2, 4, 0, 6, 0, 0, 0, }, +{a: 16, 6, 0, 4, 2, 0, 6, 0, 0, 6, 0, 0, 6, 2, 4, 4, }, +{c: 16, 4, 4, 6, 4, 4, 4, 0, 4, 0, 8, 6, 4, 6, 6, 4, }, +{7: 16, 4, 0, 0, 0, 0, 2, 6, 0, 0, 6, 8, 4, 0, 0, 2, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 4, 2, 2, }, +{e: 16, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 8, 2, }, +{f: 16, 0, 0, 2, 0, 4, 6, 0, 0, 4, 6, 0, 0, 2, 0, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:24, 4:59, 6:36, 8:6, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 0, }, +{2: 0, 8, 8, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{6: 0, 0, 0, 4, 8, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:115, 8:20, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:7, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -16, 0, 0, 0, 0, 8, -8, -8, -8, 8, -8, }, +{2: 16, 0, -8, 8, 0, -8, -8, 0, 0, -8, 8, 0, 8, 8, -16, 0, }, +{4: 16, 8, 0, -8, 0, 8, 0, 0, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, 0, 8, -8, 0, 0, -8, -8, 8, 0, -8, -8, 0, }, +{3: 16, -8, 0, 8, 0, 8, 0, 8, -8, 0, 8, 0, -8, -16, -8, 0, }, +{5: 16, 0, 8, -8, 0, -8, 0, 0, -8, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 0, 0, -8, 8, -8, -8, 8, 8, -8, -8, 0, 0, -8, 8, 0, }, +{9: 16, 0, 0, 8, 0, -8, 0, -8, 8, 0, -8, -8, 0, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 8, -8, -8, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 8, 8, -16, -8, 8, -8, -8, -8, -8, 8, -8, 0, 8, 8, 0, }, +{7: 16, -8, -8, -8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 8, 8, 0, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, -8, -8, 0, -8, 8, 0, 0, 0, 8, 0, 0, 8, -8, -8, }, +{f: 16, -8, 0, -8, 0, 8, 0, -8, 0, 0, 8, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, , x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, , x, x, , x, x, , x, , , x, }, +{c: , , x, , x, , x, x, , x, x, , , x, x, x, }, +{7: , x, x, x, , , x, x, , x, x, x, , , x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , , x, , x, x, , x, x, , , x, x, x, }, +{e: , , x, , x, , x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0001,1,}, +{0100,1100,1,}, +{1100,1011,1,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x01,0x04,0x05,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x03,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x01,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x0e,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x08,0x0b,}}, +{{0x05,0x06,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x02,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +217 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x08,0x0e,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x05,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 2, }, +{8: 0, 0, 0, 2, 4, 4, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 0, 2, 2, }, +{6: 0, 2, 0, 0, 2, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 4, 0, 2, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 2, 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 8, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 2, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 4, 2, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 0, }, +{f: 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:56, 4:21, 6:6, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:2, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 0, 4, 0, 6, 0, 6, 4, 4, 4, 6, 0, 0, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 0, 4, 6, 6, 0, 0, 6, 2, 4, 6, 0, 0, 0, 4, 2, }, +{8: 16, 0, 0, 6, 8, 4, 2, 0, 0, 2, 4, 0, 6, 0, 0, 0, }, +{3: 16, 4, 4, 0, 4, 16, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{5: 16, 0, 0, 0, 0, 4, 6, 4, 6, 6, 4, 2, 0, 0, 2, 6, }, +{6: 16, 6, 4, 4, 2, 4, 6, 6, 0, 0, 0, 6, 0, 2, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 6, 2, 8, 0, 4, 0, 6, 0, 0, 0, }, +{a: 16, 6, 0, 6, 0, 0, 4, 0, 2, 6, 0, 0, 6, 2, 4, 4, }, +{c: 16, 4, 4, 4, 4, 4, 6, 0, 4, 0, 8, 6, 4, 6, 4, 6, }, +{7: 16, 4, 0, 2, 0, 0, 0, 6, 0, 0, 6, 8, 4, 0, 2, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 4, 2, 2, }, +{e: 16, 0, 4, 6, 0, 0, 2, 0, 0, 4, 6, 0, 0, 2, 8, 0, }, +{f: 16, 0, 0, 2, 0, 4, 4, 0, 0, 4, 4, 2, 0, 2, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:24, 4:59, 6:36, 8:6, 10:2, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{6: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:115, 8:20, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:7, 8:4, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, -8, 0, 8, 0, 0, -16, 8, 0, }, +{2: 16, 0, 0, 8, 0, -16, -8, 8, 0, 0, 8, -8, 0, 8, -8, -8, }, +{4: 16, 8, 8, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, 0, 8, 0, -8, -8, 0, -8, 8, 0, -8, -8, 0, }, +{3: 16, 0, -8, 8, 0, 8, 8, 0, 0, -8, 8, 0, -8, -8, -16, 0, }, +{5: 16, -8, 0, -8, 0, -8, 8, 0, -8, 8, -8, 0, 0, 8, -8, 8, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 8, 0, }, +{9: 16, 0, 0, 8, 0, -8, 0, 0, 8, -8, -8, 0, -8, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 0, -8, 0, 8, -8, -8, 8, -8, 8, 0, }, +{c: 16, 0, 8, -16, -8, 8, 0, -8, -8, -8, 8, -8, -8, 8, 8, 8, }, +{7: 16, 0, -8, -8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 8, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 8, 0, -8, 0, -8, 0, -8, 0, 0, 8, 0, 0, 8, -8, -8, }, +{f: 16, -8, -8, -8, 0, 8, 0, 0, 0, 0, 8, 0, 8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{5: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, x, , x, x, , x, x, x, , , x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, x, , x, x, , x, x, , x, , , x, }, +{c: , x, , , x, , x, x, , x, x, , , x, x, x, }, +{7: , x, x, x, , , x, x, , x, x, x, , , x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , , x, , x, x, , x, x, , , x, x, x, }, +{e: , , , , x, , x, x, , x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0011,0010,1,}, +{0100,1100,1,}, +{1100,1011,1,}, +{1101,0001,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x07,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x0e,}}, +{{0x09,0x04,}, {0x09,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_218.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_218.txt new file mode 100644 index 0000000..2083893 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_218.txt @@ -0,0 +1,428 @@ +218 Sbox: +LUT = { +0x0c,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, }, +{5: 0, 2, 0, 2, 0, 2, 4, 2, 4, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 4, 0, 0, 2, }, +{d: 0, 4, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:52, 4:24, 6:4, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 4, 2, 6, 2, 4, 0, 6, 0, 0, 6, 0, 0, }, +{2: 16, 0, 8, 4, 4, 0, 6, 6, 4, 4, 4, 4, 4, 6, 6, 4, }, +{4: 16, 4, 8, 6, 0, 4, 8, 4, 0, 0, 2, 10, 0, 0, 0, 2, }, +{8: 16, 8, 16, 0, 8, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 0, }, +{3: 16, 2, 0, 6, 4, 6, 0, 0, 0, 0, 4, 6, 4, 0, 2, 6, }, +{5: 16, 10, 0, 6, 4, 2, 4, 2, 4, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 16, 4, 0, 2, 6, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 16, 0, 8, 0, 4, 0, 2, 2, 4, 4, 0, 0, 4, 2, 2, 0, }, +{c: 16, 4, 8, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 8, 4, 10, }, +{7: 16, 2, 0, 6, 4, 10, 0, 2, 0, 0, 0, 4, 4, 0, 0, 0, }, +{b: 16, 0, 0, 0, 6, 4, 0, 2, 0, 2, 2, 2, 4, 0, 0, 2, }, +{d: 16, 8, 0, 0, 6, 0, 0, 0, 4, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 0, 0, 6, 8, 0, 0, 0, 2, 6, 0, 4, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:30, 4:54, 6:22, 8:12, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 8, -8, -8, 0, -8, 0, 8, 0, -8, -8, 8, 0, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, -16, 8, 8, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, }, +{8: 16, 0, 8, 16, -16, 8, 0, 8, 0, -8, -16, 8, -8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 8, 8, -8, 0, -8, 0, 8, 0, 8, -8, -8, 0, }, +{5: 16, -8, 8, 0, 8, -8, -8, 0, 0, 0, -8, 0, 0, 0, -8, 8, }, +{6: 16, 8, -16, 0, 8, -8, 8, 0, 0, -8, -8, -8, 0, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, -8, 0, 8, -8, 8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -16, -8, 8, 0, -8, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, 0, 8, 8, -8, 0, 0, 0, -8, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{e: 16, 0, -8, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, 8, -16, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 0, -8, 0, 8, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , x, x, x, , , x, }, +{5: , , x, , x, x, x, , , , x, x, , x, , x, }, +{6: , , , , x, x, , x, , , x, x, , , x, x, }, +{9: , x, x, , , x, , , x, , x, , x, x, , x, }, +{a: , x, x, , , x, , , , x, x, , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , x, x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1000,1000,1,}, +{1100,1000,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 4, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,}}, +{{0x01,0x04,0x08,}, {0x04,}}, +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x02,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0b,}}, +{{0x05,0x0a,}, {0x0f,}}, +{{0x09,0x0a,}, {0x0b,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +218 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x00,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{5: 0, 2, 2, 4, 0, 0, 4, 0, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 4, 2, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 0, 0, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:52, 4:24, 6:4, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 8, 2, 10, 0, 4, 0, 4, 2, 0, 8, 0, 0, }, +{2: 16, 0, 8, 8, 16, 0, 0, 16, 0, 8, 8, 0, 0, 0, 16, 0, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 2, 0, 2, 6, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 8, 4, 4, 4, 6, 4, 0, 4, 6, 6, 4, 6, }, +{3: 16, 2, 0, 4, 8, 6, 2, 0, 0, 0, 4, 10, 4, 0, 0, 8, }, +{5: 16, 6, 6, 8, 0, 0, 4, 4, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 16, 2, 6, 4, 0, 0, 2, 4, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 16, 6, 4, 2, 0, 4, 0, 0, 0, 0, 6, 0, 2, 6, 4, 6, }, +{7: 16, 0, 4, 10, 0, 6, 0, 4, 0, 0, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 16, 6, 6, 0, 0, 0, 0, 0, 2, 2, 8, 0, 0, 4, 4, 0, }, +{e: 16, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 2, }, +{f: 16, 0, 4, 2, 0, 6, 0, 0, 0, 0, 10, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:98, 2:30, 4:54, 6:22, 8:12, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 12, 0, 4, 4, 4, 4, }, +{7: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 8, -8, 0, 0, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 16, -16, 0, 8, -16, 0, 0, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 8, -16, 8, 8, 8, 0, -8, -8, 8, -8, -8, -8, -8, }, +{3: 16, -16, -8, 0, 8, 8, 0, 0, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, 0, 8, 0, 8, -8, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 8, -8, 0, -8, 8, 0, 8, -16, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 8, 0, -8, 0, 0, -8, 8, 8, }, +{c: 16, 0, 8, -8, -8, 8, -8, -8, 0, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, -8, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 8, 8, 0, -8, 0, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, 0, -8, -8, 0, -8, 0, -8, 8, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , x, x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , x, , x, x, , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{1000,1000,1,}, +{1100,1011,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 4, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_219.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_219.txt new file mode 100644 index 0000000..59baa72 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_219.txt @@ -0,0 +1,428 @@ +219 Sbox: +LUT = { +0x08,0x00,0x0d,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x01,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, }, +{5: 0, 0, 0, 2, 0, 2, 8, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 4, 0, }, +{9: 0, 2, 2, 2, 2, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 6, 2, 0, 2, 0, 0, }, +{7: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 4, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 0, 0, }, +{e: 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:52, 4:24, 6:4, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 10, 0, 8, 2, 4, 0, 4, 0, 0, 8, 0, 2, }, +{2: 16, 0, 8, 0, 0, 0, 16, 0, 8, 0, 8, 8, 16, 0, 16, 0, }, +{4: 16, 4, 4, 4, 4, 0, 16, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{8: 16, 4, 4, 2, 4, 0, 0, 0, 8, 0, 2, 2, 4, 0, 0, 2, }, +{3: 16, 0, 0, 2, 0, 6, 8, 4, 4, 10, 4, 0, 0, 2, 0, 8, }, +{5: 16, 4, 4, 6, 4, 6, 8, 4, 0, 6, 0, 4, 4, 6, 4, 4, }, +{6: 16, 0, 4, 0, 0, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 16, 6, 6, 2, 6, 4, 0, 2, 6, 4, 0, 0, 4, 0, 0, 0, }, +{a: 16, 0, 6, 0, 0, 4, 0, 2, 10, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 6, 4, 2, 0, 6, 0, 0, 0, 0, 6, 2, 0, 6, 4, 4, }, +{7: 16, 2, 4, 0, 2, 0, 8, 2, 0, 0, 0, 4, 4, 0, 4, 2, }, +{b: 16, 0, 4, 2, 0, 2, 0, 2, 4, 2, 2, 2, 4, 0, 0, 0, }, +{d: 16, 6, 6, 0, 0, 0, 0, 0, 2, 2, 8, 0, 0, 4, 4, 0, }, +{e: 16, 2, 6, 0, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:95, 2:33, 4:57, 6:19, 8:12, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 0, 12, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{b: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, 8, 0, 0, 8, 0, -8, -16, 8, -8, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 0, 0, 8, 0, -8, 16, -16, -8, }, +{4: 16, 0, 8, 0, 0, 8, 0, -8, 0, 8, -16, 8, -8, 0, -8, -8, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{3: 16, -8, -8, 0, 0, 8, 0, -8, 0, 0, 8, 0, 8, -16, -8, 8, }, +{5: 16, -8, 8, -8, 8, -8, 8, -16, -8, 8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -16, -8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, 8, 0, }, +{9: 16, 0, 8, 8, 0, -8, -8, 8, 8, -8, -8, -8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 8, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, 0, 8, -8, -8, -8, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, -8, 0, -8, 8, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, x, x, x, , x, , x, x, , x, , x, }, +{6: , , , x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, x, x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, x, x, x, , x, , x, , , x, x, x, }, +{7: , , , , , , x, , x, , x, x, , x, , x, }, +{b: , x, x, , x, x, x, , x, , x, , x, x, , x, }, +{d: , , x, x, x, x, x, , x, , x, , , , , x, }, +{e: , , , x, x, x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0110,0101,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 4, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x05,}}, +{{0x01,0x08,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x05,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +219 Inverse Sbox: +LUT = { +0x01,0x0d,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x02,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, }, +{8: 0, 2, 0, 4, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 2, 0, 2, 0, 2, 2, }, +{5: 0, 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 0, 4, 2, 2, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 2, 4, 0, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 0, 2, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:52, 4:24, 6:4, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 4, 4, 0, 4, 0, 6, 0, 6, 2, 0, 6, 2, 0, }, +{2: 16, 0, 8, 4, 4, 0, 4, 4, 6, 6, 4, 4, 4, 6, 6, 4, }, +{4: 16, 4, 0, 4, 2, 2, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, }, +{8: 16, 10, 0, 4, 4, 0, 4, 0, 6, 0, 0, 2, 0, 0, 0, 2, }, +{3: 16, 0, 0, 0, 0, 6, 6, 4, 4, 4, 6, 0, 2, 0, 2, 6, }, +{5: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 0, 4, 4, 4, 2, 2, 0, 2, 2, 0, 2, 0, }, +{9: 16, 4, 8, 0, 8, 4, 0, 0, 6, 10, 0, 0, 4, 2, 2, 0, }, +{a: 16, 0, 0, 0, 0, 10, 6, 4, 4, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 8, 4, 10, }, +{7: 16, 0, 8, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{b: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 16, 8, 0, 4, 0, 2, 6, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{e: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 2, 0, 0, 2, 8, 4, 4, 0, 0, 4, 2, 0, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:95, 2:33, 4:57, 6:19, 8:12, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{a: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 0, 8, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, -8, 8, -8, 0, 8, -8, 0, 0, 8, -8, }, +{2: 16, 8, -8, 8, 0, -16, 8, -8, 8, -8, 8, -8, 0, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 8, -8, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 8, 0, 0, 8, 0, 8, 0, 0, -8, -8, 0, -8, -8, -8, }, +{3: 16, -8, -8, 0, 0, 8, -8, -8, -8, 0, 8, 8, 0, 0, -8, 8, }, +{5: 16, 0, 8, -8, 16, -8, 8, -16, 0, 8, -8, 0, -8, 8, -16, 0, }, +{6: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, -16, -8, 0, 8, 0, -8, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, -8, 8, 8, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, }, +{b: 16, 0, -8, 0, 0, 8, 0, -8, 0, 8, -16, -8, 8, 0, 8, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, -8, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 8, -16, -8, 0, -8, 0, 8, 8, 0, 8, 0, -8, 0, -8, 0, }, +{f: 16, -8, -8, 0, 0, 8, 0, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, , , x, , x, , x, x, , x, , x, }, +{6: , x, x, x, x, x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, , , x, , x, , x, , x, x, , x, }, +{a: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , , x, , x, , x, x, , x, , x, }, +{b: , x, x, , , , x, , x, , x, , x, x, , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0010,1110,1,}, +{0011,0010,1,}, +{0110,0101,1,}, +{1000,0101,0,}, +{1000,1001,1,}, +{1000,1100,1,}, +{1100,1011,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 4, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x02,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x05,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x0d,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x05,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x0c,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0a,}, {0x0d,}}, +{{0x01,0x0e,}, {0x02,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_220.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_220.txt new file mode 100644 index 0000000..ef4407d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_220.txt @@ -0,0 +1,416 @@ +220 Sbox: +LUT = { +0x02,0x00,0x01,0x04,0x03,0x08,0x06,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{4: 0, 2, 0, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{5: 0, 0, 2, 0, 2, 2, 6, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 2, 0, 4, 0, }, +{a: 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, 2, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 8, 0, 0, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:64, 4:15, 6:6, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 6, 4, 4, 4, 6, 4, 4, 4, 6, 4, 6, 4, 0, 0, }, +{2: 16, 4, 10, 6, 0, 6, 6, 4, 0, 0, 0, 4, 0, 4, 0, 4, }, +{4: 16, 6, 4, 6, 2, 6, 4, 4, 2, 0, 0, 6, 0, 0, 0, 0, }, +{8: 16, 4, 0, 0, 8, 0, 2, 0, 6, 0, 0, 6, 2, 0, 0, 4, }, +{3: 16, 6, 4, 6, 0, 10, 4, 6, 0, 0, 0, 4, 0, 4, 4, 0, }, +{5: 16, 4, 6, 4, 2, 6, 6, 6, 0, 2, 0, 4, 0, 0, 0, 0, }, +{6: 16, 4, 6, 6, 0, 4, 4, 6, 0, 0, 2, 6, 2, 0, 0, 0, }, +{9: 16, 4, 0, 2, 4, 0, 2, 0, 8, 2, 0, 4, 2, 0, 4, 0, }, +{a: 16, 4, 0, 2, 2, 0, 0, 0, 0, 8, 0, 6, 6, 4, 0, 0, }, +{c: 16, 6, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 6, 2, 2, }, +{7: 16, 4, 4, 4, 4, 4, 6, 6, 6, 6, 0, 8, 0, 4, 4, 4, }, +{b: 16, 6, 0, 0, 2, 0, 0, 2, 2, 6, 2, 0, 4, 0, 0, 0, }, +{d: 16, 4, 4, 0, 0, 4, 0, 0, 0, 4, 6, 4, 0, 10, 6, 6, }, +{e: 16, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 4, 0, 6, 10, 2, }, +{f: 16, 0, 4, 0, 4, 0, 0, 0, 0, 0, 2, 4, 0, 6, 2, 10, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:26, 4:56, 6:39, 8:5, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 8, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 0, 0, 0, 4, 12, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 4, 8, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:115, 8:20, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 0, -8, 8, 8, -8, -16, 0, 8, -8, }, +{2: 16, 0, -8, 0, 8, 0, 8, -8, 8, 0, 8, -8, -8, 0, -16, 0, }, +{4: 16, 0, 8, 0, 8, 8, -8, 0, 0, 0, -8, -8, 8, -8, -8, -8, }, +{8: 16, -8, 0, 0, -8, 8, 8, 8, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, -8, 0, 8, 0, -16, 0, -8, 0, 8, 8, 8, -8, -8, 0, }, +{5: 16, 0, 0, 0, 8, -8, 8, -8, -8, 0, -8, 8, -8, 0, -8, 8, }, +{6: 16, 8, -8, -8, 8, 0, -8, 0, 8, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, -8, -8, -8, 0, 0, 8, -8, 0, 8, 8, -8, 0, }, +{a: 16, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, 0, 8, -8, 8, -8, }, +{c: 16, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 8, 8, -8, -8, -16, -8, 8, 8, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, -8, 8, -8, 0, 0, 8, 0, 8, -8, 8, 0, }, +{e: 16, -8, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 8, 0, -8, 8, }, +{f: 16, 8, 0, 0, -8, 0, 8, 0, 0, -8, 8, 0, -8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , , x, x, , , x, }, +{5: , x, , x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , , x, , , x, x, }, +{9: , , x, x, x, x, x, , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, x, , x, , , , , x, , , , x, }, +{b: , , x, , x, x, x, , , , , , x, , , x, }, +{d: , , , x, , x, , , , , , , , x, , x, }, +{e: , x, x, , x, x, x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0101,0011,1,}, +{1000,1101,1,}, +{1011,0001,1,}, +{1100,0111,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x02,0x09,0x0b,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x01,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +220 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x03,0x08,0x06,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, }, +{4: 0, 0, 2, 6, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, }, +{3: 0, 0, 2, 2, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{5: 0, 2, 2, 0, 2, 0, 6, 0, 2, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 2, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 2, 2, 0, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 2, 4, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 2, 2, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 8, 0, 0, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{f: 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:64, 4:15, 6:6, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 6, 4, 6, 4, 4, 4, 4, 6, 4, 6, 4, 0, 0, }, +{2: 16, 6, 10, 4, 0, 4, 6, 6, 0, 0, 0, 4, 0, 4, 0, 4, }, +{4: 16, 4, 6, 6, 0, 6, 4, 6, 2, 2, 0, 4, 0, 0, 0, 0, }, +{8: 16, 4, 0, 2, 8, 0, 2, 0, 4, 2, 0, 4, 2, 0, 0, 4, }, +{3: 16, 4, 6, 6, 0, 10, 6, 4, 0, 0, 0, 4, 0, 4, 4, 0, }, +{5: 16, 6, 6, 4, 2, 4, 6, 4, 2, 0, 0, 6, 0, 0, 0, 0, }, +{6: 16, 4, 4, 4, 0, 6, 6, 6, 0, 0, 2, 6, 2, 0, 0, 0, }, +{9: 16, 4, 0, 2, 6, 0, 0, 0, 8, 0, 0, 6, 2, 0, 4, 0, }, +{a: 16, 4, 0, 0, 0, 0, 2, 0, 2, 8, 0, 6, 6, 4, 0, 0, }, +{c: 16, 6, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 6, 2, 2, }, +{7: 16, 4, 4, 6, 6, 4, 4, 6, 4, 6, 0, 8, 0, 4, 4, 4, }, +{b: 16, 6, 0, 0, 2, 0, 0, 2, 2, 6, 2, 0, 4, 0, 0, 0, }, +{d: 16, 4, 4, 0, 0, 4, 0, 0, 0, 4, 6, 4, 0, 10, 6, 6, }, +{e: 16, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, 4, 0, 6, 10, 2, }, +{f: 16, 0, 4, 0, 4, 0, 0, 0, 0, 0, 2, 4, 0, 6, 2, 10, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:26, 4:56, 6:39, 8:5, 10:5, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 8, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 8, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 4, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 8, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 12, 4, 0, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:115, 4:115, 8:20, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:8, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -16, 0, -8, 8, 8, -8, -8, -8, 8, -8, }, +{2: 16, 0, -8, 0, 8, -8, 8, 0, 8, 0, 8, -8, -16, 0, -8, 0, }, +{4: 16, 8, 0, 0, 8, 0, -8, -8, 8, 0, -8, -8, 8, -8, -8, 0, }, +{8: 16, 0, 0, 0, -8, 8, 8, 0, 0, 8, -8, 0, -8, -8, -8, 0, }, +{3: 16, 0, -8, 0, 8, 0, -8, -8, -8, 0, 8, 8, 8, 0, -16, 0, }, +{5: 16, -8, 8, 0, 8, -8, 8, 0, -8, 0, -8, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 8, 0, -8, 0, 0, -8, -8, 8, -8, 0, 8, 8, }, +{9: 16, 0, 0, 0, -8, 0, -8, 8, 0, 0, -8, 0, 8, 8, -8, -8, }, +{a: 16, -8, 0, 0, -8, -8, 8, -8, 0, 0, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, 8, 8, -8, -8, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, -8, 8, -8, 0, 0, 8, 0, 8, -8, 8, 0, }, +{e: 16, -8, 0, 0, -8, 0, -8, 0, 0, -8, 8, 0, 8, 0, -8, 8, }, +{f: 16, 8, 0, 0, -8, 0, 8, 0, 0, -8, 8, 0, -8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , , x, x, , , x, }, +{5: , x, , x, x, x, x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, x, , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, x, , x, , , , , x, , , , x, }, +{b: , , x, , x, x, x, , , , , , x, , , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , x, , , x, x, x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 5 */ +{0101,0001,1,}, +{1000,1101,1,}, +{1011,0010,1,}, +{1100,0111,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x0b,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x06,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,}}, +{{0x03,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x01,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x0d,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x05,0x0a,0x0f,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x02,}, {0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_221.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_221.txt new file mode 100644 index 0000000..d77c8d1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_221.txt @@ -0,0 +1,428 @@ +221 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x08,0x07,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 4, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 8, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 2, 6, 0, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 2, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 4, 0, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, }, +{d: 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, 0, }, +{e: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 6, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:58, 4:18, 6:6, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 6, 0, 6, 4, 6, 0, 0, 0, 4, 0, 0, 4, 4, }, +{2: 16, 4, 16, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 8, 4, 8, }, +{4: 16, 4, 8, 6, 0, 4, 10, 4, 0, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 2, 10, 0, 0, 2, }, +{3: 16, 6, 4, 4, 4, 8, 4, 6, 4, 4, 6, 4, 6, 0, 0, 4, }, +{5: 16, 6, 4, 6, 0, 6, 6, 4, 2, 2, 0, 4, 0, 0, 0, 0, }, +{6: 16, 4, 8, 4, 2, 4, 8, 6, 2, 0, 0, 10, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 2, 4, 0, 2, 4, 6, 0, 2, 0, 2, 2, 0, }, +{a: 16, 0, 4, 0, 0, 4, 2, 2, 8, 4, 0, 0, 4, 2, 2, 0, }, +{c: 16, 0, 4, 2, 2, 6, 0, 0, 0, 0, 4, 0, 0, 4, 0, 10, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 0, 2, 6, 4, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, }, +{d: 16, 0, 8, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 6, 4, }, +{e: 16, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 6, 6, 8, }, +{f: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 10, 0, 2, 4, 8, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:54, 6:26, 8:14, 10:6, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 4, 4, 4, 12, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{d: 0, 0, 8, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 8, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:2, 4:11, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 8, -8, -16, 8, -8, 8, 8, 0, 0, -8, 0, -8, }, +{2: 16, 0, 0, 0, 8, -16, 16, -16, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 0, 8, -16, -8, 8, 0, 0, -8, }, +{8: 16, -8, 0, 8, -8, 8, 0, 8, 0, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, -8, 8, 8, 8, -16, -8, -8, -8, 8, 8, 0, -8, 0, 8, }, +{5: 16, -8, 8, 0, 8, -8, 0, -8, -8, 8, -8, 0, 0, 0, -8, 8, }, +{6: 16, 8, -8, 0, 8, -8, 0, 8, 8, -16, -8, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 0, -8, -8, 0, 8, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, -8, 0, 8, -8, 8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, -8, 8, 0, 0, -8, 0, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 8, 0, 0, -8, -8, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, }, +{e: 16, -8, 0, 0, -8, -8, 0, 8, 0, 8, 8, -8, 0, -8, 0, 0, }, +{f: 16, 0, -8, -8, -16, 8, 0, 8, 0, 8, 8, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{7: , x, x, x, x, x, x, x, , , , , , , , x, }, +{b: , , , , x, , x, x, , , , x, x, , , x, }, +{d: , x, , x, x, , x, x, , , , x, , x, , x, }, +{e: , x, x, x, x, , x, x, , , , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0011,0010,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x02,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x0a,}, {0x05,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x02,0x05,0x07,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +221 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x08,0x07,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, }, +{4: 0, 2, 0, 6, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 2, 8, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 0, 6, 2, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 2, 4, 0, 2, }, +{7: 0, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, 0, }, +{e: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 6, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:58, 4:18, 6:6, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 4, 0, 6, 6, 4, 0, 0, 0, 6, 0, 0, 4, 4, }, +{2: 16, 4, 16, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 8, }, +{4: 16, 6, 4, 6, 0, 4, 6, 4, 0, 0, 2, 6, 2, 0, 0, 0, }, +{8: 16, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 6, 0, 0, 2, }, +{3: 16, 6, 4, 4, 6, 8, 6, 4, 4, 4, 6, 4, 4, 0, 0, 4, }, +{5: 16, 4, 8, 10, 0, 4, 6, 8, 0, 2, 0, 4, 2, 0, 0, 0, }, +{6: 16, 6, 4, 4, 0, 6, 4, 6, 2, 2, 0, 6, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 4, 4, 2, 2, 4, 8, 0, 0, 0, 2, 2, 0, }, +{a: 16, 0, 0, 2, 0, 4, 2, 0, 6, 4, 0, 0, 2, 2, 2, 0, }, +{c: 16, 0, 4, 0, 0, 6, 0, 0, 0, 0, 4, 2, 2, 4, 0, 10, }, +{7: 16, 4, 8, 8, 2, 4, 4, 10, 2, 0, 0, 6, 0, 0, 0, 0, }, +{b: 16, 0, 4, 2, 10, 6, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, }, +{d: 16, 0, 8, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 6, 4, }, +{e: 16, 4, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 6, 6, 8, }, +{f: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 10, 0, 2, 4, 8, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:54, 6:26, 8:14, 10:6, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 8, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{8: 0, 4, 4, 4, 12, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{b: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:2, 4:11, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -16, 8, 8, 0, 0, 0, 0, -8, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 16, -16, 8, 0, -8, 0, 0, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 8, -8, -8, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -8, 0, 8, 8, 8, -8, -8, -16, -8, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -8, 8, -16, 0, 8, -8, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, -8, 8, 0, -8, -8, 0, 0, -8, 8, 8, }, +{9: 16, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, 8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 8, -8, 0, 8, 0, 0, 0, }, +{c: 16, -8, 0, -8, -8, 8, 0, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, 0, -8, -16, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -8, 0, 0, -8, 0, 0, }, +{d: 16, 8, 0, 0, -8, -8, 0, -8, 0, -8, 8, -8, 0, 8, 0, 0, }, +{e: 16, -8, 0, 0, -8, -8, 0, 8, 0, 8, 8, -8, 0, -8, 0, 0, }, +{f: 16, 0, -8, -8, -16, 8, 0, 8, 0, 8, 8, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, , x, x, x, x, , , x, x, , x, x, x, }, +{7: , x, x, x, x, x, x, x, , , , , , , , x, }, +{b: , x, x, , x, x, x, x, , , , x, x, , , x, }, +{d: , x, , , x, x, x, x, , , , x, , x, , x, }, +{e: , x, x, , x, , x, x, , , , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,0x09,0x0a,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x0e,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x02,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x09,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x09,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_222.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_222.txt new file mode 100644 index 0000000..7ff021d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_222.txt @@ -0,0 +1,428 @@ +222 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x08,0x06,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{4: 0, 0, 0, 6, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{5: 0, 0, 0, 2, 2, 2, 6, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 6, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 4, 2, 2, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 4, 0, 2, }, +{7: 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 4, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 2, 0, }, +{e: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:58, 4:18, 6:6, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:1, 6:1, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 6, 4, 6, 4, 4, 4, 4, 6, 4, 6, 4, 0, 0, }, +{2: 16, 4, 16, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 8, 4, 8, }, +{4: 16, 4, 8, 6, 2, 4, 10, 4, 2, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 6, 4, 0, 4, 0, 2, 0, 8, 0, 0, 0, 6, 0, 0, 2, }, +{3: 16, 6, 4, 6, 0, 10, 4, 6, 0, 0, 0, 4, 0, 4, 4, 0, }, +{5: 16, 4, 4, 6, 2, 6, 6, 6, 0, 0, 2, 4, 0, 0, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 2, 0, 10, 2, 0, 0, 0, }, +{9: 16, 4, 0, 2, 6, 0, 2, 0, 4, 2, 0, 0, 0, 2, 2, 0, }, +{a: 16, 4, 4, 2, 0, 0, 0, 0, 4, 4, 0, 2, 8, 2, 2, 0, }, +{c: 16, 6, 4, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 8, 0, 6, }, +{7: 16, 6, 4, 4, 0, 6, 4, 6, 2, 2, 0, 6, 0, 0, 0, 0, }, +{b: 16, 4, 0, 0, 2, 0, 0, 2, 0, 6, 2, 2, 4, 0, 0, 2, }, +{d: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 8, 0, 0, 6, 10, 4, }, +{e: 16, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 10, 6, 4, }, +{f: 16, 0, 8, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 4, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:53, 6:27, 8:15, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 8, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 8, 0, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -16, 0, -8, 8, 8, -8, -8, -8, 8, -8, }, +{2: 16, 0, -8, 0, 8, -8, 16, -8, 8, 0, 8, -8, -16, 8, -16, 0, }, +{4: 16, 0, 8, -8, 8, 8, 0, 0, 0, 0, -16, -8, 8, 0, -8, -8, }, +{8: 16, -8, 8, 8, -8, 0, 0, 8, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, -8, 0, 8, 0, -16, 0, -8, 0, 8, 8, 8, -8, -8, 0, }, +{5: 16, 0, 8, -8, 8, 0, 0, -8, -8, 0, -8, 8, -8, 0, -8, 8, }, +{6: 16, 8, -16, 0, 8, -8, 0, 0, 8, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, 0, 8, -8, }, +{c: 16, 0, 8, -8, -8, 0, 0, 0, 0, -8, 8, 0, -8, -8, 8, 0, }, +{7: 16, -8, -8, 0, 8, 0, 0, 8, -8, -8, -8, -8, 8, 0, 8, 0, }, +{b: 16, 0, -8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 8, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 8, -8, -8, 8, }, +{f: 16, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, 8, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, , , , x, , , x, x, }, +{9: , , x, , x, x, x, , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, x, , x, , , , , x, , , , x, }, +{b: , , x, , x, x, x, , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, x, x, x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1000,1101,1,}, +{1011,0010,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x05,0x09,0x0c,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,}}, +{{0x03,0x08,}, {0x05,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x06,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x01,0x02,0x03,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x05,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0f,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +222 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x08,0x06,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, }, +{4: 0, 2, 0, 6, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, }, +{5: 0, 0, 4, 2, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 2, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 2, 2, 2, 0, }, +{c: 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, }, +{b: 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 2, 0, }, +{e: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:58, 4:18, 6:6, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 4:1, 6:1, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 6, 6, 4, 4, 4, 4, 6, 6, 4, 4, 0, 0, }, +{2: 16, 4, 16, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 8, 4, 8, }, +{4: 16, 6, 4, 6, 0, 6, 6, 4, 2, 2, 0, 4, 0, 0, 0, 0, }, +{8: 16, 4, 0, 2, 4, 0, 2, 0, 6, 0, 2, 0, 2, 0, 0, 2, }, +{3: 16, 6, 4, 4, 0, 10, 6, 4, 0, 0, 0, 6, 0, 4, 4, 0, }, +{5: 16, 4, 8, 10, 2, 4, 6, 8, 2, 0, 0, 4, 0, 0, 0, 0, }, +{6: 16, 4, 4, 4, 0, 6, 6, 6, 0, 0, 2, 6, 2, 0, 0, 0, }, +{9: 16, 4, 4, 2, 8, 0, 0, 0, 4, 4, 0, 2, 0, 2, 2, 0, }, +{a: 16, 4, 0, 0, 0, 0, 0, 2, 2, 4, 0, 2, 6, 2, 2, 0, }, +{c: 16, 6, 4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 8, 0, 6, }, +{7: 16, 4, 8, 8, 0, 4, 4, 10, 0, 2, 0, 6, 2, 0, 0, 0, }, +{b: 16, 6, 4, 0, 6, 0, 0, 2, 0, 8, 0, 0, 4, 0, 0, 2, }, +{d: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 8, 0, 0, 6, 10, 4, }, +{e: 16, 0, 4, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 10, 6, 4, }, +{f: 16, 0, 8, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 4, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:53, 6:27, 8:15, 10:5, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 8, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 4, 4, 4, 4, 8, 0, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 4, 8, 0, 8, 0, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 8, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 0, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 0, 4, 4, 4, 8, 4, 8, 4, 0, 0, 0, 4, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 8, 0, 4, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:7, 8:1, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -8, 8, -16, 0, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, -16, 0, 8, -8, 8, 0, 16, -8, 8, -8, -16, 0, -8, 0, }, +{4: 16, 0, 8, 0, 8, 0, -8, -8, 0, 8, -8, -8, 8, -8, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 0, 0, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 0, 8, 0, -8, 0, -16, 0, 8, 8, 8, 0, -8, 0, }, +{5: 16, 0, 8, 0, 8, -8, 8, -8, 0, 0, -8, 0, -8, 8, -16, 0, }, +{6: 16, 0, -8, -8, 8, 0, -8, 0, 0, -8, -8, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -8, -8, 0, 0, 0, 0, -8, 0, 8, 0, 8, 0, }, +{c: 16, -8, 8, -8, -8, 0, 0, -8, 0, 0, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, 0, 0, 0, 0, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 0, 8, -8, 0, -8, -8, 8, 0, }, +{d: 16, 0, 8, -8, -16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 8, 0, }, +{e: 16, -8, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, 8, -8, -8, 8, }, +{f: 16, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, 0, -8, 8, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , , , x, x, , , x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, x, x, , , , x, , , x, x, }, +{9: , x, x, x, x, , x, , x, , , , x, x, , x, }, +{a: , x, , x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , , x, , , x, x, x, }, +{7: , x, , x, x, , x, , , , , x, , , , x, }, +{b: , x, , , x, , x, , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , x, x, x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0010,0010,1,}, +{1000,1101,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +{1100,0111,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x02,0x09,0x0b,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x09,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x06,0x09,0x0f,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x05,0x09,0x0c,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0a,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x0a,}, {0x09,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_223.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_223.txt new file mode 100644 index 0000000..386e130 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_223.txt @@ -0,0 +1,418 @@ +223 Sbox: +LUT = { +0x0f,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, }, +{2: 0, 0, 6, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 4, 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 0, 6, 2, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 4, 0, 0, 6, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 6, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 6, 0, 0, }, +{e: 0, 2, 2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:171, 2:63, 4:6, 6:15, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 2, 0, 0, 0, 0, 6, 0, 4, 4, 6, 4, 6, 0, 2, }, +{2: 16, 0, 6, 2, 0, 2, 10, 0, 4, 0, 4, 4, 8, 0, 8, 0, }, +{4: 16, 0, 0, 6, 2, 6, 2, 0, 4, 4, 0, 6, 0, 6, 4, 0, }, +{8: 16, 0, 0, 0, 6, 4, 8, 4, 2, 0, 0, 0, 8, 4, 10, 2, }, +{3: 16, 2, 0, 6, 4, 6, 2, 0, 0, 0, 6, 4, 4, 0, 0, 6, }, +{5: 16, 0, 8, 0, 8, 0, 6, 2, 2, 10, 0, 4, 0, 4, 0, 4, }, +{6: 16, 6, 0, 0, 4, 2, 0, 6, 6, 2, 0, 6, 0, 0, 4, 4, }, +{9: 16, 0, 4, 6, 0, 0, 0, 6, 6, 2, 0, 0, 4, 4, 2, 6, }, +{a: 16, 4, 0, 4, 0, 0, 8, 0, 0, 6, 2, 0, 10, 2, 8, 4, }, +{c: 16, 4, 4, 0, 0, 6, 0, 2, 0, 0, 6, 0, 2, 6, 4, 6, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 8, 2, 10, 4, 0, 0, 4, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 6, 2, 4, 4, 0, 4, 0, 6, 0, 6, 0, 2, 6, 0, 0, }, +{e: 16, 2, 10, 4, 8, 0, 0, 4, 0, 8, 4, 0, 0, 2, 6, 0, }, +{f: 16, 0, 0, 0, 0, 6, 4, 4, 6, 4, 6, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:30, 4:45, 6:42, 8:12, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, 0, 8, 0, 0, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -8, 0, -8, 0, 0, 8, 0, 0, 8, -16, -8, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 0, -8, 0, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 8, 0, 8, 0, 0, -8, 8, -8, 0, -8, -8, }, +{3: 16, -8, 0, 0, 8, 8, -8, -8, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -16, 8, -8, 0, 0, -8, 0, -8, 8, -8, 8, }, +{6: 16, 0, -8, 0, 8, -8, -8, 8, 0, -8, -8, 0, 0, -8, 8, 8, }, +{9: 16, 0, 0, 0, -8, -8, -8, 8, 8, 0, -8, -8, 8, 0, -8, 8, }, +{a: 16, 0, 0, 0, -8, -8, 8, -16, -8, 8, -8, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, 0, -8, 8, 0, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -16, 0, 0, 0, 8, -8, }, +{d: 16, -8, 8, 0, -8, -8, 0, -8, 8, -8, 8, 0, 0, 0, 8, -8, }, +{e: 16, 8, 0, 0, -8, -8, 0, 8, -8, 0, 8, 8, 0, 0, -8, -16, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, x, , x, x, x, x, x, x, x, , x, x, x, x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , x, , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0101,1,}, +{0110,1010,1,}, +{1000,1000,1,}, +{1100,1011,1,}, +{1110,0010,1,}, +{1111,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x06,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x0e,}, {0x0f,}}, +{{0x0d,0x0e,}, {0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +223 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x08,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x00, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 2, 6, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 2, 6, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, }, +{3: 0, 0, 2, 2, 0, 6, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 6, 2, 0, 2, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 2, 6, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 6, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 2, 0, }, +{e: 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, }, +{f: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 6, }, +}; +Diff: 6, DDT_spectrum: {0:171, 2:63, 4:6, 6:15, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 6, 0, 4, 4, 6, 4, 6, 2, 0, }, +{2: 16, 2, 6, 0, 0, 0, 8, 0, 4, 0, 4, 4, 8, 2, 10, 0, }, +{4: 16, 0, 2, 6, 0, 6, 0, 0, 6, 4, 0, 6, 2, 4, 4, 0, }, +{8: 16, 0, 0, 2, 6, 4, 8, 4, 0, 0, 0, 2, 10, 4, 8, 0, }, +{3: 16, 0, 2, 6, 4, 6, 0, 2, 0, 0, 6, 4, 4, 0, 0, 6, }, +{5: 16, 0, 10, 2, 8, 2, 6, 0, 0, 8, 0, 4, 0, 4, 0, 4, }, +{6: 16, 6, 0, 0, 4, 0, 2, 6, 6, 0, 2, 6, 0, 0, 4, 4, }, +{9: 16, 0, 4, 4, 2, 0, 2, 6, 6, 0, 0, 0, 4, 6, 0, 6, }, +{a: 16, 4, 0, 4, 0, 0, 10, 2, 2, 6, 0, 0, 8, 0, 8, 4, }, +{c: 16, 4, 4, 0, 0, 6, 0, 0, 0, 2, 6, 2, 0, 6, 4, 6, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 4, 8, 0, 8, 4, 0, 0, 4, 10, 2, 0, 6, 2, 0, 0, }, +{d: 16, 6, 0, 6, 4, 0, 4, 0, 4, 2, 6, 0, 0, 6, 2, 0, }, +{e: 16, 0, 8, 4, 10, 0, 0, 4, 2, 8, 4, 0, 0, 0, 6, 2, }, +{f: 16, 2, 0, 0, 2, 6, 4, 4, 6, 4, 6, 0, 0, 0, 0, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:30, 4:45, 6:42, 8:12, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 0, 0, 0, 8, -16, 8, -8, 0, 0, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 8, 8, -8, -8, 8, 0, -8, -8, 8, 0, -8, -8, }, +{8: 16, 8, 0, 0, -8, 8, 0, 8, -8, 0, -8, 8, 0, 0, -8, -16, }, +{3: 16, 0, -8, 0, 8, 8, -8, -8, 0, -8, 8, 0, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -8, 8, -16, -8, 8, -8, 0, 0, 0, -8, 8, }, +{6: 16, 0, 0, -8, 8, -8, -8, 8, 0, -8, -8, 0, -8, 0, 8, 8, }, +{9: 16, -8, 8, 0, -8, -8, 0, 8, 8, -8, -8, 0, 0, 0, -8, 8, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 8, -16, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, -16, 8, 0, -8, 0, 0, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 8, 0, 8, -8, 8, -8, }, +{e: 16, 8, -8, 0, -8, -8, 0, 8, 0, 0, 8, 0, 0, 8, -16, -8, }, +{f: 16, -8, 0, 0, -8, 8, 0, 8, 0, 0, 8, -8, -8, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , x, x, x, x, x, x, x, x, x, , x, x, }, +{e: , , , x, x, x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1000,1011,1,}, +{1100,1010,1,}, +{1110,1110,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x06,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x06,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_224.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_224.txt new file mode 100644 index 0000000..e908610 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_224.txt @@ -0,0 +1,418 @@ +224 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x0f,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 6, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 6, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 6, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{6: 0, 2, 0, 2, 0, 0, 0, 6, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 6, 0, 2, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 6, 0, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:171, 2:63, 4:6, 6:15, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:1, 4:1, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 0, 4, 0, 6, 0, 6, 4, 4, 4, 6, 0, 0, }, +{2: 16, 4, 10, 0, 0, 4, 6, 0, 6, 0, 4, 4, 4, 0, 6, 0, }, +{4: 16, 0, 0, 6, 2, 6, 2, 0, 4, 4, 0, 6, 0, 6, 4, 0, }, +{8: 16, 0, 0, 0, 6, 6, 4, 6, 2, 0, 0, 0, 6, 4, 4, 2, }, +{3: 16, 4, 4, 6, 6, 10, 0, 0, 0, 0, 4, 4, 4, 0, 0, 6, }, +{5: 16, 0, 6, 0, 4, 0, 6, 2, 2, 4, 0, 6, 0, 4, 0, 6, }, +{6: 16, 6, 0, 2, 4, 0, 0, 6, 4, 2, 0, 6, 0, 0, 6, 4, }, +{9: 16, 0, 6, 6, 0, 0, 0, 4, 6, 2, 0, 0, 6, 4, 2, 4, }, +{a: 16, 6, 0, 4, 2, 0, 6, 0, 0, 6, 0, 0, 6, 2, 4, 4, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 4, 4, 0, 4, 2, 6, 0, 6, 0, 0, 6, 0, 2, }, +{e: 16, 0, 6, 4, 6, 0, 2, 4, 0, 4, 6, 0, 0, 2, 6, 0, }, +{f: 16, 0, 0, 2, 0, 6, 4, 4, 4, 6, 6, 0, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:18, 4:57, 6:54, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{6: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -16, 0, 0, 0, 0, 8, -8, -8, -8, 8, -8, }, +{2: 16, 0, -8, 8, 8, -8, 0, -8, 0, -8, 8, 0, 0, 8, -16, 0, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 0, -8, 0, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 8, 0, 8, 0, -8, -8, 8, -8, -8, -8, 0, }, +{3: 16, -8, 0, 8, 8, 8, -8, 0, -8, 0, 8, 0, 0, -16, -8, 0, }, +{5: 16, -8, 0, -8, 8, -8, 8, 0, 0, 0, -8, 0, -8, 8, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, -8, 8, 0, 0, -8, 0, 0, -8, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, -8, 8, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 8, -8, -8, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -16, 8, -8, -8, 0, 0, 8, 0, -8, 8, 8, 0, }, +{7: 16, 0, 0, -16, 8, 8, 0, 0, -8, -8, -8, -8, 0, 8, 8, 0, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{d: 16, -8, 8, -8, -8, -8, 0, 0, 8, -8, 8, 0, 0, -8, 8, 0, }, +{e: 16, 8, 0, -8, -8, -8, 0, 0, -8, 0, 8, 8, 0, 8, -8, -8, }, +{f: 16, 0, -8, -8, -8, 8, 0, 0, 0, 8, 8, -8, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , x, x, , x, x, x, x, x, x, x, , x, x, x, x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , x, , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0001,1,}, +{0100,0111,1,}, +{1000,1100,1,}, +{1100,1011,1,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,}}, +{{0x02,0x04,}, {0x0e,}}, +{{0x0a,0x04,}, {0x06,0x09,0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x03,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x03,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +224 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x08,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x04, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 4, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 2, 6, 2, 0, 0, 0, 2, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 4, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 6, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 2, 2, 0, 0, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 6, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 6, 0, 0, 0, }, +{d: 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 6, 2, }, +{f: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 0, 6, }, +}; +Diff: 6, DDT_spectrum: {0:171, 2:63, 4:6, 6:15, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:10, 2:1, 4:1, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 0, 4, 0, 6, 0, 6, 4, 4, 4, 6, 0, 0, }, +{2: 16, 4, 10, 0, 0, 4, 6, 0, 6, 0, 4, 4, 4, 0, 6, 0, }, +{4: 16, 0, 0, 6, 0, 6, 0, 2, 6, 4, 0, 6, 0, 4, 4, 2, }, +{8: 16, 0, 0, 2, 6, 6, 4, 4, 0, 2, 0, 0, 6, 4, 6, 0, }, +{3: 16, 4, 4, 6, 6, 10, 0, 0, 0, 0, 4, 4, 4, 0, 0, 6, }, +{5: 16, 0, 6, 2, 4, 0, 6, 0, 0, 6, 0, 6, 0, 4, 2, 4, }, +{6: 16, 6, 0, 0, 6, 0, 2, 6, 4, 0, 0, 6, 0, 2, 4, 4, }, +{9: 16, 0, 6, 4, 2, 0, 2, 4, 6, 0, 0, 0, 6, 6, 0, 4, }, +{a: 16, 6, 0, 4, 0, 0, 4, 2, 2, 6, 0, 0, 6, 0, 4, 6, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 6, 4, 0, 4, 0, 4, 2, 6, 0, 0, 6, 2, 0, }, +{e: 16, 0, 6, 4, 4, 0, 0, 6, 2, 4, 6, 0, 0, 0, 6, 2, }, +{f: 16, 0, 0, 0, 2, 6, 6, 4, 4, 4, 6, 0, 0, 2, 0, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:90, 2:18, 4:57, 6:54, 10:6, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, -8, 0, 8, 0, 0, -16, 8, 0, }, +{2: 16, 0, 0, 8, 8, -16, 0, 0, 0, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 0, }, +{8: 16, 8, 0, 8, -8, 8, 0, 0, -8, 0, -8, 8, 0, -8, -8, -8, }, +{3: 16, 0, -8, 8, 8, 8, 0, -8, 0, -8, 8, 0, 0, -8, -16, 0, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, -8, 8, -8, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 0, 8, -8, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, 0, 0, 8, -8, -8, 0, -8, 8, 8, }, +{c: 16, 0, 0, -16, -8, 8, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{b: 16, 0, 0, 8, -16, 8, -8, -8, 0, 0, -8, 0, -8, 8, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 8, 0, 8, -8, 8, -8, }, +{e: 16, 8, -8, -8, -8, -8, -8, 8, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, -8, 0, -8, -8, 8, 8, 0, 0, 0, 8, 0, -8, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, x, x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , x, x, x, x, x, x, x, x, x, , x, x, }, +{e: , , , , x, x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,1100,1,}, +{1000,1011,1,}, +{1100,0111,1,}, +{1101,0001,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x02,0x05,0x07,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0a,}, {0x0e,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_225.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_225.txt new file mode 100644 index 0000000..84ff362 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_225.txt @@ -0,0 +1,418 @@ +225 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, }, +{4: 0, 2, 0, 8, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 2, 0, 6, 2, 2, 0, 2, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, 0, 4, }, +{9: 0, 0, 0, 2, 0, 0, 2, 0, 8, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 4, 2, 2, 0, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 8, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 4, 2, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 6, 2, 2, }, +{e: 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:54, 4:21, 6:4, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 6, 6, 4, 4, 0, 4, 0, 4, 0, 0, 6, 0, 0, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 6, 4, 8, 4, 4, 4, 4, 4, 6, 6, 6, 0, 4, 4, 0, }, +{8: 16, 6, 0, 4, 6, 0, 4, 2, 6, 0, 4, 0, 2, 6, 0, 0, }, +{3: 16, 4, 4, 4, 0, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 16, 4, 0, 4, 6, 0, 6, 2, 6, 0, 6, 0, 0, 4, 2, 0, }, +{6: 16, 0, 4, 6, 0, 0, 0, 8, 6, 2, 0, 2, 0, 0, 0, 4, }, +{9: 16, 4, 4, 6, 4, 4, 6, 4, 8, 6, 4, 0, 6, 4, 0, 4, }, +{a: 16, 0, 0, 4, 2, 4, 2, 2, 4, 8, 0, 0, 2, 0, 4, 0, }, +{c: 16, 4, 4, 4, 4, 4, 6, 0, 4, 0, 8, 6, 4, 6, 4, 6, }, +{7: 16, 0, 0, 4, 0, 4, 2, 2, 0, 0, 4, 8, 4, 2, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 6, 2, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 4, 6, 0, 6, 0, 4, 0, 4, 0, 0, 6, 2, 2, }, +{e: 16, 0, 4, 6, 0, 0, 0, 0, 0, 4, 6, 2, 0, 0, 8, 2, }, +{f: 16, 0, 0, 0, 0, 4, 0, 4, 4, 0, 6, 0, 0, 2, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:86, 2:22, 4:72, 6:33, 8:7, 10:3, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 4, 4, 4, 0, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 8, 0, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 8, -8, 0, 0, 0, 0, 8, -8, -8, -8, 0, -16, }, +{2: 16, 0, -16, 8, 0, 0, -8, -8, 0, 0, 8, 8, 0, 8, -8, -8, }, +{4: 16, 8, 8, -8, 8, 8, -8, -8, 0, 8, -8, -16, 8, -8, 0, -8, }, +{8: 16, 0, 8, 8, -8, 0, 0, 8, 0, -8, -8, 8, -8, -8, 0, -8, }, +{3: 16, -8, -8, 8, 0, 0, 0, 0, -8, 8, 8, -8, 0, -16, 0, 8, }, +{5: 16, 0, 8, -8, 0, -8, 0, 0, -8, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 0, -8, -8, 0, 0, 0, 8, 8, 0, -8, -8, 0, -8, 0, 8, }, +{9: 16, -8, 8, 8, -8, -8, -8, 0, 8, 0, -16, -8, 8, 8, -8, 8, }, +{a: 16, 0, -8, 8, 0, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 8, }, +{c: 16, 0, 8, -16, -8, 8, 0, -8, -8, -8, 8, -8, -8, 8, 8, 8, }, +{7: 16, -8, -8, -8, 0, 0, 0, 0, 0, 0, -8, 8, 0, 8, 8, -8, }, +{b: 16, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, -8, }, +{d: 16, -8, 8, -8, -8, -8, 8, 0, 0, 0, 8, 8, 0, -8, 0, -8, }, +{e: 16, 8, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, 0, 8, -8, -8, }, +{f: 16, 0, -8, -8, 0, 0, -8, 0, 0, -8, 8, 8, 0, -8, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, , , x, , , , x, x, , x, , x, }, +{6: , x, , x, x, , x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, , x, x, , x, , , x, x, , x, , x, x, }, +{c: , x, x, , x, , x, , , , x, , , x, x, x, }, +{7: , x, , x, , , x, , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , x, , x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0010,1,}, +{0100,1100,1,}, +{0111,0100,1,}, +{1100,1001,1,}, +{1101,0011,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x02,}}, +{{0x06,0x08,}, {0x06,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,}}, +{{0x01,0x06,}, {0x0f,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x0f,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x01,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +225 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x08,0x0c,0x06,0x07,0x04,0x09,0x0a,0x0b,0x05,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, }, +{4: 0, 2, 0, 8, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{8: 0, 2, 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 2, 2, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 2, 0, 0, 0, 4, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 8, 0, 0, 0, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, 4, 4, 0, 2, 0, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 2, 2, 0, 4, 2, 0, 0, 0, }, +{d: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 6, 0, 2, }, +{e: 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 2, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:54, 4:21, 6:4, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:7, 2:4, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 6, 6, 4, 4, 0, 4, 0, 4, 0, 0, 6, 0, 0, }, +{2: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{4: 16, 6, 4, 8, 4, 4, 4, 6, 6, 4, 4, 4, 0, 4, 6, 0, }, +{8: 16, 6, 0, 4, 6, 0, 6, 0, 4, 2, 4, 0, 2, 6, 0, 0, }, +{3: 16, 4, 4, 4, 0, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 16, 4, 0, 4, 4, 0, 6, 0, 6, 2, 6, 2, 0, 6, 0, 0, }, +{6: 16, 0, 4, 4, 2, 0, 2, 8, 4, 2, 0, 2, 0, 0, 0, 4, }, +{9: 16, 4, 4, 4, 6, 4, 6, 6, 8, 4, 4, 0, 6, 4, 0, 4, }, +{a: 16, 0, 0, 6, 0, 4, 0, 2, 6, 8, 0, 0, 2, 0, 4, 0, }, +{c: 16, 4, 4, 6, 4, 4, 6, 0, 4, 0, 8, 4, 4, 4, 6, 6, }, +{7: 16, 0, 0, 6, 0, 4, 0, 2, 0, 0, 6, 8, 4, 0, 2, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 6, 2, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 4, 6, 0, 4, 0, 4, 0, 6, 2, 0, 6, 0, 2, }, +{e: 16, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, 0, 2, 8, 2, }, +{f: 16, 0, 0, 0, 0, 4, 0, 4, 4, 0, 6, 0, 0, 2, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:86, 2:22, 4:72, 6:33, 8:7, 10:3, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{3: 0, 8, 0, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{c: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 12, 4, 0, 0, 4, 0, }, +{7: 0, 0, 0, 4, 0, 0, 12, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, 0, -8, 0, -8, 0, 8, 0, 0, -16, 0, -8, }, +{2: 16, 0, -8, 8, 0, -8, -8, 0, 0, 8, 8, 0, -8, 8, 0, -16, }, +{4: 16, 8, 8, -8, 8, 0, -16, 0, 8, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, -8, 0, 8, 0, -8, 0, -8, 8, -8, -8, 0, -8, }, +{3: 16, 0, -16, 8, 0, 0, 8, -8, 0, 0, 8, -8, 0, -8, -8, 8, }, +{5: 16, -8, 8, -8, 0, -8, 8, -8, -8, 0, -8, 0, 0, 8, 0, 8, }, +{6: 16, 0, -8, -8, 0, 0, 8, 8, 0, 0, -8, 0, -8, -8, 0, 8, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 8, -8, -16, 0, 0, 8, -8, 8, }, +{a: 16, 0, -8, 8, 0, 0, -8, -8, 0, 0, -8, 0, 8, -8, 0, 8, }, +{c: 16, 8, 8, -16, -8, 8, -8, -8, -8, 0, 8, -8, -8, 8, 0, 8, }, +{7: 16, 0, -8, -8, 0, 8, -8, 0, 0, 0, -8, 0, 0, 8, 8, -8, }, +{b: 16, 0, -8, 8, 0, 0, 8, 0, 0, -8, -8, -8, 0, 8, 0, -8, }, +{d: 16, -8, 8, -8, -8, 0, 8, 0, 0, -8, 8, 0, 0, -8, 8, -8, }, +{e: 16, 0, -8, -8, 0, -8, 8, 0, 0, 0, 8, 0, 0, 8, -8, -8, }, +{f: 16, 0, -8, -8, 0, 0, -8, 0, 0, -8, 8, 8, 0, -8, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , , x, x, x, , , x, }, +{5: , x, x, x, , , x, , , , x, x, , x, , x, }, +{6: , x, x, x, x, , x, x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, x, , x, , x, x, }, +{c: , , x, , x, , x, , , , x, , , x, x, x, }, +{7: , x, , x, , , x, , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , , x, , x, , x, , , , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0010,0011,1,}, +{0100,1100,1,}, +{0101,0100,1,}, +{1100,1001,1,}, +{1101,0001,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x01,0x04,0x05,}}, +{{0x02,0x08,}, {0x0f,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x0f,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x0f,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x0e,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_226.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_226.txt new file mode 100644 index 0000000..92970e7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_226.txt @@ -0,0 +1,418 @@ +226 Sbox: +LUT = { +0x07,0x00,0x01,0x02,0x03,0x05,0x06,0x08,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 8, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 4, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 2, 0, 2, 0, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 0, 2, 4, 2, 0, 0, 0, 0, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 2, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 4, 0, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 2, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:54, 4:21, 6:4, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:1, 6:1, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{2: 16, 4, 8, 4, 0, 4, 6, 6, 4, 0, 4, 4, 4, 6, 6, 4, }, +{4: 16, 4, 4, 8, 6, 4, 6, 4, 4, 6, 4, 6, 0, 4, 4, 0, }, +{8: 16, 0, 4, 0, 4, 6, 0, 0, 4, 0, 0, 2, 10, 0, 0, 2, }, +{3: 16, 6, 4, 4, 4, 8, 6, 4, 4, 4, 4, 4, 6, 0, 0, 6, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 4, 0, 4, 4, 0, 0, 0, 0, }, +{6: 16, 6, 6, 4, 2, 4, 4, 6, 0, 2, 0, 6, 0, 0, 0, 0, }, +{9: 16, 0, 0, 6, 2, 4, 0, 2, 4, 10, 0, 0, 0, 0, 4, 0, }, +{a: 16, 0, 4, 4, 0, 4, 4, 0, 16, 4, 4, 0, 4, 4, 0, 0, }, +{c: 16, 0, 4, 0, 0, 6, 0, 0, 0, 0, 4, 2, 2, 4, 0, 10, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 0, 0, 6, 10, 4, 0, 2, 0, 2, 4, 0, 4, 0, 0, 0, }, +{d: 16, 2, 6, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 10, 0, }, +{e: 16, 2, 6, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 2, 4, }, +{f: 16, 0, 4, 4, 4, 4, 4, 0, 4, 0, 16, 0, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:18, 4:72, 6:33, 8:3, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:9, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 8, 8, -8, 8, 8, 0, -8, 0, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, -8, 0, 8, -8, 8, 0, 8, 0, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, -16, -8, 8, 8, 8, -8, -8, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, -8, 8, 0, 8, -8, 0, -8, 0, 0, -8, 0, 0, 8, -16, 8, }, +{6: 16, 8, -8, 0, 8, -8, 0, 8, 0, -8, -8, 0, -8, -8, 8, 0, }, +{9: 16, 8, 0, 0, -8, -8, -8, 8, 0, 0, -8, 0, 8, 0, -8, 0, }, +{a: 16, -8, 0, 0, -8, -8, 8, -16, 0, 8, -8, 8, 0, 0, 8, 0, }, +{c: 16, -8, 0, -8, -8, 8, 0, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 8, 0, 0, -8, 8, -8, -8, 0, 0, -8, 0, -8, 0, 8, 0, }, +{d: 16, 8, 0, 0, -8, -8, 0, -8, -8, 0, 8, -8, 0, 0, 8, 0, }, +{e: 16, -8, 0, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, 0, -8, 0, }, +{f: 16, 8, 0, -8, -16, 8, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , , x, x, x, x, x, , , , x, x, , , x, }, +{5: , x, , x, x, , x, x, , , , x, , x, , x, }, +{6: , x, x, x, x, , x, x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , , x, , x, x, , , , x, x, , , x, }, +{d: , x, , x, x, , x, x, , , , x, , x, , x, }, +{e: , x, x, x, x, , x, x, , , , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0011,1,}, +{0011,0010,1,}, +{0110,1010,1,}, +{1000,1111,1,}, +{1100,0100,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x06,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +226 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x00,0x07,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 8, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 4, }, +{3: 0, 2, 0, 0, 2, 8, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 4, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 2, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:173, 2:54, 4:21, 6:4, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:1, 6:1, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 0, 4, 4, 4, 0, 6, 6, 4, }, +{4: 16, 4, 4, 8, 0, 4, 6, 4, 6, 4, 0, 6, 6, 4, 4, 4, }, +{8: 16, 0, 0, 6, 4, 4, 0, 2, 2, 0, 0, 0, 10, 0, 0, 4, }, +{3: 16, 6, 4, 4, 6, 8, 6, 4, 4, 4, 6, 4, 4, 0, 0, 4, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 4, 0, 4, 0, 0, 0, 4, }, +{6: 16, 6, 6, 4, 0, 4, 4, 6, 2, 0, 0, 6, 2, 0, 0, 0, }, +{9: 16, 0, 4, 4, 4, 4, 4, 0, 4, 16, 0, 0, 0, 0, 4, 4, }, +{a: 16, 0, 0, 6, 0, 4, 0, 2, 10, 4, 0, 0, 2, 4, 0, 0, }, +{c: 16, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 16, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 10, 6, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, }, +{d: 16, 2, 6, 4, 0, 0, 0, 0, 0, 4, 4, 0, 0, 2, 10, 0, }, +{e: 16, 2, 6, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 10, 2, 4, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:18, 4:72, 6:33, 8:3, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{8: 0, 4, 4, 4, 12, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{b: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:9, 8:2, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, -8, -8, 8, -8, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 8, -16, 8, -8, 8, -8, 8, 0, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 8, 8, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 8, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, 0, 8, 8, 8, -8, -8, -16, -8, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, 0, 8, -8, 8, -16, -8, 8, -8, 0, 0, 0, -8, 8, }, +{6: 16, 0, -8, 0, 8, -8, -8, 8, 8, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 8, -8, 0, -8, 8, 0, 8, -16, 0, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 8, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, -8, 0, -8, -16, 8, 0, -8, 8, 0, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 8, 0, 0, -8, -8, 0, -8, -8, 0, 8, -8, 0, 0, 8, 0, }, +{e: 16, -8, 0, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , , , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, , , x, x, x, , , x, x, , x, x, x, }, +{7: , x, x, x, x, x, x, x, , , , , , , , x, }, +{b: , x, x, , x, x, x, x, , , , x, x, , , x, }, +{d: , x, , , , x, x, x, , , , x, , x, , x, }, +{e: , x, x, , , , x, x, , , , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1000,1100,1,}, +{1001,0011,1,}, +{1100,0100,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x04,}, {0x05,0x09,0x0c,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x04,0x09,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_227.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_227.txt new file mode 100644 index 0000000..322e9d6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_227.txt @@ -0,0 +1,430 @@ +227 Sbox: +LUT = { +0x08,0x00,0x01,0x0f,0x02,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0, }, +{2: 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, }, +{4: 0, 0, 0, 4, 6, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{5: 0, 0, 2, 0, 0, 0, 4, 2, 6, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 4, 0, 6, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 0, 4, 0, 4, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 8, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 8, 0, 2, 0, 2, }, +{b: 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, }, +{e: 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 4, 0, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:174, 2:54, 4:18, 6:6, 8:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:2, 4:3, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 2, 0, 0, 4, 0, 8, 4, 10, 4, 8, 2, 0, }, +{2: 16, 0, 6, 2, 0, 0, 4, 0, 10, 0, 4, 8, 4, 0, 8, 2, }, +{4: 16, 0, 0, 8, 6, 8, 2, 0, 0, 2, 4, 10, 4, 0, 0, 4, }, +{8: 16, 0, 0, 4, 8, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 0, }, +{3: 16, 2, 0, 4, 8, 6, 2, 0, 0, 0, 4, 10, 4, 0, 0, 8, }, +{5: 16, 0, 10, 0, 0, 0, 8, 2, 6, 0, 4, 8, 4, 2, 4, 0, }, +{6: 16, 8, 0, 0, 0, 2, 0, 8, 0, 6, 4, 10, 4, 4, 2, 0, }, +{9: 16, 2, 4, 2, 0, 0, 4, 0, 8, 2, 4, 0, 4, 0, 0, 2, }, +{a: 16, 4, 2, 0, 0, 0, 2, 4, 0, 8, 6, 0, 6, 0, 0, 0, }, +{c: 16, 4, 4, 6, 4, 4, 4, 6, 4, 4, 8, 0, 0, 6, 4, 6, }, +{7: 16, 4, 4, 6, 4, 4, 4, 6, 4, 4, 0, 8, 0, 6, 4, 6, }, +{b: 16, 10, 8, 0, 10, 10, 0, 0, 8, 10, 0, 0, 8, 0, 0, 0, }, +{d: 16, 8, 2, 0, 0, 0, 2, 0, 0, 4, 6, 0, 6, 4, 0, 0, }, +{e: 16, 0, 8, 0, 2, 2, 0, 2, 4, 0, 4, 0, 4, 2, 4, 0, }, +{f: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 6, 0, 6, 0, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:28, 4:50, 6:22, 8:23, 10:10, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 8, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 4, 0, 0, 4, 4, 4, 8, 0, 4, 4, 4, 8, 0, 4, 0, }, +{9: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 0, 8, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 0, 0, 4, 0, 8, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:123, 4:106, 8:20, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, 8, -8, 0, 8, 0, 0, -8, 8, -16, }, +{2: 16, 8, -8, 0, 0, -8, 0, 0, 8, 0, 8, -8, 0, 8, -16, -8, }, +{4: 16, 8, 8, 0, 0, 8, 8, 0, -8, 0, -16, 0, 0, -8, -8, -8, }, +{8: 16, 8, 8, 0, -8, 8, -8, 0, 0, 0, -8, 0, 0, 0, -8, -8, }, +{3: 16, -16, -8, 0, 8, 8, 0, 0, -8, 0, 8, 0, 0, -8, -8, 8, }, +{5: 16, -8, 8, 0, 0, -16, 0, 0, 8, -8, -8, 0, 0, 8, -8, 8, }, +{6: 16, 8, -16, 0, 0, -8, 0, 0, -8, 0, -8, 0, 8, -8, 8, 8, }, +{9: 16, -8, 8, 0, 0, -8, 0, 0, 0, 8, -8, -8, 0, 0, -8, 8, }, +{a: 16, 8, -8, 0, 0, -8, 0, -8, 0, 0, -8, 0, -8, 0, 8, 8, }, +{c: 16, 8, 8, -16, -8, 8, -8, -8, 0, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -16, 8, 8, 8, 8, 0, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, -8, -8, 16, -8, 8, -8, -8, 0, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, 8, 0, -8, 0, 8, -8, }, +{e: 16, 8, -8, 0, 0, -8, 0, 0, 0, -8, 8, 8, 0, 0, -8, -8, }, +{f: 16, -8, -8, 0, -8, 8, -8, 0, 0, 0, 8, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{3: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{6: , x, , x, x, , x, x, x, x, x, , x, x, x, x, }, +{9: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, , , , , , , , x, , , x, x, x, }, +{7: , , , , , , x, x, x, x, x, , x, x, x, x, }, +{b: , , x, , x, , x, x, x, x, x, x, , x, x, x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0001,0011,1,}, +{0010,0110,1,}, +{0011,0101,1,}, +{0100,0111,1,}, +{0100,1011,0,}, +{0100,1100,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x04,}}, +{{0x09,0x02,0x0c,}, {0x04,}}, +{{0x01,0x0a,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x0e,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,}}, +{{0x01,0x0a,}, {0x04,0x0b,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +227 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x0f,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x03, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, }, +{2: 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 4, 0, }, +{4: 0, 0, 2, 4, 4, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 6, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, }, +{5: 0, 0, 0, 2, 0, 2, 4, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 0, 4, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 6, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 6, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, }, +{d: 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 2, 0, }, +{e: 0, 2, 4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, }, +{f: 0, 0, 2, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, 0, 0, 4, }, +}; +Diff: 8, DDT_spectrum: {0:174, 2:54, 4:18, 6:6, 8:3, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:2, 4:3, 6:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 0, 0, 0, 2, 0, 8, 2, 4, 4, 4, 10, 8, 0, 0, }, +{2: 16, 0, 6, 0, 0, 0, 10, 0, 4, 2, 4, 4, 8, 2, 8, 0, }, +{4: 16, 0, 2, 8, 4, 4, 0, 0, 2, 0, 6, 6, 0, 0, 0, 0, }, +{8: 16, 2, 0, 6, 8, 8, 0, 0, 0, 0, 4, 4, 10, 0, 2, 4, }, +{3: 16, 0, 0, 8, 4, 6, 0, 2, 0, 0, 4, 4, 10, 0, 2, 8, }, +{5: 16, 0, 4, 2, 0, 2, 8, 0, 4, 2, 4, 4, 0, 2, 0, 0, }, +{6: 16, 4, 0, 0, 0, 0, 2, 8, 0, 4, 6, 6, 0, 0, 2, 0, }, +{9: 16, 0, 10, 0, 2, 0, 6, 0, 8, 0, 4, 4, 8, 0, 4, 2, }, +{a: 16, 8, 0, 2, 0, 0, 0, 6, 2, 8, 4, 4, 10, 4, 0, 0, }, +{c: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 8, 0, 0, 6, 4, 6, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 0, 0, 8, 6, 4, 6, }, +{d: 16, 8, 0, 0, 0, 0, 2, 4, 0, 0, 6, 6, 0, 4, 2, 0, }, +{e: 16, 2, 8, 0, 2, 0, 4, 2, 0, 0, 4, 4, 0, 0, 4, 2, }, +{f: 16, 0, 2, 4, 0, 8, 0, 0, 2, 0, 6, 6, 0, 0, 0, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:28, 4:50, 6:22, 8:23, 10:10, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 4, 8, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{6: 0, 0, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:123, 4:106, 8:20, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 0, -8, -8, 0, 0, 0, 8, 0, 0, -8, 8, -8, }, +{2: 16, 8, -8, 0, 0, -16, 8, -8, 0, 0, 8, 0, 0, 8, -8, -8, }, +{4: 16, 8, 8, 0, 0, 8, 0, 0, 0, -8, -8, -8, 0, 0, -8, -8, }, +{8: 16, 8, 8, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, -8, -8, -16, }, +{3: 16, -8, -16, 0, 0, 8, -8, 0, 0, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, -8, 8, 0, 0, -8, 0, -8, 0, 0, -8, 0, 8, 0, -8, 8, }, +{6: 16, 8, -8, -8, 0, -8, 0, 0, -8, 0, -8, 0, 0, 0, 8, 8, }, +{9: 16, -8, 8, 0, 0, -8, 8, 0, 0, 0, -8, 0, -8, 8, -16, 8, }, +{a: 16, 8, -8, 0, 0, -8, -8, 0, 8, 0, -16, 0, 0, -8, 8, 8, }, +{c: 16, 8, 8, -8, -16, 8, 0, -8, -8, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, -8, -8, 8, -16, 8, 0, -8, 8, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, -8, 8, -8, 0, -8, 0, 0, -8, 0, 8, 0, 0, 0, 8, -8, }, +{e: 16, 8, -8, 0, 0, -8, 0, 8, 0, 0, 8, 0, -8, 0, -8, -8, }, +{f: 16, -8, -8, 0, 0, 8, 0, 0, 0, -8, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{3: , , , x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{5: , , x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{6: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{9: , , x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, x, , x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, , , , , , , x, , , x, x, x, }, +{7: , , , x, , , x, x, x, x, x, , x, x, x, x, }, +{b: , , , , , , x, x, x, x, x, x, , x, x, x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0001,0001,1,}, +{0010,0011,1,}, +{0011,0010,1,}, +{1000,0111,0,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1100,1010,1,}, +{1110,1001,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0f,}}, +{{0x02,0x04,}, {0x03,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x02,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_228.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_228.txt new file mode 100644 index 0000000..3082baf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_228.txt @@ -0,0 +1,418 @@ +228 Sbox: +LUT = { +0x02,0x00,0x01,0x08,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 8, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 2, 0, 6, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 0, 6, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 2, 6, 2, 2, 0, 0, 2, 0, 0, 2, 0, }, +{6: 0, 0, 2, 2, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, }, +{9: 0, 0, 2, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 2, 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 6, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:69, 4:6, 6:9, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 6, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 6, 0, 0, }, +{2: 16, 4, 8, 4, 6, 6, 6, 4, 4, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 6, 4, 6, 2, 4, 6, 4, 0, 0, 0, 6, 0, 0, 0, 2, }, +{8: 16, 4, 4, 0, 6, 6, 0, 2, 6, 4, 0, 0, 6, 0, 0, 2, }, +{3: 16, 6, 4, 6, 4, 8, 4, 4, 4, 6, 4, 4, 4, 0, 0, 6, }, +{5: 16, 4, 4, 4, 0, 6, 6, 6, 2, 0, 0, 6, 0, 0, 2, 0, }, +{6: 16, 4, 6, 6, 0, 4, 4, 6, 0, 2, 0, 6, 0, 2, 0, 0, }, +{9: 16, 4, 6, 2, 4, 4, 0, 0, 6, 6, 0, 0, 6, 0, 2, 0, }, +{a: 16, 6, 4, 0, 6, 4, 2, 0, 4, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 4, 2, 2, }, +{e: 16, 0, 6, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 2, 6, 0, 0, 0, 0, 6, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:84, 2:24, 4:60, 6:51, 8:3, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -16, -8, 8, 0, 0, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -8, 8, -8, 0, -8, 8, 0, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 8, 8, 0, 0, 0, 8, -8, -8, 0, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 8, 0, 8, 0, -8, -8, 8, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 8, 8, -8, -8, -8, 0, 8, 0, 8, -16, -8, 8, }, +{5: 16, -8, 0, -8, 8, -8, 0, 0, -8, 0, -8, 8, 0, 8, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, 0, 0, 8, -8, -8, 0, 0, -8, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 0, 8, 0, -8, -8, 8, 8, -8, 0, }, +{a: 16, 0, 0, 8, -8, -8, 8, -8, -8, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -16, -8, 8, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{b: 16, 0, 0, 8, -16, 8, -8, -8, 0, 0, -8, 0, -8, 8, 8, 0, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , , , x, x, x, x, , , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0001,1,}, +{0100,1100,1,}, +{1000,1011,1,}, +{1100,0111,1,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x0a,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x03,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +228 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x08,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{2: 0, 2, 8, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 0, 2, }, +{8: 0, 0, 2, 2, 6, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 2, 0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 2, 2, 0, 0, 6, 0, 0, 2, 0, 2, 0, 0, 2, 0, }, +{6: 0, 2, 0, 0, 2, 0, 2, 6, 0, 0, 0, 2, 0, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 2, 0, 6, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 4, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:168, 2:69, 4:6, 6:9, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 6, 4, 6, 4, 4, 4, 6, 4, 4, 4, 6, 0, 0, }, +{2: 16, 6, 8, 4, 4, 4, 4, 6, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 4, 4, 6, 0, 6, 4, 6, 2, 0, 0, 6, 0, 0, 0, 2, }, +{8: 16, 4, 6, 2, 6, 4, 0, 0, 4, 6, 0, 0, 6, 0, 0, 2, }, +{3: 16, 4, 6, 4, 6, 8, 6, 4, 4, 4, 4, 4, 4, 0, 0, 6, }, +{5: 16, 4, 6, 6, 0, 4, 6, 4, 0, 2, 0, 6, 0, 0, 2, 0, }, +{6: 16, 6, 4, 4, 2, 4, 6, 6, 0, 0, 0, 6, 0, 2, 0, 0, }, +{9: 16, 6, 4, 0, 6, 4, 2, 0, 6, 4, 0, 0, 6, 0, 2, 0, }, +{a: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 6, 0, 0, 0, 0, 0, 2, 0, 2, 6, 0, 0, 4, 2, 2, }, +{e: 16, 0, 6, 0, 0, 0, 2, 0, 2, 0, 6, 0, 0, 2, 4, 2, }, +{f: 16, 0, 0, 2, 2, 6, 0, 0, 0, 0, 6, 0, 0, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:84, 2:24, 4:60, 6:51, 8:3, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:114, 8:18, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 0, -8, 8, 8, -8, 0, -16, 8, -8, }, +{2: 16, 8, -8, 8, 8, -16, 0, 0, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 0, }, +{8: 16, 8, 0, 8, -8, 8, 8, 0, 0, 0, -8, 0, -8, -8, -8, -8, }, +{3: 16, -8, -8, 8, 8, 8, 0, -8, -8, -8, 8, 8, 0, -8, -16, 8, }, +{5: 16, 0, 0, -8, 8, -8, 8, -8, -8, 8, -8, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 8, -8, 0, 8, 0, -8, -8, 8, -8, -8, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 0, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 0, -8, -16, 8, -8, -8, 0, 0, 8, 0, -8, 8, 8, 0, }, +{7: 16, 0, 0, -16, 8, 8, 0, 0, -8, -8, -8, -8, 0, 8, 8, 0, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, -8, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 8, 0, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 8, 0, 0, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, , x, x, x, , , x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0100,0111,1,}, +{1000,1100,1,}, +{1100,1011,1,}, +{1101,0001,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x03,0x09,0x0a,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x05,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x07,0x09,0x0e,}}, +{{0x09,0x06,}, {0x06,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_229.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_229.txt new file mode 100644 index 0000000..ace7503 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_229.txt @@ -0,0 +1,430 @@ +229 Sbox: +LUT = { +0x04,0x08,0x01,0x02,0x03,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 0, }, +{8: 0, 2, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 0, 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 0, 6, 2, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 6, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:63, 4:9, 6:9, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 4, 6, 4, 6, 6, 4, 6, 4, 4, 4, 0, 0, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 4, 8, 6, 0, 4, 10, 4, 0, 0, 2, 8, 0, 2, 0, 0, }, +{8: 16, 6, 4, 2, 6, 4, 0, 0, 6, 4, 0, 0, 6, 0, 0, 2, }, +{3: 16, 4, 4, 6, 4, 8, 4, 6, 6, 4, 4, 4, 6, 0, 0, 4, }, +{5: 16, 6, 4, 6, 0, 4, 6, 6, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 0, 0, 10, 0, 0, 2, 2, }, +{9: 16, 4, 8, 0, 8, 4, 0, 0, 6, 10, 0, 0, 4, 2, 2, 0, }, +{a: 16, 6, 4, 0, 4, 6, 0, 0, 4, 6, 0, 0, 6, 2, 2, 0, }, +{c: 16, 4, 4, 0, 2, 6, 2, 0, 0, 0, 6, 0, 0, 6, 4, 6, }, +{7: 16, 6, 4, 6, 0, 6, 4, 4, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:80, 2:34, 4:58, 6:34, 8:14, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 4, 12, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 8, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:123, 4:106, 8:20, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -16, 8, -8, 0, 8, -8, -8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 8, -16, 16, -16, 0, 0, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 8, -16, 8, 8, 0, -8, 0, 0, -8, -8, 8, 0, 0, -8, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, 0, 0, -8, 0, -8, -8, -8, -8, }, +{3: 16, -8, -8, 8, 8, 8, -16, -8, 0, -8, 0, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{6: 16, 8, -16, -8, 8, -8, 0, 8, 8, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 8, -16, -8, 0, 8, 0, -8, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, -8, 8, 0, 0, 8, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, -8, -8, 8, 0, -8, 0, 0, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, -8, 0, 0, -8, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 8, 0, 0, 0, -16, 8, 0, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , , x, , x, x, x, , , , , x, , x, , x, }, +{6: , , , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, , , , x, x, , x, }, +{a: , x, x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{1000,1001,1,}, +{1011,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x05,}}, +{{0x01,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x05,}}, +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,}}, +{{0x06,0x08,}, {0x02,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x02,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x0b,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x09,0x0b,}}, +{{0x01,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +229 Inverse Sbox: +LUT = { +0x08,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, }, +{4: 0, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 8, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 2, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, 2, 2, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 4, 0, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, }, +{c: 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:171, 2:63, 4:9, 6:9, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 6, 4, 6, 4, 4, 6, 4, 6, 4, 4, 0, 0, }, +{2: 16, 4, 16, 8, 4, 4, 4, 8, 8, 4, 4, 4, 8, 0, 4, 0, }, +{4: 16, 4, 4, 6, 2, 6, 6, 4, 0, 0, 0, 6, 0, 2, 0, 0, }, +{8: 16, 4, 8, 0, 6, 4, 0, 0, 8, 4, 2, 0, 10, 0, 0, 2, }, +{3: 16, 6, 4, 4, 4, 8, 4, 4, 4, 6, 6, 6, 4, 0, 0, 4, }, +{5: 16, 4, 8, 10, 0, 4, 6, 8, 0, 0, 2, 4, 0, 2, 0, 0, }, +{6: 16, 6, 4, 4, 0, 6, 6, 6, 0, 0, 0, 4, 0, 0, 2, 2, }, +{9: 16, 6, 4, 0, 6, 6, 0, 0, 6, 4, 0, 0, 4, 2, 2, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 10, 6, 0, 0, 8, 2, 2, 0, }, +{c: 16, 6, 4, 2, 0, 4, 0, 0, 0, 0, 6, 0, 2, 6, 4, 6, }, +{7: 16, 4, 8, 8, 0, 4, 4, 10, 0, 0, 0, 6, 0, 0, 2, 2, }, +{b: 16, 4, 4, 0, 6, 6, 2, 0, 4, 6, 0, 0, 6, 0, 0, 2, }, +{d: 16, 4, 0, 2, 0, 0, 2, 0, 2, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 4, 0, 0, 0, 0, 2, 2, 2, 4, 2, 0, 2, 4, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 2, 0, 0, 6, 2, 2, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:80, 2:34, 4:58, 6:34, 8:14, 10:4, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 12, 0, 0, 4, }, +{d: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{e: 0, 4, 4, 0, 4, 0, 4, 4, 0, 8, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:123, 4:106, 8:20, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, 0, 8, -16, 8, 0, -8, -8, -8, 8, -8, }, +{2: 16, 8, -16, 8, 8, -8, 0, -8, 16, -8, 0, 0, -16, 8, 0, -8, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 0, -8, 0, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, -16, 8, 0, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 8, 8, 8, -8, -8, -16, -8, 8, 0, 8, -8, 0, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 0, 0, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, -8, 8, 0, 0, 0, 8, -8, -8, 0, 8, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 0, -8, 0, 0, 8, 0, -8, 0, }, +{a: 16, 8, -8, 8, -8, -16, 8, -8, 0, 0, 0, -8, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, -8, 8, -8, -8, 0, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -16, 8, 8, 0, 8, 0, 0, -8, -8, 8, 0, 0, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, -8, 0, 8, -8, 8, -8, 0, 0, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , , , x, x, , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0010,1,}, +{0011,1010,1,}, +{0100,0111,1,}, +{0110,0101,1,}, +{1000,1000,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 2, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x09,}}, +{{0x01,0x02,0x04,}, {0x09,}}, +{{0x01,0x02,0x0c,}, {0x09,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x04,}, {0x03,}}, +{{0x02,0x0c,}, {0x02,0x09,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x06,0x09,0x0f,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x07,0x09,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x02,0x09,0x0b,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x09,0x0b,}}, +{{0x0d,0x02,}, {0x02,0x09,0x0b,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x06,0x09,0x0f,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x03,0x09,0x0a,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_230.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_230.txt new file mode 100644 index 0000000..32a6c69 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_230.txt @@ -0,0 +1,420 @@ +230 Sbox: +LUT = { +0x04,0x00,0x01,0x08,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 2, 8, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 0, 2, 0, 0, 2, 0, 0, 6, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, 0, }, +{c: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 0, 2, }, +{7: 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:172, 2:62, 4:9, 6:8, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 6, 4, 4, 4, 4, 6, 6, 4, 6, 4, 4, 0, 0, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 4, 4, 10, 0, 4, 6, 6, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 4, 4, 0, 6, 6, 0, 0, 6, 4, 0, 2, 6, 0, 2, 0, }, +{3: 16, 6, 4, 4, 6, 8, 6, 4, 4, 4, 6, 4, 4, 0, 0, 4, }, +{5: 16, 6, 6, 4, 0, 4, 10, 6, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 4, 6, 4, 0, 6, 4, 10, 0, 0, 0, 6, 4, 4, 0, 0, }, +{9: 16, 4, 6, 0, 4, 6, 0, 0, 6, 6, 0, 0, 4, 2, 0, 2, }, +{a: 16, 6, 6, 0, 4, 4, 0, 0, 4, 6, 2, 0, 6, 0, 2, 0, }, +{c: 16, 6, 4, 0, 2, 4, 0, 0, 0, 0, 6, 2, 0, 6, 4, 6, }, +{7: 16, 4, 4, 6, 0, 6, 4, 6, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 0, 0, 8, 6, 4, 6, }, +{d: 16, 4, 0, 0, 0, 0, 0, 4, 2, 0, 6, 0, 6, 8, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:78, 2:18, 4:70, 6:49, 8:7, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:113, 8:16, 12:7, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 8, -8, 8, 0, -16, 0, -8, 8, -8, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 0, -16, 8, 8, 0, 0, 8, 8, -8, -8, 0, -8, -8, 0, }, +{8: 16, 0, 0, 8, -8, 8, 0, 8, -8, -8, -8, 8, 0, 0, -8, -8, }, +{3: 16, -8, 0, 8, 8, 8, -8, -8, -16, -8, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, -16, 0, 0, -8, 8, 0, 8, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 0, 8, -16, 0, 8, 0, -8, 8, 0, }, +{9: 16, -8, 0, 8, -8, -8, 0, 0, 8, -8, 0, -8, 8, 0, -8, 8, }, +{a: 16, 8, -8, 8, -8, -8, 0, -8, -8, 8, 0, -8, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 8, 0, 0, -8, -8, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, 0, 0, -8, -8, -8, -8, 8, 0, 8, 0, }, +{b: 16, -8, -8, 8, -16, 8, 0, -8, 8, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, -8, 0, 8, -8, 0, 8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, -8, 8, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, , x, x, x, , , , , x, , x, , x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, x, , , x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , , , x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0011,0101,1,}, +{0100,0100,1,}, +{0111,0001,1,}, +{1000,1011,1,}, +{1001,0011,1,}, +{1010,0110,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x0a,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x04,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x0a,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,}}, +{{0x03,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x03,0x09,0x0a,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x03,}}, +{{0x09,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x07,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +230 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x08,0x00,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 6, 2, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 0, 0, 0, 2, 8, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 4, 0, 0, }, +{9: 0, 2, 2, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 2, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 4, 0, 0, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:172, 2:62, 4:9, 6:8, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 6:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 4, 6, 6, 4, 4, 6, 6, 4, 4, 4, 0, 0, }, +{2: 16, 4, 8, 4, 4, 4, 6, 6, 6, 6, 4, 4, 4, 0, 4, 0, }, +{4: 16, 6, 6, 10, 0, 4, 4, 4, 0, 0, 0, 6, 4, 0, 0, 4, }, +{8: 16, 4, 6, 0, 6, 6, 0, 0, 4, 4, 2, 0, 6, 0, 2, 0, }, +{3: 16, 4, 4, 4, 6, 8, 4, 6, 6, 4, 4, 6, 4, 0, 0, 4, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 4, 4, 6, 0, 4, 6, 10, 0, 0, 0, 6, 4, 4, 0, 0, }, +{9: 16, 6, 6, 0, 6, 4, 0, 0, 6, 4, 0, 0, 4, 2, 0, 2, }, +{a: 16, 6, 4, 0, 4, 4, 0, 0, 6, 6, 0, 2, 6, 0, 2, 0, }, +{c: 16, 4, 4, 0, 0, 6, 0, 0, 0, 2, 6, 2, 0, 6, 4, 6, }, +{7: 16, 6, 4, 6, 2, 4, 4, 6, 0, 0, 2, 6, 0, 0, 0, 0, }, +{b: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 0, 0, 8, 6, 4, 6, }, +{d: 16, 4, 0, 0, 0, 0, 0, 4, 2, 0, 6, 0, 6, 8, 2, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 0, 4, 0, 4, 0, 0, 2, 0, 6, 0, 6, 0, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:78, 2:18, 4:70, 6:49, 8:7, 10:3, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 8, 0, 4, 4, 4, 8, 0, 4, 4, 4, 0, 0, 4, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 8, 4, 4, 4, 4, 8, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:119, 4:113, 8:16, 12:7, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 0, -16, 8, 8, -8, -8, -8, 8, 0, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 0, -8, -8, 8, -8, 0, }, +{4: 16, 0, 0, -8, 8, 8, 0, 0, 8, 8, 0, -16, 0, -8, -8, -8, }, +{8: 16, 8, 0, 8, -8, 8, 0, 0, -8, -8, 0, 8, -8, 0, -8, -8, }, +{3: 16, -8, -8, 8, 8, 8, -8, 0, -8, -16, 0, 8, 8, -8, -8, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, 0, -16, 8, -8, 0, 0, 8, -8, -8, 8, 0, -8, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 8, 8, -8, 0, -8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, 0, -8, 8, -8, -8, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, }, +{7: 16, 0, 0, -8, 8, 8, 0, 8, -8, -8, -8, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, -16, 8, 0, -8, 8, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, -8, 0, 8, -8, 0, 8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, -8, 8, 0, 8, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, -8, 0, 8, 8, 0, -8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, , x, x, x, , , x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , , , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 7 */ +{0011,0010,1,}, +{0100,0110,1,}, +{0111,0100,1,}, +{1000,1011,1,}, +{1001,0001,1,}, +{1010,0011,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x07,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x04,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x07,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,}}, +{{0x0a,0x0c,}, {0x04,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x05,0x0a,0x0f,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,0x09,0x0b,}}, +{{0x03,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x03,0x09,0x0a,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x04,0x09,0x0d,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_231.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_231.txt new file mode 100644 index 0000000..7821847 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_231.txt @@ -0,0 +1,426 @@ +231 Sbox: +LUT = { +0x08,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 8, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 8, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 0, 0, 0, 8, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 2, 0, 8, 0, 2, 0, 2, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 0, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 8, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 6, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 6, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 6, }, +}; +Diff: 8, DDT_spectrum: {0:175, 2:65, 6:5, 8:10, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 8:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 6, 4, 6, 4, 4, 4, 4, 4, 4, 6, 4, 6, 0, 0, }, +{2: 16, 4, 8, 6, 4, 6, 4, 4, 6, 4, 4, 4, 4, 0, 6, 0, }, +{4: 16, 4, 4, 8, 6, 4, 6, 4, 4, 6, 4, 6, 0, 4, 4, 0, }, +{8: 16, 4, 4, 4, 8, 4, 4, 4, 6, 4, 6, 0, 6, 4, 6, 0, }, +{3: 16, 6, 4, 4, 4, 8, 6, 4, 4, 4, 4, 4, 6, 0, 0, 6, }, +{5: 16, 4, 6, 4, 4, 4, 8, 6, 6, 4, 4, 4, 0, 6, 0, 4, }, +{6: 16, 4, 4, 4, 4, 6, 4, 8, 4, 6, 4, 6, 0, 0, 6, 4, }, +{9: 16, 6, 4, 6, 4, 4, 4, 4, 8, 6, 4, 0, 4, 4, 0, 6, }, +{a: 16, 4, 6, 4, 4, 4, 6, 4, 4, 8, 6, 0, 6, 0, 4, 4, }, +{c: 16, 4, 4, 6, 4, 4, 4, 6, 4, 4, 8, 0, 0, 6, 4, 6, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 0, 4, 6, 0, 2, 6, 2, 0, 0, }, +{d: 16, 6, 0, 4, 4, 0, 6, 0, 4, 0, 6, 0, 2, 6, 2, 0, }, +{e: 16, 0, 6, 4, 6, 0, 0, 6, 0, 4, 4, 0, 0, 2, 6, 2, }, +{f: 16, 0, 0, 0, 0, 6, 4, 4, 6, 4, 6, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:50, 2:10, 4:95, 6:60, 8:10, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:110, 8:10, 12:10, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 12:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, 0, 8, -8, 0, 8, -8, -8, -8, 8, -16, }, +{2: 16, 8, -8, 8, 8, -8, 0, -8, 8, -8, 8, -8, 0, 8, -16, -8, }, +{4: 16, 8, 8, -8, 8, 8, 0, -8, 0, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, 8, 8, 8, -16, 8, 0, 8, -8, -8, -8, 8, -8, 0, -8, -8, }, +{3: 16, -16, -8, 8, 8, 8, -8, -8, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, -8, 8, -8, 8, -16, 8, -8, 0, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 8, -16, -8, 8, -8, -8, 8, 0, -8, -8, 8, 0, -8, 8, 8, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 8, 0, -8, -16, 8, 0, -8, 8, }, +{a: 16, 8, -8, 8, -8, -8, 8, -16, -8, 8, -8, -8, 0, 0, 8, 8, }, +{c: 16, 8, 8, -16, -8, 8, -8, -8, 0, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, -8, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, -8, 8, -8, -8, -8, 0, -8, 0, 0, 8, 8, 0, 0, 8, -8, }, +{e: 16, 8, -8, -8, -8, -8, 0, 8, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, , , x, , , , x, , , x, x, }, +{9: , x, x, x, , , , , x, , , , x, x, , x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, x, , , , , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0001,0011,1,}, +{0010,0110,1,}, +{0011,0101,1,}, +{0100,1100,1,}, +{0110,1010,1,}, +{0111,1001,1,}, +{1000,1000,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x07,0x09,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x06,0x09,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0f,}}, +{{0x05,0x0e,}, {0x03,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +231 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 2, 8, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 8, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, }, +{3: 0, 0, 2, 0, 0, 8, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 8, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 8, 0, 0, 2, 2, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 2, 0, 2, 0, 8, 0, 0, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 8, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 6, 2, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 6, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 6, }, +}; +Diff: 8, DDT_spectrum: {0:175, 2:65, 6:5, 8:10, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:4, 8:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 4, 6, 4, 4, 6, 4, 4, 6, 4, 6, 0, 0, }, +{2: 16, 6, 8, 4, 4, 4, 6, 4, 4, 6, 4, 4, 4, 0, 6, 0, }, +{4: 16, 4, 6, 8, 4, 4, 4, 4, 6, 4, 6, 6, 0, 4, 4, 0, }, +{8: 16, 6, 4, 6, 8, 4, 4, 4, 4, 4, 4, 0, 6, 4, 6, 0, }, +{3: 16, 4, 6, 4, 4, 8, 4, 6, 4, 4, 4, 4, 6, 0, 0, 6, }, +{5: 16, 4, 4, 6, 4, 6, 8, 4, 4, 6, 4, 4, 0, 6, 0, 4, }, +{6: 16, 4, 4, 4, 4, 4, 6, 8, 4, 4, 6, 6, 0, 0, 6, 4, }, +{9: 16, 4, 6, 4, 6, 4, 6, 4, 8, 4, 4, 0, 4, 4, 0, 6, }, +{a: 16, 4, 4, 6, 4, 4, 4, 6, 6, 8, 4, 0, 6, 0, 4, 4, }, +{c: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 8, 0, 0, 6, 4, 6, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 0, 4, 6, 0, 2, 6, 2, 0, 0, }, +{d: 16, 6, 0, 4, 4, 0, 6, 0, 4, 0, 6, 0, 2, 6, 2, 0, }, +{e: 16, 0, 6, 4, 6, 0, 0, 6, 0, 4, 4, 0, 0, 2, 6, 2, }, +{f: 16, 0, 0, 0, 0, 6, 4, 4, 6, 4, 6, 2, 0, 0, 2, 6, }, +}; +BCT_uniformity: 8, BCT_spectrum: {0:50, 2:10, 4:95, 6:60, 8:10, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 12, 0, 0, 4, 0, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:110, 8:10, 12:10, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 12:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 8, -8, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 0, 0, 8, -8, -8, 8, -8, -8, }, +{4: 16, 8, 8, -8, 8, 8, -8, -8, 8, 0, -8, -16, 8, 0, -8, -8, }, +{8: 16, 8, 8, 8, -8, 8, 0, 8, -8, 0, -8, 8, -8, -8, -8, -16, }, +{3: 16, -8, -16, 8, 8, 8, -8, -8, 0, -8, 8, 8, 0, -8, -8, 8, }, +{5: 16, -8, 8, -8, 8, -8, 8, -16, -8, 8, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -8, -16, 8, -8, -8, 8, 0, -8, -8, 8, -8, 0, 8, 8, }, +{9: 16, -8, 8, 8, -8, -8, 0, 8, 8, -8, -8, -8, 0, 8, -16, 8, }, +{a: 16, 8, -8, 8, -8, -8, 0, -8, 0, 8, -16, -8, 8, -8, 8, 8, }, +{c: 16, 8, 8, -8, -16, 8, 0, -8, -8, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, -8, 0, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, -8, 8, -8, -8, -8, 0, -8, 0, 0, 8, 8, 0, 0, 8, -8, }, +{e: 16, 8, -8, -8, -8, -8, 0, 8, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, -8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, x, , x, , , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, x, x, x, , , , , x, , , x, , x, x, }, +{c: , x, x, x, , , , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0001,0001,1,}, +{0010,0011,1,}, +{0011,0010,1,}, +{0100,0110,1,}, +{0110,0101,1,}, +{0111,0100,1,}, +{1000,1100,1,}, +{1100,1010,1,}, +{1110,1001,1,}, +{1111,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 0, +v=3 0, 0, 0, +(V_basis, W_spaned) pairs +{{0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x04,0x0b,0x0f,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x04,}, {0x07,0x09,0x0e,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x08,}, {0x06,0x09,0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x02,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_232.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_232.txt new file mode 100644 index 0000000..7981401 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_232.txt @@ -0,0 +1,442 @@ +232 Sbox: +LUT = { +0x04,0x00,0x08,0x02,0x03,0x05,0x0a,0x07,0x01,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{4: 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 0, 4, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 0, 0, 2, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, }, +{5: 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{9: 0, 2, 0, 2, 0, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, }, +{d: 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 0, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:164, 2:66, 4:23, 6:1, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:7, 2:5, 4:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 2, 4, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, }, +{2: 16, 4, 10, 4, 4, 4, 8, 4, 10, 4, 10, 10, 8, 4, 8, 4, }, +{4: 16, 0, 10, 4, 2, 0, 4, 4, 0, 0, 0, 6, 0, 2, 0, 0, }, +{8: 16, 0, 8, 2, 4, 0, 2, 0, 4, 4, 0, 0, 4, 0, 2, 2, }, +{3: 16, 4, 4, 2, 2, 8, 0, 2, 0, 2, 4, 0, 0, 0, 0, 4, }, +{5: 16, 2, 4, 0, 2, 2, 4, 0, 2, 0, 2, 4, 0, 0, 0, 2, }, +{6: 16, 0, 8, 4, 0, 0, 4, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{9: 16, 2, 4, 2, 0, 2, 2, 0, 4, 0, 0, 0, 4, 2, 2, 0, }, +{a: 16, 0, 10, 0, 4, 0, 0, 2, 6, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 4, 10, 0, 2, 4, 0, 2, 0, 0, 6, 0, 0, 8, 4, 8, }, +{7: 16, 2, 4, 0, 0, 2, 4, 0, 0, 2, 0, 4, 2, 2, 2, 0, }, +{b: 16, 2, 4, 0, 0, 2, 0, 2, 4, 0, 2, 2, 4, 0, 0, 2, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 4, 2, 2, 0, 0, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:58, 4:57, 6:3, 8:12, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 12, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{9: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, 8, -8, }, +{2: 16, 8, -8, 8, 8, -8, 8, -8, 8, -16, 8, -16, -8, 16, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, 8, -8, 0, 0, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -8, 0, 0, 8, 0, 0, -8, 0, 0, 0, -16, 0, }, +{3: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, -8, 8, }, +{5: 16, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, -8, 0, -8, 8, }, +{6: 16, 0, -16, -8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{9: 16, -8, 8, 0, 0, -8, -8, 0, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 8, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 8, 8, -8, -8, 0, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 8, -8, }, +{b: 16, -8, -8, 0, 0, 8, -8, 0, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -16, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 16, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, , x, , x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , x, , x, , , , x, , x, , x, , , , x, }, +{b: , x, x, , x, x, , x, , x, , , x, , , x, }, +{d: , x, x, , x, x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0010,0110,1,}, +{0111,0010,1,}, +{0111,1101,1,}, +{0111,1111,0,}, +{1010,0010,1,}, +{1010,1100,1,}, +{1010,1110,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x09,0x02,0x04,}, {0x07,}}, +{{0x01,0x02,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x0d,}}, +{{0x03,0x04,}, {0x0d,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x07,0x09,0x0e,}}, +{{0x07,0x08,}, {0x07,0x09,0x0e,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x0d,0x0e,}, {0x07,0x0a,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +232 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x00,0x05,0x0a,0x07,0x02,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 4, 0, 0, }, +{2: 0, 0, 10, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, }, +{8: 0, 2, 0, 2, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, 0, 4, }, +{5: 0, 0, 0, 4, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{6: 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{a: 0, 2, 0, 0, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 2, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 2, 4, 0, 0, }, +{7: 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 4, 0, 2, 2, }, +{d: 0, 4, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, 0, 2, 0, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:164, 2:66, 4:23, 6:1, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:7, 2:5, 4:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 4, 2, 0, 2, 0, 4, 2, 2, 4, 0, 0, }, +{2: 16, 4, 10, 10, 8, 4, 4, 8, 4, 10, 10, 4, 4, 4, 8, 4, }, +{4: 16, 2, 4, 4, 2, 2, 0, 4, 2, 0, 0, 0, 0, 2, 2, 0, }, +{8: 16, 2, 4, 2, 4, 2, 2, 0, 0, 4, 2, 0, 0, 0, 0, 2, }, +{3: 16, 4, 4, 0, 0, 8, 2, 0, 2, 0, 4, 2, 2, 0, 0, 4, }, +{5: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 0, 4, 0, 0, 2, 2, }, +{6: 16, 2, 4, 4, 0, 2, 0, 4, 0, 2, 2, 0, 2, 0, 0, 2, }, +{9: 16, 0, 10, 0, 4, 0, 2, 0, 4, 6, 0, 0, 4, 2, 0, 0, }, +{a: 16, 2, 4, 0, 4, 2, 0, 2, 0, 4, 0, 2, 0, 2, 2, 0, }, +{c: 16, 4, 10, 0, 0, 4, 2, 0, 0, 0, 6, 0, 2, 8, 4, 8, }, +{7: 16, 0, 10, 6, 0, 0, 4, 4, 0, 0, 0, 4, 2, 2, 0, 0, }, +{b: 16, 0, 8, 0, 4, 0, 0, 2, 4, 4, 0, 2, 4, 0, 2, 2, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 4, 2, 2, 0, 0, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:58, 4:57, 6:3, 8:12, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, }, +{2: 16, 16, -8, 8, 8, -8, 8, -16, 8, -8, 8, -16, -8, 8, -8, -8, }, +{4: 16, 0, 8, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 8, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, -8, -8, 0, }, +{3: 16, -16, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, -16, 0, }, +{6: 16, 0, -8, 0, 0, 0, -8, 0, 0, 0, 0, 0, -8, -8, 8, 8, }, +{9: 16, 0, 8, 8, -8, -8, 8, 0, 0, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -16, 0, -8, 8, 0, -8, 8, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 8, -8, }, +{b: 16, 0, -16, 0, -8, 0, 0, 0, 0, 8, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, 0, 0, 0, -8, 0, -8, 0, 0, -16, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, 0, 0, 0, -8, 0, -8, 0, 0, 16, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , , x, x, x, , x, x, , x, , x, , x, , x, }, +{6: , , x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , , x, x, , , , x, , x, , x, , , , x, }, +{b: , , , , x, , , x, , x, , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,1011,1,}, +{0110,0010,1,}, +{0110,1100,1,}, +{0110,1110,0,}, +{0111,0010,1,}, +{0111,1101,1,}, +{0111,1111,0,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x09,0x02,0x04,}, {0x07,}}, +{{0x01,0x02,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,}}, +{{0x06,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x02,0x05,0x07,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,}}, +{{0x05,0x08,}, {0x07,0x09,0x0e,}}, +{{0x07,0x08,}, {0x07,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0d,0x02,}, {0x01,0x06,0x07,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,}}, +{{0x05,0x0a,}, {0x07,0x09,0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x06,0x07,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_233.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_233.txt new file mode 100644 index 0000000..b3e1725 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_233.txt @@ -0,0 +1,442 @@ +233 Sbox: +LUT = { +0x04,0x00,0x08,0x02,0x03,0x05,0x06,0x07,0x01,0x09,0x0a,0x0b,0x0e,0x0d,0x0c,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 2, 0, 0, 0, 2, 0, 0, 2, 2, }, +{8: 0, 0, 2, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, 2, 0, 0, }, +{3: 0, 4, 0, 2, 2, 4, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +{6: 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 4, 2, 2, 0, 0, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 2, }, +{c: 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 2, 2, 0, }, +{b: 0, 2, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 2, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 4, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 0, 0, 4, }, +}; +Diff: 10, DDT_spectrum: {0:164, 2:66, 4:23, 6:1, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 4:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 2, 2, 4, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, }, +{2: 16, 4, 10, 4, 4, 4, 10, 4, 8, 4, 10, 8, 10, 4, 8, 4, }, +{4: 16, 0, 8, 4, 0, 0, 4, 6, 0, 0, 0, 6, 0, 0, 2, 2, }, +{8: 16, 0, 10, 0, 4, 0, 2, 0, 4, 6, 0, 0, 4, 2, 0, 0, }, +{3: 16, 4, 4, 2, 2, 8, 0, 2, 0, 2, 4, 0, 0, 0, 0, 4, }, +{5: 16, 2, 4, 2, 0, 2, 6, 0, 0, 0, 2, 4, 0, 0, 0, 2, }, +{6: 16, 0, 10, 6, 0, 0, 4, 4, 0, 0, 0, 4, 2, 2, 0, 0, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 6, 0, 0, 0, 4, 2, 2, 0, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 0, 0, 4, 0, 2, 2, }, +{c: 16, 4, 10, 2, 0, 4, 0, 0, 0, 2, 6, 0, 0, 8, 4, 8, }, +{7: 16, 2, 4, 0, 0, 2, 4, 2, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 16, 2, 4, 0, 0, 2, 0, 0, 4, 2, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 4, 2, 2, 0, 0, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:50, 4:49, 6:11, 8:12, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{b: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, 0, -8, 0, -8, 0, 0, 0, 0, -16, 0, 0, }, +{2: 16, 8, -8, 8, 8, -8, 8, -16, 8, -8, 8, -8, -16, 16, -8, -8, }, +{4: 16, 0, 0, -16, 8, 0, 0, 0, 0, 8, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 8, 8, -8, -8, 8, 0, 0, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 8, 8, 0, -8, 0, -8, 0, 0, 0, 0, -16, 0, 0, }, +{5: 16, -8, 0, -8, 8, 8, 0, 0, -8, 0, 0, -8, 0, 0, 0, 0, }, +{6: 16, 0, -8, -8, 8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 8, -8, }, +{9: 16, -8, 0, 8, -8, 0, -8, 0, 0, 0, 0, 8, 0, 0, 0, -8, }, +{a: 16, 0, -8, 8, -16, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{c: 16, 8, 8, -8, -8, 0, 0, -16, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 8, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, 0, 8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 16, 0, 0, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 16, 0, 0, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, -16, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, , x, x, x, x, , x, , x, , x, x, x, }, +{6: , x, , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, x, x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , x, x, , , x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, , , x, x, , x, , x, , , , x, x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0100,0100,1,}, +{0110,0010,1,}, +{0110,1100,1,}, +{0110,1110,0,}, +{1000,1010,1,}, +{1011,0010,1,}, +{1011,1101,0,}, +{1011,1111,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x02,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x06,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x04,0x09,0x0d,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x0b,0x04,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x0c,}, {0x06,}}, +{{0x0b,0x0c,}, {0x06,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x0b,}}, +{{0x01,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x0b,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x06,0x07,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,}}, +{{0x0d,0x0e,}, {0x06,0x0b,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +233 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x00,0x05,0x06,0x07,0x02,0x09,0x0a,0x0b,0x0e,0x0d,0x0c,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{2: 0, 0, 10, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{5: 0, 0, 2, 4, 2, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 2, }, +{6: 0, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 0, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 2, 0, 0, 4, }, +{7: 0, 0, 0, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 2, 2, 0, }, +{b: 0, 0, 2, 0, 0, 0, 0, 2, 4, 4, 0, 0, 2, 0, 0, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 2, 0, 4, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 4, 4, 0, }, +{f: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:164, 2:66, 4:23, 6:1, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 4:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 0, 0, 4, 2, 0, 2, 0, 4, 2, 2, 4, 0, 0, }, +{2: 16, 4, 10, 8, 10, 4, 4, 10, 4, 8, 10, 4, 4, 4, 8, 4, }, +{4: 16, 2, 4, 4, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, 0, 0, }, +{8: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{3: 16, 4, 4, 0, 0, 8, 2, 0, 2, 0, 4, 2, 2, 0, 0, 4, }, +{5: 16, 0, 10, 4, 2, 0, 6, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{6: 16, 2, 4, 6, 0, 2, 0, 4, 0, 0, 0, 2, 0, 0, 2, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 6, 6, 0, 0, 4, 2, 2, 0, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 4, 10, 0, 0, 4, 2, 0, 0, 0, 6, 0, 2, 8, 4, 8, }, +{7: 16, 0, 8, 6, 0, 0, 4, 4, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 16, 0, 10, 0, 4, 0, 0, 2, 4, 4, 0, 0, 6, 0, 0, 2, }, +{d: 16, 4, 4, 0, 2, 0, 0, 2, 2, 0, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 2, 0, 4, 2, 0, 0, 2, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:50, 4:49, 6:11, 8:12, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 4, 0, 12, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{3: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{5: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{b: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +{f: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:127, 4:94, 8:32, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -8, 8, 8, -8, 8, -8, 8, -16, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, -8, -8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, -8, 8, 8, 8, 0, 0, 0, -8, -8, 0, 0, -8, -8, }, +{6: 16, 0, -8, -8, 8, 0, -8, 8, 0, 0, 0, 0, 0, -8, 0, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, -8, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 8, -8, -16, 8, 0, 8, }, +{7: 16, 0, 0, -16, 8, -8, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, }, +{b: 16, 0, -8, 8, -8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 0, 8, }, +{d: 16, 0, 8, -8, -8, 0, 0, 0, 0, -16, 0, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 16, 0, 0, -8, }, +{f: 16, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, x, x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, , x, x, , x, , x, , x, x, x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, x, , , x, x, x, x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , x, , x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, , , , x, , x, , , , x, x, x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 11 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,0111,1,}, +{1000,1001,1,}, +{1010,0010,1,}, +{1010,1101,1,}, +{1010,1111,0,}, +{1011,0010,1,}, +{1011,1100,1,}, +{1011,1110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x02,0x0c,}, {0x0b,}}, +{{0x04,0x08,}, {0x0b,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x0b,}}, +{{0x01,0x04,}, {0x01,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x0a,}}, +{{0x01,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x03,0x0c,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0a,}}, +{{0x07,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x0a,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_234.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_234.txt new file mode 100644 index 0000000..eb9a042 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_234.txt @@ -0,0 +1,424 @@ +234 Sbox: +LUT = { +0x06,0x00,0x08,0x02,0x03,0x05,0x0a,0x07,0x01,0x09,0x04,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 2, 0, 0, 4, 0, 2, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 10, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, 2, }, +{3: 0, 0, 0, 4, 2, 4, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 0, 2, 4, 4, 0, 0, 0, 2, 0, 2, 0, 0, 2, }, +{6: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 0, 2, 2, 2, 4, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 2, 0, }, +{b: 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 0, }, +{d: 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, }, +{e: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 4, }, +{f: 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:164, 2:66, 4:23, 6:1, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 4:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 0, 2, 8, 4, 4, 0, 2, 0, 0, 0, 2, 0, 2, }, +{2: 16, 4, 10, 4, 4, 4, 10, 4, 10, 4, 8, 8, 8, 4, 10, 4, }, +{4: 16, 4, 10, 8, 0, 4, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{8: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 2, 2, 4, 0, 0, 2, }, +{3: 16, 8, 4, 4, 2, 4, 4, 0, 0, 2, 0, 0, 0, 2, 0, 2, }, +{5: 16, 0, 4, 0, 2, 4, 8, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{6: 16, 0, 8, 4, 2, 0, 4, 4, 0, 0, 2, 4, 2, 0, 0, 2, }, +{9: 16, 2, 4, 0, 0, 2, 2, 2, 4, 0, 0, 0, 4, 0, 2, 2, }, +{a: 16, 0, 10, 0, 4, 0, 0, 2, 6, 4, 0, 0, 4, 2, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 6, 4, }, +{7: 16, 4, 4, 4, 0, 0, 8, 0, 2, 2, 0, 4, 0, 2, 2, 0, }, +{b: 16, 2, 4, 2, 0, 2, 0, 0, 4, 0, 2, 2, 4, 2, 0, 0, }, +{d: 16, 2, 4, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 4, 0, }, +{e: 16, 0, 8, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 4, 4, }, +{f: 16, 2, 4, 0, 2, 2, 2, 2, 2, 0, 4, 0, 0, 0, 4, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:58, 4:57, 6:3, 8:12, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{4: 0, 4, 4, 8, 4, 0, 4, 4, 8, 0, 4, 0, 4, 0, 0, 4, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{5: 0, 4, 4, 8, 4, 0, 4, 4, 0, 0, 4, 0, 4, 8, 0, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, -8, -16, 8, 0, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 16, -16, -8, }, +{4: 16, 0, 8, -8, 8, -8, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 8, -16, -8, 0, }, +{5: 16, -8, 0, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, -8, 0, 8, 0, 8, 0, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, -8, 0, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, 0, -8, 8, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 8, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 8, 0, -8, -8, -8, 0, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, 0, 0, -8, 0, 8, -8, 0, 0, -8, 8, 0, 8, -8, }, +{b: 16, -8, 0, 0, 0, 8, -8, -8, 0, 0, 0, 0, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, 0, 8, -8, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 8, 0, 8, 0, 8, 0, 0, 0, 0, -8, -8, }, +{f: 16, 0, 0, 0, 0, -8, -8, 8, -8, 0, 0, 8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, , x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , x, x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , x, x, x, , , , , , x, , x, , , , x, }, +{b: , x, x, , x, x, , x, , x, , , x, , , x, }, +{d: , x, , , x, x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0011,0010,1,}, +{0110,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x09,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x0d,}}, +{{0x05,0x06,}, {0x0d,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +234 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x0a,0x05,0x00,0x07,0x02,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 2, 0, 2, }, +{2: 0, 0, 10, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 4, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{8: 0, 2, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 0, 0, 0, 0, 4, 4, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 0, 0, 2, 6, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{6: 0, 4, 0, 0, 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 2, 0, 4, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, }, +{a: 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 4, 0, 0, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 0, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 2, 2, 0, }, +{d: 0, 2, 0, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 0, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 4, }, +{f: 0, 2, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:164, 2:66, 4:23, 6:1, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 4:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 0, 8, 0, 0, 2, 0, 0, 4, 2, 2, 0, 2, }, +{2: 16, 4, 10, 10, 8, 4, 4, 8, 4, 10, 10, 4, 4, 4, 8, 4, }, +{4: 16, 0, 4, 8, 2, 4, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{8: 16, 2, 4, 0, 4, 2, 2, 2, 0, 4, 0, 0, 0, 0, 2, 2, }, +{3: 16, 8, 4, 4, 0, 4, 4, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{5: 16, 4, 10, 6, 0, 4, 8, 4, 2, 0, 0, 8, 0, 0, 0, 2, }, +{6: 16, 4, 4, 8, 0, 0, 4, 4, 2, 2, 2, 0, 0, 0, 0, 2, }, +{9: 16, 0, 10, 0, 4, 0, 0, 0, 4, 6, 0, 2, 4, 0, 0, 2, }, +{a: 16, 2, 4, 2, 4, 2, 0, 0, 0, 4, 2, 2, 0, 2, 0, 0, }, +{c: 16, 0, 8, 0, 2, 0, 2, 2, 0, 0, 4, 0, 2, 4, 4, 4, }, +{7: 16, 0, 8, 4, 2, 0, 4, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 16, 0, 8, 0, 4, 0, 2, 2, 4, 4, 0, 0, 4, 2, 2, 0, }, +{d: 16, 2, 4, 2, 0, 2, 0, 0, 0, 2, 4, 2, 2, 0, 4, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 4, 4, 4, }, +{f: 16, 2, 4, 0, 2, 2, 2, 2, 2, 0, 4, 0, 0, 0, 4, 0, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:58, 4:57, 6:3, 8:12, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +{5: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:117, 4:109, 8:26, 12:3, 16:1, }; +Lin1: 8, LAT1_spectrum: {0:4, 4:8, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 16, -8, 8, 8, -8, 8, -16, 8, -8, 8, -16, -8, 8, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, -8, -8, 0, 0, 0, 8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 8, -8, -8, -8, 0, }, +{3: 16, -16, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, -8, 8, }, +{5: 16, 0, 8, -8, 8, 0, 0, -8, 8, 8, -8, -8, 0, 0, -16, 0, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 0, 0, 0, -8, -8, -8, 8, 8, }, +{9: 16, 0, 0, 8, -8, 0, 8, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, -8, 8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, -8, -8, 0, -8, 0, 8, -8, 8, 0, 0, 8, 0, }, +{d: 16, 0, 0, 0, 0, 8, -8, -8, -8, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 8, -8, 0, 8, -8, 0, }, +{f: 16, 0, 0, 0, 0, -8, -8, 8, -8, 0, 0, 8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , , x, x, x, , x, x, , x, , x, , x, , x, }, +{6: , , x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , x, x, , , x, x, x, }, +{7: , , x, x, , , , x, , x, , x, , , , x, }, +{b: , , , , x, , , x, , x, , , x, , , x, }, +{d: , , , x, x, , , , , x, , , , x, , x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 6 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 13, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x0d,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x0d,}}, +{{0x01,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0d,0x02,}, {0x01,0x06,0x07,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_235.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_235.txt new file mode 100644 index 0000000..da830b7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_235.txt @@ -0,0 +1,446 @@ +235 Sbox: +LUT = { +0x06,0x00,0x08,0x02,0x03,0x05,0x04,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, }, +{3: 0, 2, 0, 4, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 4, 6, 2, 0, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 4, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 2, 0, }, +{7: 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:170, 2:60, 4:17, 6:7, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:2, 4:1, 6:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 2, 10, 8, 8, 0, 2, 0, 4, 0, 0, 0, 0, }, +{2: 16, 4, 10, 4, 4, 4, 8, 4, 8, 4, 8, 10, 10, 4, 10, 4, }, +{4: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 2, 8, 0, 2, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 0, 4, 6, 0, 2, 4, 0, 0, 2, }, +{3: 16, 10, 4, 8, 2, 6, 8, 4, 0, 2, 0, 4, 0, 0, 0, 0, }, +{5: 16, 4, 4, 4, 0, 8, 10, 10, 0, 0, 2, 4, 0, 0, 0, 2, }, +{6: 16, 4, 10, 4, 0, 4, 8, 6, 0, 0, 0, 8, 2, 0, 0, 2, }, +{9: 16, 2, 4, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 6, 4, }, +{7: 16, 8, 4, 10, 0, 4, 8, 4, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 16, 2, 4, 0, 0, 2, 0, 0, 6, 2, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{e: 16, 0, 8, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:44, 4:46, 6:10, 8:19, 10:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 0, 4, 4, 0, 4, 12, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -8, -8, 8, -8, 0, 0, 0, -8, -16, 8, 0, }, +{2: 16, 8, -16, 8, 8, -8, 8, -8, 8, -8, 8, -8, -8, 16, -8, -16, }, +{4: 16, 0, 16, -16, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 8, 8, 0, -8, -8, -8, 0, 0, -8, 0, }, +{3: 16, 0, 0, 8, 8, 8, -8, -8, -8, 0, 0, 0, 8, -16, -8, 0, }, +{5: 16, -8, 0, -8, 8, 0, 0, -8, -8, 0, 0, 8, -8, 0, -8, 16, }, +{6: 16, 0, -16, -8, 8, 0, 0, 8, 8, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, -8, 0, 8, -8, 0, -8, 8, 0, 0, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 8, 0, -8, -8, -8, 0, -8, 0, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 8, 0, 0, 8, -8, 0, 0, -8, 8, 0, 8, -16, }, +{b: 16, -8, 0, 8, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 8, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, , x, , , , x, x, , , x, }, +{5: , x, , , x, x, x, x, , , , x, , x, , x, }, +{6: , x, , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , x, , , x, x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0100,0100,1,}, +{0110,0100,1,}, +{1000,1010,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,1110,1,}, +{1111,0010,1,}, +{1111,0101,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 6, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x0f,}}, +{{0x01,0x02,0x04,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x0f,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x0f,}}, +{{0x0b,0x0c,}, {0x0f,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0e,}, {0x03,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +235 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x06,0x05,0x00,0x07,0x02,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 2, 0, 0, 0, }, +{2: 0, 0, 10, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 4, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{8: 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, }, +{3: 0, 2, 0, 0, 0, 6, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, }, +{5: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{6: 0, 4, 0, 0, 0, 0, 2, 6, 0, 0, 2, 0, 0, 0, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 2, 0, 0, 2, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 4, 0, 0, }, +{7: 0, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 6, 0, 2, 0, 0, }, +{b: 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 0, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 0, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:170, 2:60, 4:17, 6:7, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:2, 4:1, 6:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 0, 10, 4, 4, 2, 0, 0, 8, 2, 0, 0, 0, }, +{2: 16, 4, 10, 8, 10, 4, 4, 10, 4, 8, 10, 4, 4, 4, 8, 4, }, +{4: 16, 4, 4, 10, 0, 8, 4, 4, 0, 0, 0, 10, 0, 2, 2, 0, }, +{8: 16, 2, 4, 0, 4, 2, 0, 0, 2, 6, 0, 0, 0, 0, 2, 2, }, +{3: 16, 10, 4, 8, 0, 6, 8, 4, 2, 0, 0, 4, 2, 0, 0, 0, }, +{5: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 0, 8, 0, 0, 2, 2, }, +{6: 16, 8, 4, 8, 0, 4, 10, 6, 0, 0, 2, 4, 0, 0, 0, 2, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 2, 4, 0, 6, 2, 0, 0, 0, 4, 2, 0, 2, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 2, 0, 0, 2, 4, 0, 2, 4, 4, 4, }, +{7: 16, 4, 10, 8, 2, 4, 4, 8, 0, 0, 0, 6, 0, 2, 0, 0, }, +{b: 16, 0, 10, 0, 4, 0, 0, 2, 6, 4, 0, 0, 4, 2, 0, 0, }, +{d: 16, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 2, 2, 2, 4, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 0, 2, 0, 6, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 0, 2, 2, 2, 0, 4, 0, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:44, 4:46, 6:10, 8:19, 10:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 4, 0, 12, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{3: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +{5: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 8, -8, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 16, -8, 8, 8, -8, 8, -8, 8, -16, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 8, -8, -8, 0, 0, 0, 0, 16, -8, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, -8, 0, 0, 0, 0, -8, -8, 0, }, +{3: 16, -16, 0, 8, 8, 0, -8, -8, -8, 0, 0, 8, 0, 0, -8, 8, }, +{5: 16, 0, 8, -16, 8, 0, 0, -8, 0, 16, -8, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -8, 8, -8, -8, 8, 0, 0, 0, 0, -16, -8, 8, 8, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, -8, 0, 0, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -16, 0, 0, 0, 0, 0, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 8, 8, 0, -16, -8, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, -8, 0, -8, 8, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 8, -8, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , , , , x, x, , , x, }, +{5: , , x, , x, , x, x, , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, , x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,0101,1,}, +{0110,1100,1,}, +{1000,1001,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 6, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x0a,}}, +{{0x01,0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x02,0x04,}, {0x0b,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x0a,}}, +{{0x04,0x08,}, {0x06,0x0b,0x0d,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x0b,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x07,0x08,}, {0x0a,}}, +{{0x01,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x0b,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_236.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_236.txt new file mode 100644 index 0000000..a2a2a32 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_236.txt @@ -0,0 +1,446 @@ +236 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 10, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 6, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 6, 4, 0, 0, 0, 0, 2, 2, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 0, 2, 0, 0, 2, 4, 2, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, 0, 2, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 2, 2, }, +{7: 0, 2, 0, 4, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:170, 2:60, 4:17, 6:7, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 4, 2, 8, 8, 10, 0, 0, 0, 4, 0, 0, 0, 2, }, +{2: 16, 4, 10, 4, 4, 4, 8, 4, 10, 4, 10, 10, 8, 4, 8, 4, }, +{4: 16, 8, 8, 10, 0, 8, 10, 8, 0, 2, 0, 8, 2, 0, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 8, 4, 10, 0, 6, 8, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{5: 16, 4, 4, 4, 0, 10, 10, 8, 0, 0, 0, 4, 2, 2, 0, 0, }, +{6: 16, 4, 10, 4, 2, 4, 8, 6, 0, 0, 2, 8, 0, 0, 0, 0, }, +{9: 16, 2, 4, 0, 2, 0, 0, 2, 4, 2, 0, 0, 6, 0, 2, 0, }, +{a: 16, 0, 10, 0, 6, 0, 0, 0, 4, 4, 0, 2, 4, 2, 0, 0, }, +{c: 16, 0, 8, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 10, 4, 8, 0, 4, 8, 4, 2, 0, 0, 6, 0, 0, 0, 2, }, +{b: 16, 0, 4, 2, 2, 2, 0, 0, 6, 2, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:40, 4:42, 6:14, 8:19, 10:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 4, 4, 12, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, 0, -8, 8, -8, 0, 8, 0, -8, -16, 0, 0, }, +{2: 16, 8, -8, 8, 8, -8, 8, -8, 8, -16, 8, -16, -8, 16, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 0, 16, -16, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 8, 8, 0, -8, -8, -8, 0, 8, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, -8, 8, -8, 0, -8, 0, 0, -8, 16, -8, 0, 0, 8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 8, 0, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -8, -8, -8, 8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, 0, 8, -8, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 8, 8, 0, 8, 0, 0, -8, -16, 8, 0, 0, -8, }, +{b: 16, 0, 0, 8, -8, 8, -8, -8, 0, 0, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , , x, x, , , x, }, +{5: , , x, x, x, x, x, x, , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , x, x, x, , , x, , , , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0100,1100,1,}, +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,1000,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 6, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0a,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0a,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x0b,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x0d,0x02,}, {0x07,0x0a,0x0d,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x07,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +236 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, }, +{2: 0, 0, 10, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, }, +{8: 0, 2, 0, 0, 4, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, }, +{3: 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{5: 0, 0, 0, 6, 0, 0, 6, 0, 0, 0, 2, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 4, 6, 2, 0, 0, 0, 0, 0, 2, 0, }, +{9: 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{a: 0, 0, 0, 2, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 2, }, +{7: 0, 0, 2, 0, 0, 0, 0, 4, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:170, 2:60, 4:17, 6:7, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 4, 8, 0, 8, 4, 4, 2, 0, 0, 10, 0, 0, 0, 2, }, +{2: 16, 4, 10, 8, 8, 4, 4, 10, 4, 10, 8, 4, 4, 4, 10, 4, }, +{4: 16, 4, 4, 10, 0, 10, 4, 4, 0, 0, 2, 8, 2, 0, 0, 0, }, +{8: 16, 2, 4, 0, 4, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, 2, }, +{3: 16, 8, 4, 8, 0, 6, 10, 4, 0, 0, 0, 4, 2, 2, 0, 0, }, +{5: 16, 8, 8, 10, 0, 8, 10, 8, 0, 0, 2, 8, 0, 2, 0, 0, }, +{6: 16, 10, 4, 8, 0, 4, 8, 6, 2, 0, 0, 4, 0, 0, 2, 0, }, +{9: 16, 0, 10, 0, 4, 0, 0, 0, 4, 4, 0, 2, 6, 0, 2, 0, }, +{a: 16, 0, 4, 2, 6, 2, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 4, 6, }, +{7: 16, 4, 10, 8, 0, 4, 4, 8, 0, 2, 0, 6, 0, 0, 0, 2, }, +{b: 16, 0, 8, 2, 6, 0, 2, 0, 6, 4, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 4, 0, 0, 2, 2, 0, 0, 2, 4, 0, 0, 2, 6, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 2, 4, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 2, 4, 2, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:40, 4:42, 6:14, 8:19, 10:14, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:131, 4:92, 8:28, 12:4, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 8, -8, 0, 8, -8, 0, -8, 0, 0, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 0, -8, 8, 16, -8, -8, 0, 0, -8, -8, 8, 0, 0, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, 0, -8, 0, -8, -8, 0, 0, }, +{3: 16, -16, 0, 8, 8, 0, -8, -8, -8, 0, 8, 8, 0, -8, 0, 0, }, +{5: 16, 0, 16, -16, 8, 0, 0, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 8, -16, -8, 8, 0, 0, -8, 8, -8, 0, 0, 8, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, -8, }, +{a: 16, 0, 0, 8, -8, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -16, -8, 8, 0, 8, 8, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 0, 8, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, -8, 0, 0, -8, -8, 0, 8, 0, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -8, 0, 0, 8, -8, 0, 8, 0, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , , , , x, , x, x, , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 13 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1000,1110,1,}, +{1100,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 6, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x02,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x02,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x03,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x02,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_237.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_237.txt new file mode 100644 index 0000000..11785d0 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_237.txt @@ -0,0 +1,428 @@ +237 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x04,0x0c,0x07,0x05,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + + + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, }, +{2: 0, 0, 4, 2, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{4: 0, 0, 0, 10, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 2, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 4, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 0, 2, 4, 0, 4, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 2, 0, 0, 2, 0, 6, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 4, 0, 0, 6, 0, 2, }, +{7: 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{b: 0, 4, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 4, 4, }, +{f: 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:3, 4:4, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 16, 4, 8, 10, 2, 6, 4, 8, 0, 0, 0, 4, 0, 0, 0, 2, }, +{4: 16, 4, 4, 10, 4, 10, 4, 4, 8, 10, 4, 8, 4, 10, 8, 4, }, +{8: 16, 0, 2, 8, 4, 0, 0, 0, 4, 0, 4, 2, 2, 4, 2, 0, }, +{3: 16, 4, 4, 4, 2, 8, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, }, +{5: 16, 4, 0, 4, 4, 4, 16, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{6: 16, 0, 4, 8, 0, 4, 0, 4, 2, 0, 2, 4, 2, 0, 2, 0, }, +{9: 16, 0, 2, 4, 4, 2, 4, 0, 4, 2, 0, 0, 2, 8, 0, 0, }, +{a: 16, 4, 0, 10, 2, 0, 4, 2, 0, 6, 0, 0, 8, 0, 4, 8, }, +{c: 16, 4, 0, 10, 8, 0, 4, 2, 4, 0, 8, 0, 0, 6, 0, 2, }, +{7: 16, 0, 0, 4, 0, 8, 4, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 2, 2, 8, 0, 2, 4, 0, 4, 0, }, +{d: 16, 4, 0, 4, 0, 0, 0, 2, 4, 0, 4, 2, 0, 8, 2, 2, }, +{e: 16, 0, 2, 8, 0, 0, 0, 0, 2, 4, 2, 2, 4, 0, 4, 4, }, +{f: 16, 0, 2, 4, 0, 2, 4, 0, 0, 8, 2, 0, 0, 2, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:42, 4:69, 6:3, 8:18, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{2: 0, 4, 8, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 4, 4, 4, 8, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 8, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 0, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 12, 4, 4, }, +{9: 0, 4, 4, 4, 8, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{a: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, -16, 8, 8, -8, }, +{2: 16, 0, -8, 8, 8, 8, 0, -8, 0, -8, 8, 0, 0, -8, -16, 0, }, +{4: 16, 8, 8, -8, 8, 8, -8, -16, 8, 8, -8, -8, 16, -16, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, -8, }, +{3: 16, -8, 0, 8, 0, 0, -8, 8, -8, 0, 8, 0, 0, -8, -8, 0, }, +{5: 16, 0, 0, -8, 0, 0, 8, 8, 0, 0, -8, 8, -16, -8, -8, 8, }, +{6: 16, 0, -8, -8, 0, 0, -8, 8, 0, -8, -8, 0, 0, 8, 8, 0, }, +{9: 16, -8, 0, 8, 0, -8, 0, -8, 0, 0, -8, 0, 0, 8, -8, 8, }, +{a: 16, 8, -8, 8, -8, 0, 0, -8, 0, 8, -16, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, 8, -8, 8, 0, 0, -8, 8, 0, }, +{7: 16, -8, 0, -8, 0, 0, 8, -8, -8, 0, -8, 0, 0, 8, 8, 0, }, +{b: 16, 0, 0, 8, 0, -8, 0, 8, -8, 0, -8, -8, 0, -8, 8, 0, }, +{d: 16, -8, 0, -8, 0, -8, 0, 8, 0, 0, 8, 0, 0, -8, 8, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 8, -8, 0, 8, -8, 0, }, +{f: 16, 0, 0, -8, 0, -8, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, x, x, , , x, x, x, , , x, }, +{5: , x, x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , x, x, x, , , x, x, , , x, x, , , x, x, }, +{9: , x, x, x, x, , x, x, x, , x, , x, x, , x, }, +{a: , x, , x, x, , x, , , x, , , x, , x, x, }, +{c: , x, , , x, , x, x, , , x, , , x, x, x, }, +{7: , x, x, x, , , x, x, , , x, x, , , , x, }, +{b: , x, , x, x, , x, , , , , , x, , , x, }, +{d: , x, , , x, , , x, , , x, , , x, , x, }, +{e: , , , , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0100,1100,1,}, +{0110,0100,1,}, +{1011,0001,1,}, +{1011,0100,0,}, +{1011,0101,1,}, +{1100,1010,1,}, +{1101,0100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x0b,}}, +{{0x01,0x02,0x04,}, {0x0b,}}, +{{0x01,0x0a,0x04,}, {0x0b,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x03,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x0b,0x04,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x03,0x0c,}, {0x04,}}, +{{0x09,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x0b,}}, +{{0x03,0x08,}, {0x09,}}, +{{0x05,0x08,}, {0x0b,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x02,}, {0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x0b,}}, +{{0x05,0x06,}, {0x0b,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x03,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x0b,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +237 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x08,0x0c,0x07,0x04,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, }, +{2: 0, 4, 4, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 2, 10, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, }, +{8: 0, 0, 2, 0, 4, 2, 4, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 6, 2, 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{9: 0, 0, 0, 0, 4, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 2, 6, 0, 2, 4, 0, 0, 0, }, +{c: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 0, 2, 2, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 0, 4, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 0, 0, 0, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 4, 0, 2, }, +{e: 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 0, 2, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:3, 4:4, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 16, 4, 8, 4, 2, 4, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{4: 16, 4, 10, 10, 8, 4, 4, 8, 4, 10, 10, 4, 4, 4, 8, 4, }, +{8: 16, 0, 2, 4, 4, 2, 4, 0, 4, 2, 8, 0, 2, 0, 0, 0, }, +{3: 16, 4, 6, 10, 0, 8, 4, 4, 2, 0, 0, 8, 0, 0, 0, 2, }, +{5: 16, 4, 4, 4, 0, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{6: 16, 0, 8, 4, 0, 0, 4, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{9: 16, 0, 0, 8, 4, 2, 0, 2, 4, 0, 4, 0, 2, 4, 2, 0, }, +{a: 16, 4, 0, 10, 0, 0, 4, 0, 2, 6, 0, 2, 8, 0, 4, 8, }, +{c: 16, 4, 0, 4, 4, 0, 0, 2, 0, 0, 8, 2, 0, 4, 2, 2, }, +{7: 16, 0, 4, 8, 2, 4, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 2, 2, 8, 0, 2, 4, 0, 4, 0, }, +{d: 16, 4, 0, 10, 4, 0, 4, 0, 8, 0, 6, 2, 0, 8, 0, 2, }, +{e: 16, 0, 0, 8, 2, 2, 0, 2, 0, 4, 0, 0, 4, 2, 4, 4, }, +{f: 16, 0, 2, 4, 0, 2, 4, 0, 0, 8, 2, 0, 0, 2, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:42, 4:69, 6:3, 8:18, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{5: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{9: 0, 8, 8, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 8, }, +{b: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:5, 4:7, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, -8, 0, 0, 8, 8, 0, -8, 8, -8, }, +{2: 16, 0, 0, 8, 0, -8, 0, 8, 0, 0, 8, -8, -8, 0, -8, -8, }, +{4: 16, 16, 8, -8, 8, 8, -8, -16, 8, 8, -8, -16, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, 0, 0, 8, -8, -8, 0, -8, 8, -8, 0, -8, 0, }, +{3: 16, 0, -8, 8, 8, 0, 0, -8, 8, -8, 8, -8, 0, 0, -16, 0, }, +{5: 16, -16, 0, -8, 0, 0, 8, 8, 0, 0, -8, -8, 0, 8, -8, 8, }, +{6: 16, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{9: 16, 0, 0, 8, -8, 0, -8, 8, 0, -8, -8, 8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -8, 0, 8, -16, -8, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, 0, 0, -8, 8, -8, 0, 8, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, -8, 8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, 0, -8, 0, 8, -8, 0, -8, -8, 0, -8, 8, 0, }, +{d: 16, 0, 8, -16, -8, 8, 0, -8, 0, -8, 8, -8, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 0, 8, 8, 0, -8, -8, 0, }, +{f: 16, 0, 0, -8, 0, -8, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, x, x, x, , x, x, }, +{4: , , x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , , x, x, x, , x, x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , , x, x, x, , x, x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , , x, , , x, , , x, , , x, , x, }, +{e: , , x, x, x, , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0001,0001,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0100,1101,1,}, +{0110,0100,1,}, +{0111,0100,1,}, +{1100,1010,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x04,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x0a,0x04,}, {0x01,}}, +{{0x04,0x08,}, {0x01,0x06,0x07,}}, +{{0x02,0x08,}, {0x0c,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x0b,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0b,0x04,}, {0x01,0x06,0x07,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x0e,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x09,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,}}, +{{0x07,0x08,}, {0x09,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,}}, +{{0x09,0x02,}, {0x03,}}, +{{0x0d,0x02,}, {0x04,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,}}, +{{0x0d,0x06,}, {0x04,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_238.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_238.txt new file mode 100644 index 0000000..6dad335 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_238.txt @@ -0,0 +1,428 @@ +238 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x08,0x05,0x0c,0x07,0x04,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, }, +{2: 0, 0, 10, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{9: 0, 0, 0, 2, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 2, 6, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 4, 0, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 2, 4, 2, 2, 0, 0, }, +{b: 0, 4, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 2, 4, 0, }, +{e: 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, }, +{f: 0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 16, 4, 10, 10, 10, 4, 4, 8, 4, 8, 8, 4, 4, 4, 10, 4, }, +{4: 16, 4, 10, 6, 0, 4, 8, 4, 0, 0, 0, 8, 2, 2, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 0, 4, 4, 0, 2, 6, 0, 2, 0, }, +{3: 16, 4, 4, 4, 0, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 16, 4, 4, 8, 2, 0, 4, 4, 2, 0, 0, 0, 0, 0, 2, 2, }, +{6: 16, 0, 8, 4, 0, 0, 4, 4, 2, 2, 2, 4, 0, 0, 0, 2, }, +{9: 16, 0, 4, 2, 6, 4, 2, 0, 6, 8, 0, 0, 0, 0, 0, 0, }, +{a: 16, 4, 8, 0, 4, 4, 2, 2, 10, 6, 0, 0, 8, 0, 0, 0, }, +{c: 16, 4, 8, 0, 0, 4, 2, 2, 0, 0, 6, 0, 0, 8, 4, 10, }, +{7: 16, 0, 4, 8, 0, 4, 0, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{b: 16, 4, 4, 0, 4, 0, 0, 2, 0, 10, 0, 2, 6, 0, 0, 0, }, +{d: 16, 4, 4, 0, 0, 0, 0, 2, 0, 0, 10, 2, 0, 6, 4, 0, }, +{e: 16, 0, 10, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 6, 4, 4, }, +{f: 16, 0, 4, 2, 0, 4, 2, 0, 0, 0, 8, 0, 0, 0, 6, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:30, 4:61, 6:11, 8:14, 10:11, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{9: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, -8, 0, 0, 8, 8, 0, -8, 8, -8, }, +{2: 16, 16, -8, 8, 8, -8, 8, -8, 8, -8, 8, -8, -8, 8, -16, -16, }, +{4: 16, 0, 8, -8, 8, 0, 0, -16, 8, 8, -8, 0, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 8, -8, -8, }, +{3: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 8, -8, 0, -8, -8, 8, }, +{5: 16, 0, 0, -8, 0, -8, 0, 8, 0, 0, -8, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, -8, -8, 0, 0, 8, 8, }, +{9: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, -8, 0, 8, -8, -8, 8, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 8, -16, 0, 0, 0, 8, 8, }, +{c: 16, 0, 8, -16, -8, 0, 0, -8, 0, -8, 8, 0, -8, 0, 8, 8, }, +{7: 16, 0, 0, -8, 0, 8, 0, -8, 0, 0, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, -8, 0, -8, -8, 8, -8, }, +{d: 16, 0, 0, -8, 0, -8, -8, 8, -8, 0, 8, 0, 0, 0, 8, -8, }, +{e: 16, 0, -8, -8, -8, 0, 8, 8, 0, 0, 8, 0, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, 0, 8, -8, -8, -8, 0, 8, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, x, x, x, , , x, x, , x, , x, }, +{6: , , x, x, , x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, x, , x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, , , x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , , x, x, , x, , , x, , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,1100,1,}, +{0110,0100,1,}, +{1100,1010,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x06,}}, +{{0x0b,0x04,}, {0x06,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x03,}}, +{{0x07,0x08,}, {0x03,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +238 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x08,0x05,0x0c,0x07,0x04,0x09,0x0a,0x0b,0x06,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, }, +{2: 0, 0, 10, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 2, 6, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 2, }, +{8: 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 0, 0, 4, 0, 2, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 2, 2, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 0, 0, 0, 0, 4, 4, 0, 2, 2, 0, 2, 2, 0, 0, }, +{9: 0, 0, 0, 0, 4, 4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 0, 2, 0, 4, }, +{7: 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 0, 4, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{d: 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 2, 0, }, +{e: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, 4, 2, }, +{f: 0, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, 0, 0, 0, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 16, 4, 10, 10, 10, 4, 4, 8, 4, 8, 8, 4, 4, 4, 10, 4, }, +{4: 16, 4, 10, 6, 0, 4, 8, 4, 2, 0, 0, 8, 0, 0, 0, 2, }, +{8: 16, 0, 10, 0, 4, 0, 2, 0, 6, 4, 0, 0, 4, 0, 2, 0, }, +{3: 16, 4, 4, 4, 0, 16, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 16, 4, 4, 8, 0, 0, 4, 4, 2, 2, 2, 0, 0, 0, 0, 2, }, +{6: 16, 0, 8, 4, 0, 0, 4, 4, 0, 2, 2, 4, 2, 2, 0, 0, }, +{9: 16, 0, 4, 0, 4, 4, 2, 2, 6, 10, 0, 0, 0, 0, 0, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 2, 8, 6, 0, 2, 10, 0, 0, 0, }, +{c: 16, 4, 8, 0, 0, 4, 0, 2, 0, 0, 6, 2, 0, 10, 4, 8, }, +{7: 16, 0, 4, 8, 2, 4, 0, 4, 0, 0, 0, 4, 2, 2, 2, 0, }, +{b: 16, 4, 4, 2, 6, 0, 0, 0, 0, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 0, 0, 8, 2, 0, 6, 6, 0, }, +{e: 16, 0, 10, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 4, 4, 6, }, +{f: 16, 0, 4, 0, 0, 4, 2, 2, 0, 0, 10, 0, 0, 0, 4, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:30, 4:61, 6:11, 8:14, 10:11, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 4, 4, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 8, 4, 4, 4, 0, 4, 4, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{9: 0, 8, 4, 4, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 12, 4, 0, 4, 0, 0, }, +{7: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:8, 4:4, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, -8, 0, 0, 8, 8, 0, -8, 8, -8, }, +{2: 16, 16, -8, 8, 8, -8, 8, -8, 8, -8, 8, -8, -8, 8, -16, -16, }, +{4: 16, 0, 0, -8, 8, 8, 0, 0, 8, 0, -8, -16, 8, 0, -8, -8, }, +{8: 16, 0, 0, 8, -8, 0, 0, 0, 0, 0, -8, 8, -8, 8, -8, -8, }, +{3: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 8, -8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 0, 0, 0, -8, 0, 8, -8, -8, 0, 0, -8, 8, }, +{6: 16, 0, 0, -8, 0, -8, 0, -8, 0, 0, -8, 8, -8, 0, 8, 8, }, +{9: 16, 0, 0, 8, 0, 0, 0, 0, -8, -8, -8, 8, 0, -8, -8, 8, }, +{a: 16, 0, -8, 8, -8, -8, 0, 0, 0, 0, -16, -8, 8, 0, 8, 8, }, +{c: 16, 0, 0, -16, -8, 8, 0, 0, 0, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 0, 0, 0, 8, 0, -8, -8, 8, 0, 0, 8, -8, }, +{b: 16, 0, 0, 8, 0, 0, 0, 0, -8, 8, -8, -8, 0, -8, 8, -8, }, +{d: 16, 0, 8, -8, 0, 0, -8, 0, -8, 0, 8, -8, 0, 0, 8, -8, }, +{e: 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, 0, -8, -8, 0, 0, -8, 0, -8, 0, 8, 8, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , , x, x, x, , , x, }, +{5: , , x, x, x, , x, x, , , x, x, , x, , x, }, +{6: , , x, x, , x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, , , x, x, , x, , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, , , , x, , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , , x, , , x, , , x, , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0100,1100,1,}, +{0111,0100,1,}, +{1100,1010,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,}}, +{{0x09,0x04,}, {0x07,}}, +{{0x0b,0x04,}, {0x07,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x02,}}, +{{0x07,0x08,}, {0x02,}}, +{{0x01,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x09,}}, +{{0x0d,0x06,}, {0x09,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0a,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_239.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_239.txt new file mode 100644 index 0000000..90a87c5 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_239.txt @@ -0,0 +1,428 @@ +239 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x0c,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, }, +{8: 0, 0, 0, 2, 6, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, }, +{5: 0, 2, 0, 2, 0, 0, 4, 4, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 2, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 2, 4, 0, 0, 4, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 0, 0, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 4, 4, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 4, }, +}; +Diff: 10, DDT_spectrum: {0:172, 2:54, 4:23, 6:5, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:11, 2:1, 6:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 4, 4, 4, 6, 0, 6, 0, 4, 0, 0, 6, 0, 0, }, +{2: 16, 4, 10, 8, 8, 4, 4, 10, 4, 10, 8, 4, 4, 4, 10, 4, }, +{4: 16, 4, 8, 6, 0, 4, 8, 4, 0, 0, 2, 10, 0, 0, 0, 2, }, +{8: 16, 4, 8, 2, 6, 4, 0, 0, 8, 4, 0, 2, 10, 0, 0, 0, }, +{3: 16, 4, 4, 4, 4, 10, 0, 0, 0, 0, 4, 6, 6, 0, 0, 6, }, +{5: 16, 6, 4, 10, 0, 0, 4, 4, 2, 0, 2, 0, 0, 0, 0, 0, }, +{6: 16, 0, 10, 4, 0, 0, 6, 4, 0, 2, 0, 4, 0, 2, 0, 0, }, +{9: 16, 6, 4, 2, 10, 0, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, }, +{a: 16, 0, 10, 0, 4, 0, 2, 0, 6, 4, 0, 0, 4, 0, 2, 0, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 8, 4, 10, }, +{7: 16, 0, 4, 8, 0, 6, 0, 6, 0, 0, 0, 4, 2, 0, 2, 0, }, +{b: 16, 0, 4, 0, 8, 6, 0, 2, 0, 6, 0, 0, 4, 0, 0, 2, }, +{d: 16, 6, 4, 0, 2, 0, 2, 0, 0, 0, 10, 0, 0, 4, 4, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 0, 4, 0, 0, 6, 0, 0, 0, 2, 8, 2, 0, 0, 6, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:24, 4:51, 6:21, 8:12, 10:15, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:11, 4:1, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 8, -16, 8, 8, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, 0, -8, -16, 0, 0, 0, -8, -8, }, +{3: 16, -16, -8, 8, 8, 8, -8, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 8, -8, -8, 0, 0, 0, -8, 0, -8, 0, 0, 8, }, +{6: 16, 0, -8, -8, 8, -8, 8, 0, 0, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, -8, 0, 0, 0, 0, -8, -8, 8, -8, 0, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 8, -8, 0, 0, 8, 0, 0, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, -8, 0, 0, 0, -8, 0, 8, 0, 0, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, 0, 0, 0, -8, 8, -8, -8, 0, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, 0, -8, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 0, -8, 0, 8, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , x, x, x, , , x, }, +{5: , , x, , x, x, x, , , , x, x, , x, , x, }, +{6: , , , , x, x, , x, , , x, x, , , x, x, }, +{9: , , x, x, x, x, , , x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , x, x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0100,1,}, +{1000,1100,1,}, +{1100,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x07,}}, +{{0x0d,0x06,}, {0x07,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0f,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0f,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x0b,}}, +{{0x09,0x0e,}, {0x0b,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +239 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x08,0x05,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x04,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, }, +{3: 0, 4, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 0, 0, 2, }, +{5: 0, 2, 0, 4, 0, 0, 4, 2, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 4, 4, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 2, 0, 0, 4, 0, 2, 0, 4, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 0, 2, 4, 4, 0, 0, 2, 0, 0, 2, }, +{c: 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 0, 4, }, +{7: 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 4, 2, }, +{f: 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:172, 2:54, 4:23, 6:5, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:11, 2:1, 6:3, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 4, 4, 4, 6, 0, 6, 0, 4, 0, 0, 6, 0, 0, }, +{2: 16, 4, 10, 8, 8, 4, 4, 10, 4, 10, 8, 4, 4, 4, 10, 4, }, +{4: 16, 4, 8, 6, 2, 4, 10, 4, 2, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 4, 8, 0, 6, 4, 0, 0, 10, 4, 2, 0, 8, 2, 0, 0, }, +{3: 16, 4, 4, 4, 4, 10, 0, 0, 0, 0, 4, 6, 6, 0, 0, 6, }, +{5: 16, 6, 4, 8, 0, 0, 4, 6, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 16, 0, 10, 4, 0, 0, 4, 4, 0, 0, 0, 6, 2, 0, 2, 0, }, +{9: 16, 6, 4, 0, 8, 0, 2, 0, 4, 6, 0, 0, 0, 0, 2, 0, }, +{a: 16, 0, 10, 0, 4, 0, 0, 2, 4, 4, 0, 0, 6, 0, 0, 2, }, +{c: 16, 4, 8, 2, 0, 4, 2, 0, 0, 0, 6, 0, 0, 10, 4, 8, }, +{7: 16, 0, 4, 10, 2, 6, 0, 4, 0, 0, 0, 4, 0, 0, 0, 2, }, +{b: 16, 0, 4, 0, 10, 6, 0, 0, 0, 4, 2, 2, 4, 0, 0, 0, }, +{d: 16, 6, 4, 0, 0, 0, 0, 2, 2, 0, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 4, 4, 6, }, +{f: 16, 0, 4, 2, 0, 6, 0, 0, 0, 0, 10, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:102, 2:24, 4:51, 6:21, 8:12, 10:15, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 12, 0, 4, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 8, 8, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:11, 4:1, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, 0, 0, 0, 0, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 8, -16, 8, 0, 0, 0, -8, -8, 8, -8, 0, 0, -8, }, +{3: 16, -16, -8, 8, 8, 8, -8, 0, -8, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 8, -8, 8, -8, 0, -8, 0, 8, -8, 0, 0, -8, 0, 0, }, +{6: 16, 0, -8, -8, 8, -8, 0, 0, 0, 0, -8, 8, -8, 8, 0, 0, }, +{9: 16, 0, 8, 8, -8, -8, 0, 8, -8, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, 0, 8, 0, -8, -8, 0, 0, 0, 8, }, +{c: 16, 0, 8, -16, -8, 8, 0, -8, 0, 0, 8, -8, -8, 0, 0, 8, }, +{7: 16, 0, -8, -8, 8, 8, 0, 8, 0, -8, -8, 0, 0, -8, 0, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, -8, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, -8, 0, 0, -8, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 0, 0, 8, 0, 8, 0, 0, -8, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, 0, 8, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , x, x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , x, , x, x, , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , x, , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,1100,1,}, +{1000,1000,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x0c,}, {0x04,0x0b,0x0f,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,}}, +{{0x05,0x06,}, {0x01,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0e,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x0a,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0a,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,}}, +{{0x09,0x0e,}, {0x06,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_240.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_240.txt new file mode 100644 index 0000000..c6936fa --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_240.txt @@ -0,0 +1,428 @@ +240 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x08,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 4, }, +{2: 0, 0, 10, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 4, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 2, 0, 4, 0, 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, }, +{5: 0, 2, 0, 0, 0, 2, 6, 2, 0, 2, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 2, 0, 2, 0, 0, 6, 0, 0, 2, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 0, 2, 0, 2, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 4, 2, 2, 0, }, +{c: 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 2, 2, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, 4, }, +{f: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:170, 2:60, 4:17, 6:7, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:2, 4:1, 6:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 6, 0, 6, 4, 6, 0, 0, 0, 4, 0, 0, 4, 4, }, +{2: 16, 4, 10, 4, 4, 4, 10, 4, 8, 4, 10, 8, 10, 4, 8, 4, }, +{4: 16, 4, 8, 6, 0, 4, 8, 4, 2, 2, 0, 10, 0, 0, 0, 0, }, +{8: 16, 0, 10, 0, 4, 0, 0, 2, 4, 4, 0, 0, 6, 0, 0, 2, }, +{3: 16, 6, 4, 6, 0, 10, 4, 6, 0, 0, 0, 4, 0, 4, 4, 0, }, +{5: 16, 6, 4, 4, 0, 6, 6, 6, 0, 2, 0, 4, 2, 0, 0, 0, }, +{6: 16, 4, 10, 4, 2, 4, 8, 6, 0, 0, 2, 8, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 0, 2, 4, 2, 0, 2, 4, 2, 2, 0, }, +{a: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 0, 2, 4, 2, 2, 0, }, +{c: 16, 0, 10, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 4, 4, 6, }, +{7: 16, 6, 4, 6, 2, 6, 4, 4, 2, 0, 0, 6, 0, 0, 0, 0, }, +{b: 16, 0, 4, 2, 2, 0, 2, 0, 4, 2, 2, 0, 4, 0, 0, 2, }, +{d: 16, 0, 4, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 6, 10, 0, }, +{e: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 10, 6, 8, }, +{f: 16, 4, 4, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 8, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:34, 4:54, 6:22, 8:11, 10:12, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{4: 0, 4, 0, 8, 4, 4, 4, 0, 8, 4, 4, 4, 0, 0, 4, 0, }, +{8: 0, 0, 4, 4, 12, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 4, 0, 8, 4, 4, 4, 0, 0, 4, 4, 4, 0, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 0, 4, 0, 8, 4, }, +{f: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 8, 4, 0, 8, 4, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 8, 0, -8, 8, 0, 8, 8, -8, -8, -16, 0, 0, }, +{2: 16, 8, -8, 8, 8, -8, 8, -16, 8, -8, 8, -8, -16, 16, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, 0, -8, 0, 8, -16, -8, 8, 0, -8, 0, }, +{8: 16, 0, 0, 8, -8, 0, 0, 8, 8, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, 0, 0, 8, 0, -8, -8, 0, -8, 8, 8, 8, -16, 0, 0, }, +{5: 16, -8, 0, 0, 8, -8, 0, -8, -8, 8, -8, 8, -8, 0, 0, 8, }, +{6: 16, 8, -8, -8, 8, 0, 0, 8, 0, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, -8, -8, 0, 8, 0, -8, -8, 0, 8, 0, 0, 0, }, +{a: 16, 0, -8, 0, -8, 0, 0, -8, 0, 8, -8, 0, 8, 0, 8, -8, }, +{c: 16, 0, 8, -8, -8, 0, 8, -8, 0, -8, 8, 0, -8, 0, 0, 0, }, +{7: 16, -8, 0, 0, 8, 8, 0, 8, -8, -8, -8, -8, 8, 0, 0, -8, }, +{b: 16, 0, 0, 0, -8, 8, 0, -8, 0, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, }, +{e: 16, 0, -8, -8, -16, -8, 0, 8, 0, 8, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 8, -8, 8, 8, 0, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , , , x, x, , , x, }, +{5: , , x, x, x, x, x, x, , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, , , , x, x, , x, }, +{a: , x, , , x, x, , x, , x, , , x, , x, x, }, +{c: , x, , x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, x, , , x, , , , x, , , , x, }, +{b: , x, , , x, x, , x, , , , , x, , , x, }, +{d: , , , x, x, x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0110,0010,1,}, +{1000,1110,1,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x03,}}, +{{0x0b,0x0c,}, {0x03,}}, +{{0x01,0x08,}, {0x0d,}}, +{{0x03,0x08,}, {0x0d,}}, +{{0x05,0x08,}, {0x0f,}}, +{{0x07,0x08,}, {0x0f,}}, +{{0x01,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x0a,}}, +{{0x01,0x0a,}, {0x0d,}}, +{{0x05,0x0a,}, {0x09,}}, +{{0x09,0x0a,}, {0x0d,}}, +{{0x0d,0x0a,}, {0x09,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +240 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x08,0x07,0x06,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 4, }, +{2: 0, 0, 10, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 6, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{6: 0, 2, 0, 0, 2, 2, 2, 6, 2, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 4, 0, 0, 0, 4, 0, 0, 2, 0, 2, 2, 0, }, +{a: 0, 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 2, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, 4, }, +{f: 0, 4, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:170, 2:60, 4:17, 6:7, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:2, 4:1, 6:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 4, 0, 6, 6, 4, 0, 0, 0, 6, 0, 0, 4, 4, }, +{2: 16, 4, 10, 8, 10, 4, 4, 10, 4, 8, 10, 4, 4, 4, 8, 4, }, +{4: 16, 6, 4, 6, 0, 6, 4, 4, 0, 2, 0, 6, 2, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 0, 2, 2, 4, 2, 2, 2, 0, 0, 2, }, +{3: 16, 6, 4, 4, 0, 10, 6, 4, 0, 0, 0, 6, 0, 4, 4, 0, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 0, 2, 4, 2, 0, 0, 0, }, +{6: 16, 6, 4, 4, 2, 6, 6, 6, 2, 0, 0, 4, 0, 0, 0, 0, }, +{9: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 0, 2, 4, 2, 2, 0, }, +{a: 16, 0, 4, 2, 4, 0, 2, 0, 2, 4, 0, 0, 2, 2, 2, 0, }, +{c: 16, 0, 10, 0, 0, 0, 0, 2, 0, 0, 4, 0, 2, 4, 4, 6, }, +{7: 16, 4, 8, 10, 0, 4, 4, 8, 2, 2, 0, 6, 0, 0, 0, 0, }, +{b: 16, 0, 10, 0, 6, 0, 2, 0, 4, 4, 0, 0, 4, 0, 0, 2, }, +{d: 16, 0, 4, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 6, 10, 0, }, +{e: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 10, 6, 8, }, +{f: 16, 4, 4, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 8, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:34, 4:54, 6:22, 8:11, 10:12, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 4, 8, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 0, 4, 4, 12, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 8, 4, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 4, 8, 4, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 4, 0, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:121, 4:107, 8:22, 12:5, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:6, 4:6, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 8, 0, 0, 8, -8, 8, 8, -8, -8, -8, 0, 0, }, +{2: 16, 16, -8, 8, 8, -8, 8, -8, 8, -16, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 0, 0, 8, 8, -8, -8, 0, 8, -8, -8, 8, -8, 0, -8, }, +{8: 16, 0, 0, 0, -8, 8, 0, 8, 0, -8, -8, 0, -8, 0, 0, 0, }, +{3: 16, -16, 0, 0, 8, 0, 0, -8, -8, -8, 8, 8, 8, -8, 0, 0, }, +{5: 16, 0, 8, -8, 8, 0, 0, -16, 0, 8, -8, 0, -8, 8, -8, 0, }, +{6: 16, 0, 0, 0, 8, -8, -8, 8, 0, -8, -8, 8, -8, -8, 0, 8, }, +{9: 16, 0, 8, 0, -8, 0, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, }, +{a: 16, 0, 0, 0, -8, -8, 0, -8, 0, 8, -8, 0, 8, 0, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 8, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, 0, -8, -16, -8, 8, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 8, -8, 0, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -8, 0, -8, -8, -8, -8, 8, 0, 8, 0, 0, 8, }, +{e: 16, 0, -8, -8, -16, -8, 0, 8, 0, 8, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -8, 0, -8, 8, -8, 8, 8, 0, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , x, , , , x, x, , , x, }, +{5: , , x, x, x, , x, x, , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, , , , x, x, , x, }, +{a: , , x, x, x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , , x, , , x, x, x, }, +{7: , , x, x, x, , , x, , , , x, , , , x, }, +{b: , , x, , x, , , x, , , , , x, , , x, }, +{d: , , , , x, , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 8 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1000,1110,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x03,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x0f,}}, +{{0x01,0x0c,}, {0x01,}}, +{{0x03,0x0c,}, {0x01,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x0f,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_241.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_241.txt new file mode 100644 index 0000000..3117dc6 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_241.txt @@ -0,0 +1,432 @@ +241 Sbox: +LUT = { +0x04,0x00,0x08,0x02,0x03,0x05,0x06,0x07,0x01,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, 2, 0, 2, 2, 0, }, +{8: 0, 0, 2, 0, 6, 0, 2, 0, 4, 0, 0, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 2, 2, 8, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, 2, }, +{6: 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 0, 4, 2, 0, 0, 2, }, +{9: 0, 2, 0, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 6, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:58, 4:11, 6:9, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 6, 6, 4, 4, 6, 4, 6, 4, 4, 4, 4, 0, 0, }, +{2: 16, 4, 10, 4, 4, 4, 10, 4, 8, 4, 10, 8, 10, 4, 8, 4, }, +{4: 16, 4, 8, 6, 0, 4, 8, 4, 0, 0, 0, 10, 0, 2, 2, 0, }, +{8: 16, 4, 10, 0, 6, 4, 2, 0, 8, 4, 0, 0, 8, 0, 0, 2, }, +{3: 16, 4, 4, 6, 6, 8, 4, 6, 4, 6, 4, 4, 4, 0, 0, 4, }, +{5: 16, 6, 4, 6, 0, 6, 6, 4, 0, 0, 2, 4, 0, 0, 0, 2, }, +{6: 16, 4, 10, 4, 0, 4, 8, 6, 0, 0, 0, 8, 2, 0, 0, 2, }, +{9: 16, 6, 4, 0, 6, 6, 0, 0, 6, 4, 0, 0, 4, 2, 2, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 10, 6, 0, 0, 8, 2, 2, 0, }, +{c: 16, 4, 10, 0, 2, 4, 0, 2, 0, 0, 6, 0, 0, 8, 4, 8, }, +{7: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 16, 6, 4, 0, 4, 6, 0, 0, 4, 6, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 4, 2, 2, 0, 0, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:76, 2:30, 4:63, 6:29, 8:18, 10:9, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 4, 12, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 4, 0, 0, 12, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{3: 0, 4, 4, 0, 4, 8, 4, 4, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 4, 4, 0, 4, 12, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 4, 0, 0, 4, 4, 4, 0, 8, 4, 4, 4, 0, 8, 4, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:105, 8:18, 12:7, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 8, -8, -8, 8, -8, 8, 0, -8, -8, -16, 8, -8, }, +{2: 16, 8, -8, 8, 8, -8, 8, -16, 8, -8, 8, -8, -16, 16, -8, -8, }, +{4: 16, 0, 8, -16, 8, 0, 0, -8, 0, 8, -8, 0, 8, 0, -8, -8, }, +{8: 16, 0, 8, 8, -8, 0, 8, 8, 0, -8, -8, 0, -8, 0, -16, 0, }, +{3: 16, 0, -8, 8, 8, 8, -8, -8, -8, -8, 0, 8, 8, -16, -8, 8, }, +{5: 16, -8, 8, -8, 8, 0, 0, -8, -8, 8, 0, 0, -8, 0, -8, 8, }, +{6: 16, 0, -16, -8, 8, 0, 0, 8, 8, -8, -8, 0, -8, 0, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 0, -8, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -16, -8, 0, -8, 0, 8, -8, 0, 8, 0, 8, 0, }, +{c: 16, 8, 8, -8, -8, 0, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 0, 8, -8, -8, 0, 0, 8, 0, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, -8, -8, 0, 8, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, 0, 0, -8, 0, -8, 0, -8, 8, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 8, 0, -8, 8, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 8, 0, 8, 0, 8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, , x, x, x, , , , , x, , x, , x, }, +{6: , x, , , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, , x, x, , , , , x, , , x, x, x, }, +{7: , x, , , x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, x, , x, x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0010,0110,1,}, +{0100,0100,1,}, +{0110,0010,1,}, +{1000,1010,1,}, +{1010,1100,1,}, +{1011,0010,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,1000,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x04,0x09,0x0d,}}, +{{0x03,0x04,}, {0x04,0x09,0x0d,}}, +{{0x09,0x04,}, {0x04,}}, +{{0x0b,0x04,}, {0x04,}}, +{{0x01,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x0c,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x0a,}}, +{{0x01,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x09,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x02,}, {0x06,0x0b,0x0d,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +241 Inverse Sbox: +LUT = { +0x01,0x08,0x03,0x04,0x00,0x05,0x06,0x07,0x02,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{2: 0, 0, 10, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 6, 0, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{8: 0, 2, 0, 0, 6, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, }, +{3: 0, 0, 0, 0, 0, 8, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{5: 0, 0, 2, 4, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, }, +{6: 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 2, 2, 0, 0, 0, 2, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 0, 2, 4, 0, 0, }, +{7: 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 0, 0, 2, 0, 0, 0, 0, 2, 0, 4, 0, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 0, 0, }, +{e: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:58, 4:11, 6:9, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 4, 4, 6, 4, 6, 4, 4, 6, 6, 4, 0, 0, }, +{2: 16, 4, 10, 8, 10, 4, 4, 10, 4, 8, 10, 4, 4, 4, 8, 4, }, +{4: 16, 6, 4, 6, 0, 6, 6, 4, 0, 0, 0, 4, 0, 2, 2, 0, }, +{8: 16, 6, 4, 0, 6, 6, 0, 0, 6, 4, 2, 0, 4, 0, 0, 2, }, +{3: 16, 4, 4, 4, 4, 8, 6, 4, 6, 4, 4, 6, 6, 0, 0, 4, }, +{5: 16, 4, 10, 8, 2, 4, 6, 8, 0, 0, 0, 4, 0, 0, 0, 2, }, +{6: 16, 6, 4, 4, 0, 6, 4, 6, 0, 0, 2, 6, 0, 0, 0, 2, }, +{9: 16, 4, 8, 0, 8, 4, 0, 0, 6, 10, 0, 0, 4, 2, 2, 0, }, +{a: 16, 6, 4, 0, 4, 6, 0, 0, 4, 6, 0, 0, 6, 2, 2, 0, }, +{c: 16, 4, 10, 0, 0, 4, 2, 0, 0, 0, 6, 0, 2, 8, 4, 8, }, +{7: 16, 4, 8, 10, 0, 4, 4, 8, 0, 0, 0, 6, 0, 2, 2, 0, }, +{b: 16, 4, 10, 0, 8, 4, 0, 2, 4, 8, 0, 0, 6, 0, 0, 2, }, +{d: 16, 4, 4, 2, 0, 0, 0, 0, 2, 2, 8, 2, 0, 4, 4, 0, }, +{e: 16, 0, 8, 2, 0, 0, 0, 0, 2, 2, 4, 2, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 2, 4, 2, 2, 0, 0, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:76, 2:30, 4:63, 6:29, 8:18, 10:9, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 0, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 4, 0, 12, 4, 0, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{3: 0, 0, 0, 0, 4, 8, 0, 0, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 4, 4, 0, 4, 4, 4, 12, 0, 4, 4, 0, 0, 0, }, +{c: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 8, 0, 0, 8, 4, 4, }, +{7: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:105, 8:18, 12:7, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 8, -8, 8, 0, -8, -8, 0, 8, -8, }, +{2: 16, 16, -8, 8, 8, -8, 8, -8, 8, -16, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 0, -8, -8, 0, 8, 0, 0, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, -8, -8, 0, 0, -8, -8, -8, 0, }, +{3: 16, -16, -8, 8, 8, 8, -8, -8, -8, -8, 0, 8, 8, 0, -8, 8, }, +{5: 16, 0, 8, -8, 8, 0, 8, -8, 0, 8, -8, 0, -8, 0, -16, 0, }, +{6: 16, 0, -8, -8, 8, 0, -8, 8, 0, -8, 0, 0, -8, -8, 8, 8, }, +{9: 16, 0, 8, 8, -16, -8, 0, 8, 0, -8, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, -8, 8, 0, 0, 8, -8, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -16, 0, -8, 8, 0, -8, 8, 8, 0, }, +{7: 16, 0, -8, -16, 8, 0, 0, 8, 0, -8, -8, 0, 8, 0, 8, -8, }, +{b: 16, 0, -16, 8, -8, 0, 0, -8, 8, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, 0, 0, -8, 0, -8, 0, -8, 8, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 8, 0, 8, 0, -8, 8, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 8, 0, 8, 0, 8, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , x, x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , x, x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , , x, , x, , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, x, x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,1011,1,}, +{0100,0111,1,}, +{0110,1100,1,}, +{1000,1001,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x06,}}, +{{0x02,0x08,}, {0x01,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x0d,}}, +{{0x02,0x04,}, {0x01,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x0d,}}, +{{0x02,0x0c,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x0a,0x0c,}, {0x06,}}, +{{0x01,0x04,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_242.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_242.txt new file mode 100644 index 0000000..42e66b1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_242.txt @@ -0,0 +1,432 @@ +242 Sbox: +LUT = { +0x08,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 0, 0, 2, 0, 2, 6, 2, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 2, 0, 0, 0, 0, 6, 0, 2, 0, 4, 0, 0, 2, 0, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 2, 0, 0, 0, 2, 0, 0, 6, 0, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 6, 2, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 2, 0, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:58, 4:11, 6:9, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:2, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 6, 6, 4, 6, 4, 4, 4, 4, 4, 6, 0, 0, }, +{2: 16, 4, 10, 4, 4, 4, 10, 4, 10, 4, 8, 8, 8, 4, 10, 4, }, +{4: 16, 4, 8, 6, 2, 4, 8, 4, 0, 0, 0, 10, 2, 0, 0, 0, }, +{8: 16, 4, 8, 0, 6, 4, 0, 0, 8, 4, 2, 0, 10, 0, 0, 2, }, +{3: 16, 6, 4, 6, 4, 8, 4, 4, 4, 6, 4, 4, 4, 0, 0, 6, }, +{5: 16, 4, 4, 6, 0, 6, 6, 6, 2, 0, 0, 4, 0, 2, 0, 0, }, +{6: 16, 4, 10, 4, 0, 4, 8, 6, 0, 2, 0, 8, 0, 0, 2, 0, }, +{9: 16, 6, 4, 2, 6, 4, 0, 0, 6, 6, 0, 0, 4, 0, 2, 0, }, +{a: 16, 4, 10, 0, 4, 4, 2, 0, 8, 6, 0, 0, 8, 2, 0, 0, }, +{c: 16, 4, 8, 2, 0, 4, 0, 0, 0, 0, 6, 2, 0, 8, 4, 10, }, +{7: 16, 6, 4, 6, 0, 4, 4, 6, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 4, 4, 0, 6, 6, 0, 2, 4, 6, 2, 0, 6, 0, 0, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:82, 2:24, 4:59, 6:33, 8:16, 10:11, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 4, 4, 0, 4, 0, 4, 4, 0, 0, 12, 0, 4, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 4, 0, 4, 0, 4, 4, 8, 0, 4, 0, 4, 8, 0, 4, }, +{e: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 12, 0, }, +{f: 0, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 8, 0, 4, 8, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:105, 8:18, 12:7, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 8, -8, 0, 8, 0, -8, -16, 8, -8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 16, -16, -8, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 8, -16, 8, 0, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 8, 8, 8, -8, -8, -8, 0, 8, 0, 8, -16, -8, 8, }, +{5: 16, -8, 8, -8, 8, -8, 0, -8, 0, 0, -8, 8, 0, 0, -8, 8, }, +{6: 16, 8, -16, -8, 8, -8, 0, 8, 0, -8, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, -8, -8, 8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, -8, 8, -16, 0, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -16, -8, 8, 0, -8, 0, -8, 8, -8, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 8, 0, 8, 0, 0, -8, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, -8, -8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, , , , x, x, , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0100,1100,1,}, +{0110,1010,1,}, +{1000,1000,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x01,0x02,0x04,}, {0x0d,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x04,}}, +{{0x0b,0x0c,}, {0x04,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x06,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x07,}}, +{{0x09,0x0e,}, {0x07,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +242 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x08,0x05,0x06,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, }, +{2: 0, 0, 10, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, }, +{4: 0, 0, 0, 6, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 8, 2, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{5: 0, 0, 2, 4, 0, 0, 6, 0, 0, 2, 0, 0, 0, 2, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, 2, 0, 2, 0, }, +{9: 0, 0, 2, 0, 4, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 2, 6, 0, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 0, 0, 4, 2, 0, }, +{e: 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:58, 4:11, 6:9, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:2, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 4, 4, 4, 6, 4, 4, 6, 4, 4, 6, 4, 6, 0, 0, }, +{2: 16, 4, 10, 8, 8, 4, 4, 10, 4, 10, 8, 4, 4, 4, 10, 4, }, +{4: 16, 4, 4, 6, 0, 6, 6, 4, 2, 0, 2, 6, 0, 0, 0, 0, }, +{8: 16, 6, 4, 2, 6, 4, 0, 0, 6, 4, 0, 0, 6, 0, 0, 2, }, +{3: 16, 6, 4, 4, 4, 8, 6, 4, 4, 4, 4, 4, 6, 0, 0, 6, }, +{5: 16, 4, 10, 8, 0, 4, 6, 8, 0, 2, 0, 4, 0, 2, 0, 0, }, +{6: 16, 6, 4, 4, 0, 4, 6, 6, 0, 0, 0, 6, 2, 0, 2, 0, }, +{9: 16, 4, 10, 0, 8, 4, 2, 0, 6, 8, 0, 0, 4, 0, 2, 0, }, +{a: 16, 4, 4, 0, 4, 6, 0, 2, 6, 6, 0, 0, 6, 2, 0, 0, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 8, 4, 10, }, +{7: 16, 4, 8, 10, 0, 4, 4, 8, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 4, 8, 2, 10, 4, 0, 0, 4, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 6, 4, 0, 0, 0, 2, 0, 0, 2, 8, 0, 0, 4, 6, 0, }, +{e: 16, 0, 10, 0, 0, 0, 0, 2, 2, 0, 4, 0, 0, 6, 4, 4, }, +{f: 16, 0, 4, 0, 2, 6, 0, 0, 0, 0, 10, 2, 0, 0, 4, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:82, 2:24, 4:59, 6:33, 8:16, 10:11, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 12, LAT_spectrum: {0:125, 4:105, 8:18, 12:7, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 8, -8, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 8, -8, -8, 8, -8, -8, }, +{4: 16, 0, 8, -8, 8, 8, -8, -8, 0, 0, -8, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, 0, 0, -8, 0, -8, -8, -8, -8, }, +{3: 16, -16, -8, 8, 8, 8, -8, -8, -8, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 8, -8, 8, -8, 8, -16, 0, 8, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, -8, -8, 8, -8, -8, 8, 0, 0, -8, 8, -8, 0, 8, 0, }, +{9: 16, 0, 8, 8, -8, -8, 0, 8, 0, -8, -8, 0, 0, 8, -16, 0, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 0, -8, 0, 8, -8, 8, 8, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -16, 8, 8, 0, 8, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, 0, -8, -8, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 8, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 8, 0, 8, -8, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 10 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0111,1,}, +{0110,0101,1,}, +{1000,1100,1,}, +{1100,1011,1,}, +{1110,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 3, +v=3 3, 0, 0, +(V_basis, W_spaned) pairs +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,}}, +{{0x06,0x08,}, {0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x0a,0x04,}, {0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x06,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,}}, +{{0x09,0x06,}, {0x0e,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_243.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_243.txt new file mode 100644 index 0000000..aae556b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_243.txt @@ -0,0 +1,466 @@ +243 Sbox: +LUT = { +0x08,0x00,0x0a,0x02,0x03,0x05,0x04,0x07,0x06,0x09,0x01,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + +ANF of components: +y0 + + + = + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{2: 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{5: 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, 2, 0, }, +{6: 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{9: 0, 4, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 0, 0, 0, 4, }, +{b: 0, 2, 0, 2, 0, 4, 0, 0, 2, 0, 2, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 4, 0, }, +}; +Diff: 12, DDT_spectrum: {0:173, 2:48, 4:33, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 4:4, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 0, 4, 6, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, }, +{2: 16, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 16, 8, 8, 8, 8, }, +{4: 16, 0, 8, 4, 0, 0, 4, 4, 0, 2, 0, 4, 2, 0, 2, 2, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 6, 8, 2, 6, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{5: 16, 0, 8, 0, 0, 2, 4, 2, 0, 0, 0, 4, 2, 4, 2, 4, }, +{6: 16, 0, 8, 4, 2, 0, 4, 4, 2, 0, 2, 4, 0, 2, 0, 0, }, +{9: 16, 4, 8, 0, 0, 6, 0, 2, 4, 0, 0, 0, 6, 0, 2, 0, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 2, 8, 2, 0, 0, 4, 0, 2, 0, 2, 4, 0, 4, 0, 4, }, +{b: 16, 6, 8, 2, 0, 4, 0, 0, 6, 0, 2, 0, 4, 0, 0, 0, }, +{d: 16, 0, 8, 0, 0, 2, 4, 2, 0, 2, 4, 4, 0, 0, 4, 2, }, +{e: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 2, 8, 2, 2, 0, 4, 0, 0, 0, 4, 4, 0, 2, 4, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:36, 4:52, 6:12, 8:24, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{c: 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{d: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{e: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +}; +Lin: 12, LAT_spectrum: {0:151, 4:62, 8:40, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -16, 0, 0, }, +{2: 16, 8, -16, 8, 16, -8, 16, -8, 8, -16, 8, -16, -8, 16, -8, -16, }, +{4: 16, 0, 0, -8, 0, 0, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -16, 0, 0, }, +{5: 16, -8, 0, -8, 0, -8, 0, -8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, 0, 0, 8, 0, -16, -8, 0, 0, 0, 8, 0, }, +{9: 16, -8, 0, 8, 0, -8, -16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 0, 8, 0, 8, 0, 0, 0, -16, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, 0, 8, -16, -8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 16, }, +{e: 16, 8, -16, -8, 0, -8, 0, 8, 8, 0, 8, 0, -8, 0, -8, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, 8, 0, 0, -16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, , x, , x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , x, , x, , , , x, , x, , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0010,0010,1,}, +{0010,1100,0,}, +{0010,1110,1,}, +{0100,1100,1,}, +{0101,0010,0,}, +{0101,1001,1,}, +{0101,1011,1,}, +{0110,1100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,0010,0,}, +{1000,1000,1,}, +{1000,1010,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1111,0010,1,}, +{1111,1101,0,}, +{1111,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 13, +v=3 7, 7, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x02,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x02,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x02,0x05,0x07,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x03,0x04,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x0b,0x04,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0b,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x05,0x06,}, {0x07,0x0a,0x0d,}}, +{{0x09,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x0d,0x06,}, {0x05,0x0a,0x0f,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x05,0x07,}}, +{{0x09,0x0e,}, {0x02,0x05,0x07,}}, +{{0x0d,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +243 Inverse Sbox: +LUT = { +0x01,0x0a,0x03,0x04,0x06,0x05,0x08,0x07,0x00,0x09,0x02,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 2, 0, 0, 4, 0, 0, 2, 2, 0, 0, 2, }, +{2: 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 4, 2, 2, 0, 0, 2, }, +{8: 0, 4, 0, 0, 4, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 4, 2, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, }, +{6: 0, 2, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 2, 4, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 2, 4, 2, 0, 2, 2, 0, 0, 0, }, +{a: 0, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 4, 2, 2, 4, 0, 0, }, +{7: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 0, 0, 0, 0, 2, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 2, 4, 0, }, +}; +Diff: 12, DDT_spectrum: {0:173, 2:48, 4:33, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 4:4, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 8, 0, 0, 6, 0, 0, 4, 0, 0, 2, 6, 0, 0, 2, }, +{2: 16, 8, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, }, +{4: 16, 0, 8, 4, 0, 2, 0, 4, 0, 0, 4, 2, 2, 0, 4, 2, }, +{8: 16, 4, 8, 0, 4, 6, 0, 2, 0, 6, 0, 0, 0, 0, 0, 2, }, +{3: 16, 6, 8, 0, 0, 4, 2, 0, 6, 0, 0, 0, 4, 2, 0, 0, }, +{5: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 16, 2, 8, 4, 0, 0, 2, 4, 2, 0, 4, 0, 0, 2, 4, 0, }, +{9: 16, 0, 8, 0, 4, 0, 0, 2, 4, 6, 0, 2, 6, 0, 0, 0, }, +{a: 16, 6, 8, 2, 6, 4, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 2, 0, 2, 4, 2, 2, 4, 4, 4, }, +{7: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 16, 0, 8, 2, 6, 0, 2, 0, 6, 4, 0, 0, 4, 0, 0, 0, }, +{d: 16, 0, 8, 0, 0, 2, 4, 2, 0, 2, 4, 4, 0, 0, 4, 2, }, +{e: 16, 0, 8, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 4, 4, 4, }, +{f: 16, 2, 8, 2, 2, 0, 4, 0, 0, 0, 4, 4, 0, 2, 4, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:36, 4:52, 6:12, 8:24, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 4, 0, 4, 12, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +}; +Lin: 12, LAT_spectrum: {0:151, 4:62, 8:40, 12:2, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 8:3, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 0, 0, -8, 8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 16, -8, -8, 16, -16, -16, }, +{4: 16, 0, 0, -8, 0, 16, -8, -8, 0, 0, 0, -8, 0, 0, 0, 0, }, +{8: 16, 0, 0, 8, 0, 0, 0, 8, -8, 0, 0, 0, -8, -16, 0, 0, }, +{3: 16, -16, 0, 8, 0, 0, -8, -8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 0, 16, -16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -8, 0, -16, -8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -8, 0, 0, 8, 0, -8, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, 8, -16, 0, 0, }, +{c: 16, 0, 0, -8, -8, 0, 0, -8, 0, -8, 0, 0, 0, 0, 16, 0, }, +{7: 16, 0, -16, -8, 8, 0, 8, 8, 8, -8, 0, -8, -8, 0, 0, 0, }, +{b: 16, 0, 0, 8, -8, 0, 0, -8, 0, 8, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -8, 0, 0, 0, -8, -8, 0, 0, 0, -8, 0, 0, 16, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 8, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, -8, 0, 0, 0, 8, -8, 0, 0, 0, 8, 0, 0, -16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , x, , x, x, , , x, }, +{5: , , , , x, , x, x, , x, , x, , x, , x, }, +{6: , , , x, x, x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , x, , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , , , , , , x, , x, , , , x, , x, }, +{e: , , , x, x, x, , , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1100,0010,0,}, +{1100,1001,1,}, +{1100,1011,1,}, +{1101,0010,0,}, +{1101,1000,1,}, +{1101,1010,1,}, +{1110,0010,1,}, +{1110,1100,0,}, +{1110,1110,1,}, +{1111,0010,1,}, +{1111,1101,0,}, +{1111,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 13, +v=3 7, 7, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x02,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x04,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x03,0x0d,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,}}, +{{0x09,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x07,0x08,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x09,0x0b,0x0d,0x0f,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x02,0x0d,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_244.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_244.txt new file mode 100644 index 0000000..6507a79 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_244.txt @@ -0,0 +1,450 @@ +244 Sbox: +LUT = { +0x08,0x00,0x06,0x02,0x03,0x05,0x01,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y1 = + + x1 + x2 + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + + x1 + x2 + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 2, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, }, +{3: 0, 0, 0, 4, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, }, +{5: 0, 2, 0, 0, 0, 4, 6, 0, 2, 0, 0, 0, 0, 2, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 6, 2, 2, 0, 4, 0, 0, 0, 0, }, +{9: 0, 2, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 4, 0, }, +{a: 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 0, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 4, 0, 0, 2, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, }, +}; +Diff: 12, DDT_spectrum: {0:179, 2:42, 4:27, 6:6, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:9, 2:3, 4:1, 6:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 8, 10, 2, 4, 4, 8, 0, 0, 0, 4, 0, 2, 0, 0, }, +{2: 16, 8, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, }, +{4: 16, 4, 8, 6, 2, 4, 8, 4, 0, 0, 0, 10, 2, 0, 0, 0, }, +{8: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 4, 8, 8, 0, 6, 4, 10, 0, 2, 0, 4, 0, 0, 0, 2, }, +{5: 16, 10, 8, 4, 0, 8, 6, 4, 2, 0, 0, 4, 0, 2, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 10, 6, 2, 2, 0, 8, 0, 0, 0, 0, }, +{9: 16, 2, 8, 2, 2, 0, 0, 0, 4, 0, 4, 0, 4, 2, 4, 0, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 8, 2, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 4, 4, }, +{7: 16, 8, 8, 4, 0, 10, 4, 4, 0, 0, 0, 6, 2, 0, 0, 2, }, +{b: 16, 0, 8, 0, 0, 2, 0, 2, 4, 2, 4, 0, 4, 0, 4, 2, }, +{d: 16, 2, 8, 0, 4, 0, 2, 0, 2, 4, 4, 0, 0, 2, 4, 0, }, +{e: 16, 0, 8, 0, 0, 0, 2, 2, 2, 2, 4, 0, 0, 4, 4, 4, }, +{f: 16, 0, 8, 0, 4, 2, 0, 0, 0, 4, 4, 2, 2, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:36, 4:58, 6:6, 8:30, 10:6, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{e: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 8, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:135, 4:90, 8:24, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:1, 8:3, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 8, -8, -8, 8, 0, 0, 0, 0, -8, -16, 8, -8, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 16, -8, -8, 16, -16, -16, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 8, 0, -8, 0, -8, -8, 0, -8, 8, }, +{3: 16, 0, -8, 0, 8, 8, -8, -8, 0, 0, 0, 0, 8, -16, -8, 8, }, +{5: 16, -16, 8, 0, 8, -8, 0, -8, -8, 0, 0, 8, 0, 0, -8, 8, }, +{6: 16, 0, -8, -8, 8, -8, 0, 8, 0, -8, -16, 0, 0, 0, 8, 8, }, +{9: 16, 0, 8, 0, -8, -8, -8, 8, 0, 0, 0, 0, 8, 0, -8, -8, }, +{a: 16, 0, -8, 8, -8, -8, 8, -16, 8, 0, 0, 0, 0, 0, 8, -8, }, +{c: 16, 0, 8, -8, -8, 8, 0, -8, 0, -8, 0, 0, 0, 0, 8, -8, }, +{7: 16, -16, -8, 0, 8, 8, 0, 8, -8, 0, 0, -8, 0, 0, 8, -8, }, +{b: 16, 0, -8, 0, -8, 8, -8, -8, 0, 0, 0, 0, -8, 0, 8, 8, }, +{d: 16, 0, 8, 0, -8, -8, 0, -8, -8, 0, 0, -8, 0, 0, 8, 8, }, +{e: 16, 0, -8, -8, -8, -8, 0, 8, 0, 8, 0, 0, 0, 0, -8, 8, }, +{f: 16, 0, -8, 0, -8, 8, 0, 8, -8, 0, 0, 8, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , x, , , , x, x, , , x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , , , , , x, , x, , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , , , x, , x, , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 15 */ +{0001,0010,0,}, +{0001,0101,1,}, +{0001,0111,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0110,1010,1,}, +{1000,1000,1,}, +{1100,0010,0,}, +{1100,0100,1,}, +{1100,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 7, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0d,}}, +{{0x05,0x02,0x08,}, {0x01,}}, +{{0x01,0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0d,}}, +{{0x09,0x02,0x0c,}, {0x01,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x0d,}}, +{{0x03,0x0c,}, {0x0d,}}, +{{0x09,0x0c,}, {0x01,}}, +{{0x0b,0x0c,}, {0x01,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x06,0x07,}}, +{{0x09,0x0a,}, {0x06,0x0b,0x0d,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,}}, +{{0x01,0x0e,}, {0x0d,}}, +{{0x05,0x0e,}, {0x01,}}, +{{0x09,0x0e,}, {0x01,}}, +{{0x0d,0x0e,}, {0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +244 Inverse Sbox: +LUT = { +0x01,0x06,0x03,0x04,0x08,0x05,0x02,0x07,0x00,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, 0, 4, 0, 2, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 6, 0, 4, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, }, +{8: 0, 2, 0, 2, 4, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 4, }, +{3: 0, 0, 0, 0, 0, 6, 4, 0, 0, 0, 0, 2, 2, 0, 0, 2, }, +{5: 0, 0, 0, 4, 0, 0, 6, 2, 0, 0, 0, 0, 0, 2, 2, 0, }, +{6: 0, 4, 0, 0, 0, 2, 0, 6, 0, 0, 0, 0, 2, 0, 2, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 0, 0, 2, 4, 2, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 2, 2, 4, 0, 0, 2, }, +{d: 0, 2, 0, 0, 0, 0, 2, 0, 2, 4, 4, 0, 0, 2, 0, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 2, 0, 4, 2, }, +}; +Diff: 12, DDT_spectrum: {0:179, 2:42, 4:27, 6:6, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:9, 2:3, 4:1, 6:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 6, 8, 4, 0, 4, 10, 4, 2, 0, 0, 8, 0, 2, 0, 0, }, +{2: 16, 8, 16, 8, 16, 8, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, }, +{4: 16, 10, 8, 6, 0, 8, 4, 4, 2, 0, 2, 4, 0, 0, 0, 0, }, +{8: 16, 2, 8, 2, 4, 0, 0, 0, 2, 4, 2, 0, 0, 4, 0, 4, }, +{3: 16, 4, 8, 4, 0, 6, 8, 4, 0, 0, 0, 10, 2, 0, 0, 2, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 0, 0, 0, 4, 0, 2, 2, 0, }, +{6: 16, 8, 8, 4, 0, 10, 4, 6, 0, 0, 0, 4, 2, 0, 2, 0, }, +{9: 16, 0, 8, 0, 4, 0, 2, 2, 4, 4, 0, 0, 4, 2, 2, 0, }, +{a: 16, 0, 8, 0, 4, 2, 0, 2, 0, 4, 0, 0, 2, 4, 2, 4, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 4, 8, 10, 0, 4, 4, 8, 0, 0, 2, 6, 0, 0, 0, 2, }, +{b: 16, 0, 8, 2, 4, 0, 0, 0, 4, 4, 2, 2, 4, 0, 0, 2, }, +{d: 16, 2, 8, 0, 4, 0, 2, 0, 2, 4, 4, 0, 0, 2, 4, 0, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 8, 0, 4, 2, 0, 0, 0, 4, 4, 2, 2, 0, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:36, 4:58, 6:6, 8:30, 10:6, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 8, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 4, 0, 8, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{6: 0, 0, 4, 0, 4, 4, 0, 12, 4, 0, 4, 4, 0, 4, 0, 0, }, +{9: 0, 8, 0, 8, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{7: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 0, 4, 0, 8, }, +{b: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:135, 4:90, 8:24, 12:6, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:1, 8:3, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 8, -8, 0, 8, -8, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 16, -16, 16, 8, -16, 16, -16, 8, -8, 8, -16, -8, 8, -8, -8, }, +{4: 16, 0, 8, 0, 8, 8, -16, -8, 0, 0, 0, -8, 8, -8, -8, 0, }, +{8: 16, 0, 8, 0, -8, 8, 0, 8, 0, 0, 0, -8, -8, -8, -8, 0, }, +{3: 16, -16, -8, 0, 8, 8, 0, -8, -8, 0, 0, 8, 0, 0, -8, 8, }, +{5: 16, 0, 8, -16, 8, -8, 0, -8, 0, 8, -8, 8, 0, 0, -8, 0, }, +{6: 16, 0, -8, 0, 8, -8, -16, 8, 0, 0, 0, 8, -8, -8, 8, 0, }, +{9: 16, 0, 8, 0, -8, -8, 0, 8, 0, -8, -8, 8, 0, 0, -8, 0, }, +{a: 16, 0, -8, 0, -8, -8, 0, -8, 0, 0, 0, 8, 8, -8, 8, 0, }, +{c: 16, 0, 8, 0, -16, 8, 0, -8, 0, -8, 0, 8, -8, 0, 8, -8, }, +{7: 16, 0, -8, -16, 8, 8, 0, 8, 0, -8, -8, -8, 0, 0, 8, 0, }, +{b: 16, 0, -8, 0, -8, 8, 0, -8, 0, 8, -8, -8, 0, 0, 8, 0, }, +{d: 16, 0, 8, 0, -8, -8, 0, -8, -8, 0, 0, -8, 0, 0, 8, 8, }, +{e: 16, 0, -8, 0, -8, -8, 0, 8, 8, 0, 8, -8, 0, 8, -16, 0, }, +{f: 16, 0, -8, 0, -8, 8, 0, 8, -8, 0, 0, 8, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, , , x, x, x, , x, }, +{2: , , x, , x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , x, x, , x, , , , x, x, , , x, }, +{5: , , x, , x, , x, x, , , , x, , x, , x, }, +{6: , , , , x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , x, x, , , , x, x, , x, }, +{a: , , , , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , x, , , , , , , x, , , , x, }, +{b: , , , , x, , , x, , , , , x, , , x, }, +{d: , , x, , , , , x, , , , , , x, , x, }, +{e: , , , , , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 15 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0010,0,}, +{0100,0101,1,}, +{0100,0111,1,}, +{0101,0010,0,}, +{0101,0100,1,}, +{0101,0110,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1000,1100,1,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 7, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x05,}}, +{{0x01,0x02,0x08,}, {0x01,}}, +{{0x05,0x02,0x08,}, {0x04,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,0x04,}, {0x05,}}, +{{0x01,0x02,0x0c,}, {0x01,}}, +{{0x09,0x02,0x0c,}, {0x04,}}, +{{0x04,0x08,}, {0x05,0x08,0x0d,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x06,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0a,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x05,}}, +{{0x0b,0x04,}, {0x05,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,}}, +{{0x03,0x08,}, {0x01,}}, +{{0x05,0x08,}, {0x04,}}, +{{0x07,0x08,}, {0x04,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,}}, +{{0x09,0x06,}, {0x05,}}, +{{0x0d,0x06,}, {0x05,}}, +{{0x01,0x0a,}, {0x01,}}, +{{0x05,0x0a,}, {0x04,}}, +{{0x09,0x0a,}, {0x01,}}, +{{0x0d,0x0a,}, {0x04,}}, +{{0x01,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_245.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_245.txt new file mode 100644 index 0000000..ff18a4d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_245.txt @@ -0,0 +1,466 @@ +245 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0e,0x08,0x0a,0x09,0x0c,0x0d,0x0b,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{4: 0, 2, 2, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 0, 4, 0, 0, 2, 2, 2, 0, }, +{3: 0, 2, 2, 0, 0, 4, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 4, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 2, 0, 2, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 0, }, +{7: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 6, 2, 0, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 6, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 6, 0, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:170, 2:57, 4:21, 6:7, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:5, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 0, 2, 0, 2, 0, 4, 0, 2, 8, 0, 0, 4, }, +{2: 16, 2, 4, 4, 8, 2, 2, 0, 0, 4, 4, 2, 0, 0, 0, 0, }, +{4: 16, 2, 2, 2, 4, 0, 4, 4, 0, 0, 0, 2, 4, 8, 0, 0, }, +{8: 16, 0, 4, 0, 6, 0, 4, 0, 0, 8, 0, 8, 2, 10, 2, 4, }, +{3: 16, 2, 2, 0, 0, 4, 2, 2, 4, 8, 0, 4, 0, 4, 0, 0, }, +{5: 16, 2, 4, 2, 0, 2, 4, 2, 8, 0, 4, 0, 4, 0, 0, 0, }, +{6: 16, 0, 2, 2, 4, 2, 2, 4, 4, 0, 0, 4, 0, 0, 0, 8, }, +{9: 16, 0, 0, 0, 2, 8, 4, 4, 6, 4, 8, 0, 0, 0, 2, 10, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 8, 6, 0, 0, 10, 0, 2, 2, }, +{c: 16, 4, 0, 4, 10, 0, 8, 0, 4, 2, 6, 0, 0, 8, 2, 0, }, +{7: 16, 4, 0, 2, 0, 4, 2, 2, 0, 0, 8, 2, 0, 4, 0, 4, }, +{b: 16, 8, 0, 0, 0, 0, 0, 4, 2, 10, 4, 4, 8, 6, 2, 0, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 0, 8, 8, 4, 0, 0, 0, 0, 10, 4, 4, 2, 2, 6, }, +{f: 16, 0, 4, 4, 0, 0, 0, 8, 10, 0, 2, 0, 6, 4, 2, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:91, 2:50, 4:49, 6:7, 8:21, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 8, 0, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 8, }, +{d: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:114, 4:112, 8:28, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:4, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 0, 0, 0, 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{4: 16, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +{8: 16, 8, 0, 8, -16, 0, 8, 0, -8, 0, -8, 8, 0, -8, 0, -8, }, +{3: 16, -8, -8, 0, 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{6: 16, 0, -8, -8, 16, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, -16, 0, -8, 8, 0, -8, 0, -8, 0, 8, -8, 8, }, +{a: 16, 0, -8, 8, -16, -8, 0, 0, 0, 8, -8, -8, 8, 0, 0, 8, }, +{c: 16, 8, 8, -8, -16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{b: 16, -8, 0, 0, -16, -8, 0, -8, 8, 0, 0, 8, 8, 0, 8, -8, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -8, -16, 8, 8, 8, 0, 0, 8, 0, -8, -8, -8, 0, }, +{f: 16, -8, -8, 0, -16, 8, -8, 0, 8, 8, 0, 0, -8, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, x, , x, x, , , x, x, }, +{5: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{6: , x, x, , , x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, , x, , x, x, x, x, , , x, x, x, }, +{a: , x, x, , , x, , x, x, x, x, , x, , x, x, }, +{c: , , x, x, , x, , x, x, x, x, , x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, x, , x, , , , x, x, }, +{d: , , , x, , , , x, x, x, x, , , x, x, x, }, +{e: , , x, , , x, , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 15 */ +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 0, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x06,0x08,}, {0x05,0x08,0x0d,}}, +{{0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x03,0x08,0x0b,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x01,0x08,0x09,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +245 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x09,0x0b,0x0a,0x0e,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 4, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 0, }, +{3: 0, 2, 2, 0, 0, 4, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 0, 2, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, 0, 2, 2, 0, 2, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 2, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 2, 2, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 6, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 6, 2, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, 4, }, +}; +Diff: 6, DDT_spectrum: {0:170, 2:57, 4:21, 6:7, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:6, 2:5, 4:4, 6:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 2, 0, 2, 2, 0, 0, 4, 4, 4, 8, 0, 0, 0, }, +{2: 16, 2, 4, 2, 4, 2, 4, 2, 0, 8, 0, 0, 0, 0, 0, 4, }, +{4: 16, 4, 4, 2, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 8, 4, }, +{8: 16, 0, 8, 4, 6, 0, 0, 4, 2, 4, 10, 0, 0, 2, 8, 0, }, +{3: 16, 2, 2, 0, 0, 4, 2, 2, 8, 4, 0, 4, 0, 0, 4, 0, }, +{5: 16, 0, 2, 4, 4, 2, 4, 2, 4, 0, 8, 2, 0, 0, 0, 0, }, +{6: 16, 2, 0, 4, 0, 2, 2, 4, 4, 0, 0, 2, 4, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, 4, 8, 4, 6, 8, 4, 0, 2, 2, 0, 10, }, +{a: 16, 4, 4, 0, 8, 8, 0, 0, 4, 6, 2, 0, 10, 2, 0, 0, }, +{c: 16, 0, 4, 0, 0, 0, 4, 0, 8, 0, 6, 8, 4, 2, 10, 2, }, +{7: 16, 2, 2, 2, 8, 4, 0, 4, 0, 0, 0, 2, 4, 0, 4, 0, }, +{b: 16, 8, 0, 4, 2, 0, 4, 0, 0, 10, 0, 0, 8, 2, 4, 6, }, +{d: 16, 0, 0, 8, 10, 4, 0, 0, 0, 0, 8, 4, 6, 2, 2, 4, }, +{e: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 16, 4, 0, 0, 4, 0, 0, 8, 10, 2, 0, 4, 0, 2, 6, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:91, 2:50, 4:49, 6:7, 8:21, 10:7, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:114, 4:112, 8:28, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:4, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, }, +{2: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{4: 16, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{8: 16, 8, 8, 0, -16, 0, 0, 8, -8, -8, 0, 8, 0, 0, -8, -8, }, +{3: 16, -8, -8, 0, 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, -8, 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -16, -8, 0, 0, 8, 0, -8, -8, 8, 0, 0, 8, }, +{a: 16, 8, 0, 8, -16, 0, 8, -8, -8, 0, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, -16, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, 8, }, +{7: 16, 0, -8, 0, 16, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{b: 16, -8, -8, 0, -16, 8, 8, 0, 8, 8, 0, 0, -8, -8, 0, 0, }, +{d: 16, 0, 0, 0, -16, 8, -8, -8, 0, 0, 0, 8, -8, 8, 8, -8, }, +{e: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, -8, -16, -8, 0, 8, 0, 8, 8, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, x, , , , x, x, x, x, x, , , , x, }, +{9: , x, x, x, , x, , x, x, x, x, , x, x, x, x, }, +{a: , , x, x, , , , x, x, x, x, , x, , x, x, }, +{c: , x, , x, , x, , x, x, x, x, , x, x, , x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, , , , , x, , x, x, , x, , x, x, }, +{d: , x, , x, , x, , , x, x, , , x, x, , x, }, +{e: , , , x, , , , x, x, x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 15 */ +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 0, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_246.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_246.txt new file mode 100644 index 0000000..11d7100 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_246.txt @@ -0,0 +1,478 @@ +246 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0d,0x09,0x08,0x0b,0x0c,0x0a,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 2, 2, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, 4, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 2, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 0, 2, 4, }, +{7: 0, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:174, 2:51, 4:21, 6:9, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 4, 2, 0, 2, 8, 0, 0, 2, 0, 4, 0, 0, }, +{2: 16, 0, 10, 2, 0, 2, 10, 0, 8, 0, 8, 8, 8, 0, 8, 0, }, +{4: 16, 2, 0, 4, 4, 2, 2, 4, 0, 4, 8, 2, 0, 0, 0, 0, }, +{8: 16, 8, 0, 8, 10, 0, 8, 0, 10, 0, 8, 0, 0, 8, 2, 2, }, +{3: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{5: 16, 2, 10, 0, 4, 0, 10, 2, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 16, 2, 2, 2, 0, 4, 0, 4, 0, 4, 8, 2, 0, 0, 0, 4, }, +{9: 16, 4, 4, 4, 6, 4, 0, 0, 10, 6, 0, 0, 6, 4, 0, 0, }, +{a: 16, 0, 0, 0, 0, 8, 8, 8, 8, 10, 10, 0, 2, 2, 0, 8, }, +{c: 16, 0, 4, 4, 6, 4, 0, 4, 0, 6, 10, 0, 0, 0, 6, 4, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 4, 0, 0, 0, 8, 0, 2, 0, 4, 2, 2, 2, }, +{d: 16, 0, 0, 0, 6, 0, 8, 0, 0, 0, 2, 0, 6, 4, 4, 2, }, +{e: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{f: 16, 0, 0, 0, 0, 0, 8, 0, 2, 6, 0, 0, 4, 2, 6, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:40, 4:42, 6:10, 8:27, 10:10, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +{2: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:4, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{4: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 8, 8, -16, 0, 0, 16, 0, -8, -8, 0, 0, 0, -16, 0, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, -8, 8, 0, -8, 0, -8, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 16, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, -16, -8, 0, 0, 8, -8, -8, 0, 8, 0, 0, 0, }, +{a: 16, 8, 0, 0, -16, 0, 0, -16, -8, 0, 0, -8, 0, 0, 16, 8, }, +{c: 16, 8, 0, -8, -16, 8, 0, 0, -8, 0, 8, -8, -8, 0, 0, 8, }, +{7: 16, 0, -8, 0, 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, -16, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, -8, -8, 0, -16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, , , , x, , , x, , x, , x, , x, }, +{6: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{9: , x, , , , , x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, , , x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , , x, , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, x, x, , x, x, , x, }, +{d: , x, , , , , , , , x, , , , x, , x, }, +{e: , , x, x, , , x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x04,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x01,0x08,0x09,}}, +{{0x0d,0x06,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +246 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x0a,0x09,0x0d,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 2, 0, 4, 2, 0, 0, }, +{3: 0, 2, 2, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 0, 0, 4, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 2, 2, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 4, }, +}; +Diff: 6, DDT_spectrum: {0:174, 2:51, 4:21, 6:9, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:3, 4:3, 6:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 8, 4, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{2: 16, 2, 10, 0, 0, 0, 10, 2, 4, 0, 4, 8, 4, 0, 4, 0, }, +{4: 16, 4, 2, 4, 8, 2, 0, 2, 4, 0, 4, 2, 0, 0, 0, 0, }, +{8: 16, 4, 0, 4, 10, 4, 4, 0, 6, 0, 6, 0, 4, 6, 0, 0, }, +{3: 16, 2, 2, 2, 0, 4, 0, 4, 4, 8, 4, 2, 0, 0, 0, 0, }, +{5: 16, 0, 10, 2, 8, 2, 10, 0, 0, 8, 0, 8, 0, 8, 0, 8, }, +{6: 16, 2, 0, 4, 0, 2, 2, 4, 0, 8, 4, 2, 0, 0, 4, 0, }, +{9: 16, 8, 8, 0, 10, 8, 0, 0, 10, 8, 0, 0, 8, 0, 2, 2, }, +{a: 16, 0, 0, 4, 0, 4, 4, 4, 6, 10, 6, 0, 0, 0, 4, 6, }, +{c: 16, 0, 8, 8, 8, 0, 0, 8, 0, 10, 10, 0, 2, 2, 8, 0, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, 0, 0, 0, 0, 6, 2, 0, 0, 4, 6, 2, 4, }, +{d: 16, 4, 0, 0, 8, 0, 4, 0, 4, 2, 0, 0, 2, 4, 2, 2, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 4, 6, }, +{f: 16, 0, 0, 0, 2, 0, 4, 4, 0, 8, 4, 0, 2, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:96, 2:40, 4:42, 6:10, 8:27, 10:10, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 0, }, +{2: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:4, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, -8, 0, 16, -8, 8, 0, 0, -8, 0, -8, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 8, 8, -16, 8, 0, 0, 0, -8, -8, 8, -8, 0, 0, -8, }, +{3: 16, 0, -8, 0, 16, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{6: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 8, 8, -16, 0, 0, 16, 0, -8, -8, 0, 0, 0, -16, 0, }, +{a: 16, 8, -8, 0, -16, -8, 0, 0, -8, 8, 0, -8, 8, 0, 0, 8, }, +{c: 16, 8, 0, 0, -16, 0, 0, -16, -8, 0, 0, -8, 0, 0, 16, 8, }, +{7: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{b: 16, -8, -8, 0, -16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +{d: 16, -8, 0, 0, -16, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, }, +{f: 16, 0, 0, -8, -16, 8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, , , x, , x, x, x, x, , , , x, }, +{6: , x, x, x, , , x, x, x, , x, x, , x, x, x, }, +{9: , x, , , , , x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, , , x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , , x, , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , x, , , , , x, , x, x, x, , , , , x, }, +{e: , , x, x, , , x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1110,0101,1,}, +{1110,1001,1,}, +{1110,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x08,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_247.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_247.txt new file mode 100644 index 0000000..f13f2db --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_247.txt @@ -0,0 +1,466 @@ +247 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0a,0x0c,0x08,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 2, 2, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 4, 2, 0, 2, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 2, 2, }, +{7: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 4, 4, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 0, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:172, 2:50, 4:30, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 2, 4, 4, 2, 0, 2, 8, 0, 0, 2, 0, 4, 0, 0, }, +{2: 16, 0, 10, 2, 4, 2, 10, 0, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 16, 2, 0, 4, 4, 2, 2, 4, 0, 4, 8, 2, 0, 0, 0, 0, }, +{8: 16, 4, 4, 4, 8, 4, 4, 4, 6, 4, 6, 0, 6, 4, 6, 0, }, +{3: 16, 4, 0, 2, 4, 4, 2, 2, 0, 4, 0, 2, 8, 0, 0, 0, }, +{5: 16, 2, 10, 0, 4, 0, 10, 2, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 16, 2, 2, 2, 4, 4, 0, 4, 0, 0, 0, 2, 0, 4, 8, 0, }, +{9: 16, 8, 0, 0, 6, 0, 0, 0, 4, 4, 2, 0, 6, 0, 0, 2, }, +{a: 16, 4, 4, 0, 4, 0, 4, 4, 0, 16, 4, 0, 4, 0, 0, 4, }, +{c: 16, 0, 0, 8, 6, 0, 0, 0, 6, 0, 4, 0, 0, 4, 2, 2, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 6, 8, 0, 0, 2, 0, 0, 0, 4, 4, 6, 2, }, +{d: 16, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 0, 16, 4, 4, }, +{e: 16, 0, 0, 0, 6, 0, 0, 8, 0, 4, 6, 0, 2, 0, 4, 2, }, +{f: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:36, 4:60, 6:12, 8:15, 10:4, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 8, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:114, 4:112, 8:28, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{2: 16, 0, -8, 0, 16, 0, 8, -8, 0, -8, 0, -8, 0, 8, -8, -8, }, +{4: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 8, 8, 8, -16, 8, 0, 8, -8, -8, -8, 8, -8, 0, -8, -8, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, -8, 8, 0, -8, 0, -8, 0, -8, 8, 0, 0, }, +{6: 16, 0, -8, 0, 16, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, -8, -8, 0, 8, 8, }, +{c: 16, 0, 8, -8, -16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{b: 16, -8, 0, 0, -16, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, }, +{d: 16, -8, 0, -8, -16, -8, 0, 8, 8, 0, 8, 0, 8, 0, -8, 0, }, +{e: 16, 8, -8, 0, -16, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , x, , x, x, x, , , x, }, +{5: , x, x, , , , x, , , x, , x, , x, , x, }, +{6: , x, , x, , , , x, x, , x, x, , , x, x, }, +{9: , x, x, , , , , , x, x, x, , x, x, , x, }, +{a: , x, x, x, , , , , x, x, x, , x, , x, x, }, +{c: , x, , x, , , , , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , , , , x, , x, , x, , , x, }, +{d: , x, , , , , , , , x, , , , x, , x, }, +{e: , , , x, , , , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 15 */ +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +247 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x0a,0x0c,0x08,0x0b,0x09,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 2, 2, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 4, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 4, 0, 0, 0, 2, 2, }, +{7: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 4, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +}; +Diff: 8, DDT_spectrum: {0:172, 2:50, 4:30, 6:2, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{2: 16, 2, 10, 0, 4, 0, 10, 2, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 16, 4, 2, 4, 4, 2, 0, 2, 0, 0, 8, 2, 0, 4, 0, 0, }, +{8: 16, 4, 4, 4, 8, 4, 4, 4, 6, 4, 6, 0, 6, 4, 6, 0, }, +{3: 16, 2, 2, 2, 4, 4, 0, 4, 0, 0, 0, 2, 8, 4, 0, 0, }, +{5: 16, 0, 10, 2, 4, 2, 10, 0, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 16, 2, 0, 4, 4, 2, 2, 4, 0, 4, 0, 2, 0, 0, 8, 0, }, +{9: 16, 8, 0, 0, 6, 0, 0, 0, 4, 0, 6, 0, 2, 4, 0, 2, }, +{a: 16, 0, 4, 4, 4, 4, 4, 0, 4, 16, 0, 0, 0, 0, 4, 4, }, +{c: 16, 0, 0, 8, 6, 0, 0, 0, 2, 4, 4, 0, 0, 0, 6, 2, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 6, 8, 0, 0, 6, 4, 0, 0, 4, 0, 2, 2, }, +{d: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 16, 0, 4, }, +{e: 16, 0, 0, 0, 6, 0, 0, 8, 0, 0, 2, 0, 6, 4, 4, 2, }, +{f: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:36, 4:60, 6:12, 8:15, 10:4, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 8, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:114, 4:112, 8:28, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, -8, 0, 16, -8, 8, 0, 0, -8, 0, -8, -8, 8, 0, -8, }, +{4: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 8, 8, 8, -16, 8, 0, 8, -8, -8, -8, 8, -8, 0, -8, -8, }, +{3: 16, 0, -8, 0, 16, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, 0, 8, -8, -8, 0, -8, 0, 0, 8, -8, 0, }, +{6: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 0, -16, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +{c: 16, 8, 0, 0, -16, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, }, +{7: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{b: 16, 0, -8, 8, -16, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, -8, 0, -8, -16, 8, 0, -8, 8, 0, 8, 0, -8, 0, 8, 0, }, +{e: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, }, +{f: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , , x, , x, x, x, , , x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , x, x, x, , , , x, x, , x, x, , , x, x, }, +{9: , x, , x, , , , , x, x, x, , x, x, , x, }, +{a: , x, x, x, , , , , x, x, x, , x, , x, x, }, +{c: , , x, x, , , , , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , , , x, , x, , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , x, x, , , , , x, , x, , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 15 */ +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 1, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,0x08,0x0a,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_248.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_248.txt new file mode 100644 index 0000000..70cbf0f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_248.txt @@ -0,0 +1,478 @@ +248 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x08,0x0b,0x06,0x07,0x04,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, }, +{3: 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 2, 4, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 4, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 4, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 0, 8, 10, 0, 0, 8, 8, 0, 0, 8, 2, 0, 2, }, +{2: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 8, 16, 8, }, +{4: 16, 0, 0, 4, 6, 8, 2, 0, 0, 2, 0, 6, 4, 0, 0, 0, }, +{8: 16, 8, 0, 2, 4, 0, 0, 6, 6, 0, 0, 4, 2, 0, 0, 0, }, +{3: 16, 10, 8, 8, 0, 10, 8, 8, 0, 0, 0, 8, 0, 2, 0, 2, }, +{5: 16, 0, 0, 2, 4, 8, 4, 6, 2, 0, 0, 0, 6, 0, 0, 0, }, +{6: 16, 0, 0, 0, 2, 8, 6, 4, 4, 6, 0, 2, 0, 0, 0, 0, }, +{9: 16, 8, 0, 4, 6, 0, 6, 0, 4, 2, 0, 2, 0, 0, 0, 0, }, +{a: 16, 8, 0, 6, 0, 0, 4, 2, 2, 4, 0, 0, 6, 0, 0, 0, }, +{c: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 16, 0, 0, 6, 0, 8, 0, 2, 6, 4, 0, 4, 2, 0, 0, 0, }, +{b: 16, 8, 0, 0, 2, 0, 2, 4, 0, 6, 0, 6, 4, 0, 0, 0, }, +{d: 16, 2, 8, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 8, 2, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 2, 8, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:120, 2:28, 4:16, 6:16, 8:36, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{5: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +{f: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:4, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 16, -8, -8, 16, -8, -8, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 0, 0, 0, 8, 0, 8, 0, -8, -16, 0, 0, 0, 0, -8, }, +{3: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, 8, -8, 0, -8, 0, }, +{6: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -16, 0, 0, 0, 0, 8, }, +{9: 16, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, -8, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{c: 16, 0, 0, -8, -8, 0, 8, -8, 8, -8, 16, -8, -8, 0, 0, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, -8, 8, 0, 8, 0, }, +{b: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, 8, -8, 0, 8, 0, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, -8, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, -8, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, , , x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , , x, x, x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, , , x, x, , x, x, , x, x, , , x, }, +{b: , , x, , , x, x, , x, x, , , , , , x, }, +{d: , , , x, x, , x, , x, x, , , x, x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 3, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +248 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x08,0x0b,0x06,0x07,0x04,0x09,0x0a,0x05,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 4, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{3: 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 0, 2, 0, 2, 4, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 4, 2, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 4, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 0, 8, 10, 0, 0, 8, 8, 0, 0, 8, 2, 0, 2, }, +{2: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 8, 16, 8, }, +{4: 16, 0, 0, 4, 2, 8, 2, 0, 4, 6, 0, 6, 0, 0, 0, 0, }, +{8: 16, 8, 0, 6, 4, 0, 4, 2, 6, 0, 0, 0, 2, 0, 0, 0, }, +{3: 16, 10, 8, 8, 0, 10, 8, 8, 0, 0, 0, 8, 0, 2, 0, 2, }, +{5: 16, 0, 0, 2, 0, 8, 4, 6, 6, 4, 0, 0, 2, 0, 0, 0, }, +{6: 16, 0, 0, 0, 6, 8, 6, 4, 0, 2, 0, 2, 4, 0, 0, 0, }, +{9: 16, 8, 0, 0, 6, 0, 2, 4, 4, 2, 0, 6, 0, 0, 0, 0, }, +{a: 16, 8, 0, 2, 0, 0, 0, 6, 2, 4, 0, 4, 6, 0, 0, 0, }, +{c: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 16, 0, 0, 6, 4, 8, 0, 2, 2, 0, 0, 4, 6, 0, 0, 0, }, +{b: 16, 8, 0, 4, 2, 0, 6, 0, 0, 6, 0, 2, 4, 0, 0, 0, }, +{d: 16, 2, 8, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 8, 2, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 2, 8, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:120, 2:28, 4:16, 6:16, 8:36, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{4: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 4, 8, 8, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 0, 0, 8, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 8, 0, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 8, LAT1_spectrum: {0:6, 4:4, 8:6, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 16, -8, 0, 0, -8, 0, -8, 0, -8, 16, -8, -8, 16, -8, -8, }, +{4: 16, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, -8, 8, 0, -8, 0, }, +{8: 16, 0, 8, 0, 0, 0, 0, 0, 0, 0, -16, 8, -8, 0, -8, 0, }, +{3: 16, -16, 0, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, 8, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -16, 0, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, 0, 0, -16, -8, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -8, 0, 8, -8, 8, -8, 16, -8, -8, 0, 0, 0, }, +{7: 16, 0, 0, 0, 0, 8, 0, 8, 0, -8, -16, 0, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, 0, -8, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, 0, -8, -8, }, +{f: 16, 0, 0, -8, -8, 0, -8, 0, -8, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , , x, , , x, x, , x, x, , x, x, , , x, }, +{5: , , x, x, x, x, x, , x, x, , x, x, x, , x, }, +{6: , , x, x, x, x, x, x, x, x, , x, x, , x, x, }, +{9: , , x, x, x, x, x, , x, x, , , x, x, , x, }, +{a: , , x, x, x, x, x, , x, x, , , , , x, x, }, +{c: , x, , x, x, x, x, , x, x, x, , x, x, x, x, }, +{7: , , x, , , x, x, , x, x, , x, x, , , x, }, +{b: , , x, , , x, x, , x, x, , , , , , x, }, +{d: , , , x, x, x, x, , x, x, , , x, x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 3, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x06,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_249.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_249.txt new file mode 100644 index 0000000..122b68a --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_249.txt @@ -0,0 +1,478 @@ +249 Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x05,0x0a,0x07,0x03,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, }, +{8: 0, 0, 4, 2, 4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{3: 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, }, +{9: 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 4, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 6, 4, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:2, 4:4, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 0, 4, 8, 2, 2, 2, 4, 0, 0, 0, 0, 4, 0, 2, 4, }, +{8: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{3: 16, 4, 4, 2, 2, 8, 2, 0, 2, 0, 4, 0, 0, 0, 0, 4, }, +{5: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 4, 4, 0, 0, 0, 10, 4, 2, 0, 2, 10, 8, 0, 4, }, +{9: 16, 0, 4, 0, 2, 2, 2, 4, 8, 0, 0, 0, 4, 0, 2, 4, }, +{a: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{c: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{7: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 4, 0, 0, 0, 10, 4, 2, 0, 2, 10, 8, 0, 4, }, +{d: 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 16, 0, 0, }, +{e: 16, 4, 4, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 8, 4, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:40, 4:64, 8:20, 10:8, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, 16, -8, }, +{2: 16, 8, 0, 8, 8, -8, 16, -8, 0, -8, 0, 0, -16, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, -16, 0, }, +{8: 16, 8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, -8, }, +{3: 16, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, -16, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{6: 16, 0, -8, -8, 0, -8, 0, 0, 8, -8, -8, 8, 0, -8, 16, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, -16, 8, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 16, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, -8, 0, -8, 0, 0, -8, 8, 0, -8, 8, 0, 0, 16, -8, }, +{d: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -16, 0, 16, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 8, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , , x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, , x, , x, , x, , , , x, }, +{b: , , x, , x, , , x, , x, , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0101,0010,0,}, +{0101,1101,1,}, +{0101,1111,1,}, +{1011,0010,1,}, +{1011,1101,1,}, +{1011,1111,0,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0e,}}, +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x03,0x04,0x08,}, {0x0e,}}, +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x05,0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x05,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x01,0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x07,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +249 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x05,0x0a,0x07,0x03,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 4, }, +{8: 0, 0, 4, 2, 4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{3: 0, 0, 0, 2, 2, 4, 2, 0, 2, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 4, 2, 0, 2, 4, 0, 2, 0, 0, 0, 0, 0, 2, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, 2, 4, 0, 0, }, +{9: 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 4, }, +{a: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 6, 4, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, }, +{e: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:2, 4:4, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{2: 16, 4, 16, 4, 8, 4, 8, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{4: 16, 0, 4, 8, 2, 2, 2, 4, 0, 0, 0, 0, 4, 0, 2, 4, }, +{8: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{3: 16, 4, 4, 2, 2, 8, 2, 0, 2, 0, 4, 0, 0, 0, 0, 4, }, +{5: 16, 0, 8, 2, 4, 2, 4, 0, 2, 4, 0, 4, 0, 0, 2, 0, }, +{6: 16, 0, 4, 4, 0, 0, 0, 10, 4, 2, 0, 2, 10, 8, 0, 4, }, +{9: 16, 0, 4, 0, 2, 2, 2, 4, 8, 0, 0, 0, 4, 0, 2, 4, }, +{a: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{c: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{7: 16, 2, 8, 0, 4, 0, 4, 2, 0, 4, 2, 4, 2, 0, 0, 0, }, +{b: 16, 0, 4, 4, 0, 0, 0, 10, 4, 2, 0, 2, 10, 8, 0, 4, }, +{d: 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 16, 0, 0, }, +{e: 16, 4, 4, 2, 2, 0, 2, 0, 2, 0, 4, 0, 0, 0, 8, 4, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:40, 4:64, 8:20, 10:8, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 8, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{8: 0, 4, 4, 4, 8, 0, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{a: 0, 0, 4, 0, 4, 4, 0, 4, 4, 8, 4, 4, 8, 4, 0, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 8, LAT1_spectrum: {0:2, 4:10, 8:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 0, -8, 0, 0, -8, 0, 8, -8, 0, -8, 16, -8, }, +{2: 16, 8, 0, 8, 8, -8, 16, -8, 0, -8, 0, 0, -16, 8, -16, -8, }, +{4: 16, 0, 0, -8, 0, 8, 0, 0, 0, 8, 0, 0, 0, -8, -16, 0, }, +{8: 16, 8, 0, 8, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, -8, }, +{3: 16, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, -8, -16, 8, }, +{5: 16, 0, 0, 0, 8, -8, 0, -8, 0, 0, 0, 0, 0, 8, -16, 0, }, +{6: 16, 0, -8, -8, 0, -8, 0, 0, 8, -8, -8, 8, 0, -8, 16, 0, }, +{9: 16, -8, 0, 0, -8, 0, 0, 8, 0, 0, 0, 0, 0, 0, -16, 8, }, +{a: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 16, 0, }, +{7: 16, 0, -8, 0, 0, 0, 0, 0, -8, 0, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, -8, 0, -8, 0, 0, -8, 8, 0, -8, 8, 0, 0, 16, -8, }, +{d: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, -16, 0, 16, 0, }, +{e: 16, 0, 0, -8, -8, 0, 0, 8, 0, 8, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 16, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , x, , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , x, x, x, x, x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, , x, x, x, , , x, x, , x, }, +{a: , , x, , x, x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, x, , x, , x, , x, , x, , , , x, }, +{b: , , x, , x, , , x, , x, , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0101,0010,0,}, +{0101,1101,1,}, +{0101,1111,1,}, +{1011,0010,1,}, +{1011,1101,1,}, +{1011,1111,0,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0e,}}, +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x03,0x04,0x08,}, {0x0e,}}, +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x05,0x02,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x05,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x01,0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x01,0x04,0x05,0x0a,0x0b,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x0e,}}, +{{0x02,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x0e,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x0b,0x04,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x0e,}}, +{{0x03,0x08,}, {0x0e,}}, +{{0x05,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x07,0x08,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x02,}, {0x05,0x0b,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x0e,}}, +{{0x09,0x06,}, {0x05,0x0b,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x05,0x0e,}, {0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x05,0x0b,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_250.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_250.txt new file mode 100644 index 0000000..33b57b7 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_250.txt @@ -0,0 +1,478 @@ +250 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0e,0x09,0x08,0x0b,0x0c,0x0d,0x0a,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 6, 2, 2, 0, 0, 0, 0, 2, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 6, 2, 0, }, +{7: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 0, 4, 2, 2, 4, 8, 0, 2, 4, 0, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 4, 8, 0, 8, 4, 0, 0, 6, 10, 2, 0, 4, 0, 0, 2, }, +{3: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{5: 16, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 4, 8, 4, }, +{6: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 0, 16, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 10, 6, 2, 0, 8, 0, 0, 2, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 8, 0, 2, 6, 10, 4, }, +{7: 16, 4, 0, 2, 0, 4, 2, 2, 0, 0, 4, 2, 0, 8, 4, 0, }, +{b: 16, 16, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 4, 0, 2, 10, 6, 8, }, +{f: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:44, 6:4, 8:28, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{7: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 16, -16, 8, -8, 8, -8, 0, 0, -16, 8, -8, 0, }, +{4: 16, 0, 0, -8, 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, -8, }, +{8: 16, 0, 8, 8, -16, 0, 0, 8, 0, -8, -8, -8, 0, 0, -8, 8, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{6: 16, 8, -8, -8, 16, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, -8, }, +{9: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{a: 16, 0, -8, 8, -16, 0, 0, -8, 0, 8, -8, -8, 0, 0, 8, 8, }, +{c: 16, 0, 8, -8, -16, 0, 0, -8, 0, -8, 8, 8, 0, 0, 8, -8, }, +{7: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{b: 16, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -16, 0, 0, 8, 0, 8, 8, 8, 0, 0, -8, -8, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, , , x, x, x, , x, x, }, +{5: , , x, x, , x, x, x, , x, x, x, , x, x, x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, x, , x, x, x, x, }, +{a: , x, x, , , x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, , x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , x, , x, , x, x, }, +{d: , , , x, , x, , x, , x, x, , , x, x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0011,0010,1,}, +{0011,1001,1,}, +{0011,1011,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1011,1001,0,}, +{1011,1011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 3, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x03,0x08,0x0b,}}, +{{0x03,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +250 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0a,0x09,0x0e,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 4, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 4, 6, 0, 0, 0, 2, 0, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 4, 4, 4, 0, 0, 4, 4, 4, 16, 0, 4, 0, }, +{2: 16, 0, 16, 16, 8, 0, 0, 16, 0, 8, 8, 0, 0, 0, 8, 0, }, +{4: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 4, 0, 0, 0, 4, 2, 0, 4, 2, 2, 2, }, +{3: 16, 4, 0, 0, 4, 4, 4, 0, 16, 4, 4, 4, 0, 0, 4, 0, }, +{5: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 16, 4, 4, 0, 6, 8, 0, 0, 8, 10, 0, 0, 4, 2, 0, 2, }, +{a: 16, 8, 4, 0, 10, 4, 0, 0, 8, 6, 0, 0, 4, 2, 0, 2, }, +{c: 16, 0, 4, 0, 2, 0, 0, 0, 0, 2, 8, 4, 4, 2, 4, 2, }, +{7: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 4, 0, 0, 0, 0, 8, 2, 0, 4, 2, 2, 2, }, +{d: 16, 0, 4, 0, 0, 0, 4, 0, 8, 0, 6, 8, 4, 2, 10, 2, }, +{e: 16, 0, 4, 0, 0, 0, 8, 0, 8, 0, 10, 4, 4, 2, 6, 2, }, +{f: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:44, 6:4, 8:28, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{b: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{d: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{f: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -8, 0, 16, -8, 0, -8, 16, -8, 0, -8, -8, 0, -8, -8, }, +{4: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, -16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{3: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{6: 16, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 8, -16, 0, 8, 8, 0, -8, -8, 0, 0, -8, -8, 0, }, +{a: 16, 0, 0, 8, -16, -8, 8, 0, 0, 0, -8, -8, 8, -8, 0, 8, }, +{c: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, 0, -8, 0, -16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, -16, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, 8, }, +{e: 16, 0, 0, -8, -16, -8, -8, 8, 0, 0, 8, 0, 8, 8, -8, 0, }, +{f: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, x, x, , x, x, x, x, }, +{a: , , x, x, , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, , , , , x, , x, x, , x, , x, x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x01,0x08,0x09,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_251.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_251.txt new file mode 100644 index 0000000..d8adcca --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_251.txt @@ -0,0 +1,478 @@ +251 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0f,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0a, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 2, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 2, 2, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 0, 4, 0, 4, 4, 16, 4, 0, 4, 0, 4, 0, }, +{2: 16, 0, 16, 0, 0, 0, 16, 0, 8, 0, 8, 16, 8, 0, 8, 0, }, +{4: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 8, 8, 0, 0, 6, 4, 0, 0, 10, 2, 0, 2, }, +{3: 16, 4, 0, 4, 16, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 0, 4, 0, 0, 8, 4, 2, 0, 4, 2, 2, 2, }, +{a: 16, 4, 4, 0, 0, 0, 0, 0, 4, 4, 2, 0, 8, 2, 2, 2, }, +{c: 16, 0, 4, 4, 8, 0, 0, 8, 0, 4, 6, 0, 0, 2, 10, 2, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 4, 0, 8, 4, 0, 0, 10, 4, 0, 0, 6, 2, 0, 2, }, +{d: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{e: 16, 0, 4, 4, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 8, 2, }, +{f: 16, 0, 4, 8, 8, 0, 0, 4, 0, 4, 10, 0, 0, 2, 6, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:44, 6:4, 8:28, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{c: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:5, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{2: 16, 0, -8, 0, 16, -8, 16, -8, 0, -8, 0, -8, -8, 16, -8, -8, }, +{4: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{8: 16, -8, 8, 8, -16, 0, 0, 8, 8, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{5: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{6: 16, 0, -8, 0, 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{9: 16, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, }, +{a: 16, 0, -8, 0, -16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{c: 16, 8, 8, -8, -16, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, }, +{7: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -16, 8, 0, 0, 8, 0, -8, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{e: 16, 0, -8, 0, -16, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 8, 0, -8, -16, 0, 0, 8, -8, 0, 8, 8, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , , x, x, x, , x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, , x, , x, x, x, x, , x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, , x, , , x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, , , , x, x, x, , x, x, , x, x, x, }, +{d: , x, , x, , , x, x, x, x, x, x, x, , x, x, }, +{e: , x, , x, , , x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x05,0x08,0x0d,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +251 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0a,0x09,0x0f,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 4, 0, 2, }, +{7: 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 6, 2, 2, 0, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 4, 6, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 4, 2, 2, 0, 4, 0, 2, 8, 0, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 4, 0, 2, 0, 4, 2, 2, 0, 0, 4, 2, 0, 0, 4, 8, }, +{8: 16, 0, 0, 0, 8, 16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 8, }, +{3: 16, 4, 0, 2, 8, 4, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{5: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 4, 0, 2, 0, 4, 2, 2, 0, 0, 8, 2, 0, 4, 0, 4, }, +{9: 16, 4, 8, 0, 6, 4, 0, 0, 8, 4, 0, 0, 10, 2, 2, 0, }, +{a: 16, 16, 0, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 6, 0, 0, 8, 4, 10, }, +{7: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 0, 0, 6, 2, 2, 0, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 10, 0, 0, 4, 8, 6, }, +{f: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:100, 2:40, 4:44, 6:4, 8:28, 10:4, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:5, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 0, 16, -16, 8, -8, 8, -8, 0, 0, -16, 8, -8, 0, }, +{4: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, -8, }, +{6: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{9: 16, 0, 8, 8, -16, 0, 0, 8, 0, -8, -8, 8, 0, 0, -8, -8, }, +{a: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{c: 16, 0, 8, -8, -16, 0, 0, -8, 0, -8, 8, -8, 0, 0, 8, 8, }, +{7: 16, 8, -8, -8, 16, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, -8, 8, -16, 0, 0, -8, 0, 8, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, -8, -16, 0, 0, 8, 0, 8, 8, -8, 0, 0, -8, 8, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , , x, x, x, x, x, x, x, x, , x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , x, x, , , , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 3, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x03,0x08,0x0b,}}, +{{0x03,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_252.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_252.txt new file mode 100644 index 0000000..5b74066 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_252.txt @@ -0,0 +1,478 @@ +252 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0a,0x0f,0x09,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 4, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 2, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, 2, 0, 4, }, +{7: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 6, 0, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 6, 0, 0, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 2, 4, 0, 2, 2, 0, 8, 0, 2, 4, 0, 0, 0, }, +{2: 16, 0, 4, 4, 0, 4, 4, 0, 16, 4, 4, 0, 4, 4, 0, 0, }, +{4: 16, 0, 2, 2, 8, 2, 2, 4, 0, 0, 0, 4, 0, 0, 4, 4, }, +{8: 16, 0, 4, 4, 16, 4, 4, 8, 0, 4, 4, 8, 4, 4, 8, 8, }, +{3: 16, 4, 0, 2, 4, 4, 2, 2, 0, 4, 0, 2, 8, 0, 0, 0, }, +{5: 16, 4, 2, 0, 4, 2, 4, 2, 0, 0, 4, 2, 0, 8, 0, 0, }, +{6: 16, 0, 2, 2, 8, 2, 2, 4, 0, 0, 0, 4, 0, 0, 4, 4, }, +{9: 16, 4, 8, 0, 4, 4, 0, 0, 8, 6, 0, 0, 10, 0, 2, 2, }, +{a: 16, 16, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, }, +{c: 16, 0, 0, 0, 8, 0, 0, 4, 0, 2, 2, 4, 2, 2, 4, 4, }, +{7: 16, 4, 2, 4, 4, 2, 0, 2, 0, 0, 8, 2, 0, 4, 0, 0, }, +{b: 16, 4, 4, 0, 4, 8, 0, 0, 8, 10, 0, 0, 6, 0, 2, 2, }, +{d: 16, 4, 0, 4, 4, 0, 8, 0, 8, 0, 10, 0, 0, 6, 2, 2, }, +{e: 16, 0, 0, 0, 8, 0, 0, 4, 0, 2, 2, 4, 2, 2, 4, 4, }, +{f: 16, 4, 0, 8, 4, 0, 4, 0, 8, 0, 6, 0, 0, 10, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:40, 4:60, 6:4, 8:24, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 4, 4, 4, 0, 0, 8, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{6: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{a: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 0, 8, 8, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{d: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:4, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{2: 16, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{4: 16, 0, -8, -8, 16, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{8: 16, 8, 0, 0, -16, 8, 8, 16, -8, 0, 0, 8, -8, -8, -16, -8, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, 0, 16, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, }, +{6: 16, 0, -8, -8, 16, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, -8, 8, -16, -8, 0, 0, 0, 8, -8, -8, 8, 0, 0, 8, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, 0, -16, 8, 8, 0, 0, 0, 0, 0, -8, -8, 0, 0, }, +{7: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{b: 16, -8, -8, 8, -16, 0, -8, 0, 8, 8, -8, 0, 0, 8, 0, 0, }, +{d: 16, -8, 8, -8, -16, -8, 0, 0, 8, -8, 8, 0, 8, 0, 0, 0, }, +{e: 16, 8, 0, 0, -16, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, 8, -8, -16, 0, -8, 0, 0, -8, 8, -8, 0, 8, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, , , x, x, x, , x, x, }, +{6: , x, , , , , , x, x, , , x, , , x, x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, x, x, , x, x, x, , , x, x, x, , x, x, }, +{e: , , , , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x03,0x08,0x0b,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x06,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +252 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x0f,0x0a,0x08,0x0b,0x0c,0x0d,0x0e,0x09, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 4, 4, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{4: 0, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, }, +{3: 0, 0, 4, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 6, 4, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 2, 6, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 6, 0, 2, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:44, 4:30, 6:4, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 0, 4, 4, 0, 4, 16, 0, 4, 4, 4, 0, 4, }, +{2: 16, 4, 4, 2, 4, 0, 2, 2, 8, 0, 0, 2, 4, 0, 0, 0, }, +{4: 16, 2, 4, 2, 4, 2, 0, 2, 0, 0, 0, 4, 0, 4, 0, 8, }, +{8: 16, 4, 0, 8, 16, 4, 4, 8, 4, 0, 8, 4, 4, 4, 8, 4, }, +{3: 16, 0, 4, 2, 4, 4, 2, 2, 4, 0, 0, 2, 8, 0, 0, 0, }, +{5: 16, 2, 4, 2, 4, 2, 4, 2, 0, 0, 0, 0, 0, 8, 0, 4, }, +{6: 16, 2, 0, 4, 8, 2, 2, 4, 0, 0, 4, 2, 0, 0, 4, 0, }, +{9: 16, 0, 16, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{a: 16, 8, 4, 0, 4, 4, 0, 0, 6, 8, 2, 0, 10, 0, 2, 0, }, +{c: 16, 0, 4, 0, 4, 0, 4, 0, 0, 8, 2, 8, 0, 10, 2, 6, }, +{7: 16, 2, 0, 4, 8, 2, 2, 4, 0, 0, 4, 2, 0, 0, 4, 0, }, +{b: 16, 4, 4, 0, 4, 8, 0, 0, 10, 8, 2, 0, 6, 0, 2, 0, }, +{d: 16, 0, 4, 0, 4, 0, 8, 0, 0, 8, 2, 4, 0, 6, 2, 10, }, +{e: 16, 0, 0, 4, 8, 0, 0, 4, 2, 0, 4, 0, 2, 2, 4, 2, }, +{f: 16, 0, 0, 4, 8, 0, 0, 4, 2, 0, 4, 0, 2, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:40, 4:60, 6:4, 8:24, 10:4, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{a: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{c: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:4, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{4: 16, 0, -8, 0, 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{8: 16, 16, 8, 0, -16, 8, 0, 8, -16, -8, 0, 8, -8, 0, -8, -8, }, +{3: 16, 0, -8, 0, 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{5: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{6: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, -16, 0, 0, -16, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 8, -16, -8, -8, 0, 0, 0, -8, -8, 8, 8, 0, 8, }, +{c: 16, 0, -8, -8, -16, 0, 8, 0, 0, 8, 8, -8, 0, -8, 0, 8, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, 0, -8, 8, -16, 0, -8, -8, 0, 8, -8, 0, 0, 8, 8, 0, }, +{d: 16, 0, 0, -8, -16, -8, 8, -8, 0, 0, 8, 0, 8, -8, 8, 0, }, +{e: 16, 0, 0, 0, -16, 0, 0, 8, 0, 0, 0, 8, 0, 0, -8, -8, }, +{f: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , , x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , x, x, , x, x, x, , x, x, x, , x, x, x, }, +{5: , , x, x, , x, x, x, , , x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{9: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, , , x, x, x, , x, x, x, , x, x, x, }, +{d: , , x, , , x, x, x, , , x, x, x, , x, x, }, +{e: , , x, x, , x, x, x, x, , x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0001,0001,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,1000,1,}, +{1001,1001,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x01,0x08,0x09,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x01,0x08,0x09,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_253.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_253.txt new file mode 100644 index 0000000..26b5b4c --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_253.txt @@ -0,0 +1,502 @@ +253 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0c,0x09,0x08,0x0b,0x0a,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 2, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:3, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{3: 16, 4, 0, 2, 8, 4, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{5: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{6: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{9: 16, 4, 0, 0, 4, 4, 0, 0, 8, 4, 2, 0, 0, 2, 2, 2, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 16, 4, 0, 2, 8, 4, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{b: 16, 4, 0, 0, 8, 4, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +{d: 16, 4, 0, 0, 4, 4, 0, 0, 8, 4, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 4, 0, 0, 8, 4, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:64, 8:24, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{4: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:1, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, 0, 0, 16, -8, 8, -16, 8, 0, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, 16, 16, -16, 0, 0, 16, 0, -16, -16, 0, 0, 0, -16, 0, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{6: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{9: 16, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{b: 16, 0, 0, 0, -16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{d: 16, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, }, +{e: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, , , x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , x, x, x, x, , , x, }, +{5: , , x, , , x, x, , , x, , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, , , , x, , , x, x, x, , x, x, , x, }, +{a: , x, , , , x, , , , x, x, , x, , x, x, }, +{c: , x, , , , x, , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, , , , x, x, , x, , , x, }, +{d: , , , , , x, , , , x, , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0010,0110,1,}, +{0010,1000,0,}, +{0010,1110,1,}, +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1010,1000,1,}, +{1010,1110,0,}, +{1100,0100,1,}, +{1100,1000,1,}, +{1100,1100,0,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +253 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0a,0x09,0x0c,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:3, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 16, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 0, 16, 16, 16, 0, 0, 16, 0, 16, 16, 0, 0, 0, 16, 0, }, +{4: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 16, 8, 4, 4, 4, 4, 0, 8, 8, 4, 4, 8, }, +{3: 16, 4, 0, 0, 16, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 16, 8, 4, 0, 16, 4, 8, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{a: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{c: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{7: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{e: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{f: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:64, 8:24, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:1, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -16, 0, 16, -16, 0, 0, 16, -16, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 0, 0, 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{8: 16, 0, 0, 8, -16, 16, 8, 8, 0, 0, -8, 8, -16, -8, -8, -8, }, +{3: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{6: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 16, 8, -16, 0, 8, 8, 0, -16, -8, 8, 0, -8, -8, -8, }, +{a: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{e: 16, 0, 0, -8, -16, 0, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{f: 16, 0, 0, -8, -16, 0, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , x, x, x, , , x, }, +{5: , , x, x, , , x, , , x, x, x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , , , , , , , x, x, x, , x, x, , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , , , , , , , x, x, , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,1001,0,}, +{0010,1011,1,}, +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,1001,1,}, +{1010,1011,0,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_254.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_254.txt new file mode 100644 index 0000000..5de764d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_254.txt @@ -0,0 +1,502 @@ +254 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0d,0x09,0x08,0x0b,0x0c,0x0a,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, }, +{3: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 4, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 4, 2, }, +{7: 0, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 4, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 4, 4, 4, 0, 4, 16, 4, 0, 0, 0, 4, 0, 4, }, +{2: 16, 0, 16, 0, 0, 0, 16, 0, 16, 0, 16, 16, 16, 0, 16, 0, }, +{4: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 8, 4, 4, 8, 4, 4, 8, 16, 4, 4, 0, 4, 4, 0, 8, }, +{3: 16, 4, 0, 4, 4, 4, 0, 4, 16, 4, 0, 0, 0, 4, 0, 4, }, +{5: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 4, 4, 8, 4, 8, 4, 4, 16, 8, 4, 0, 4, 8, 0, 4, }, +{a: 16, 0, 4, 4, 0, 4, 4, 0, 16, 4, 4, 0, 4, 4, 0, 0, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 4, 0, 4, 4, 16, 0, 4, 0, 4, 0, 0, 4, }, +{d: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:64, 8:24, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{4: 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{c: 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, }, +{7: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, }, +{f: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{2: 16, 0, 0, 0, 16, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, }, +{4: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{8: 16, -8, 8, 8, -16, 0, 0, 16, 8, -8, -8, -8, 0, 0, -16, 8, }, +{3: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{5: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{6: 16, 0, -8, 0, 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{9: 16, -8, 8, 8, -16, -16, 0, 0, 8, -8, -8, -8, 16, 0, 0, 8, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 8, 0, -8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, 0, -8, 0, 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{d: 16, 8, 0, -8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{5: , , x, , , x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{9: , , , , , x, x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, , x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , x, x, , x, x, x, , x, x, , x, }, +{d: , , , , , x, , , , x, , , , x, , x, }, +{e: , x, x, x, , x, x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0011,0010,1,}, +{0011,1001,1,}, +{0011,1011,0,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1011,1001,0,}, +{1011,1011,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +254 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0a,0x09,0x0d,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 2, 2, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 4, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 4:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 8, 4, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{8: 16, 4, 0, 0, 8, 4, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +{3: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{5: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 4, 0, 2, 8, 4, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{9: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{a: 16, 4, 0, 0, 4, 4, 0, 0, 8, 4, 2, 0, 0, 2, 2, 2, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 4, 0, 0, 4, 4, 0, 0, 8, 4, 2, 0, 0, 2, 2, 2, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 4, 0, 0, 8, 4, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:32, 4:64, 8:24, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{2: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{4: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{8: 16, 0, 0, 0, -16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, 8, 0, 0, 16, -8, 8, -16, 8, 0, 0, -8, -8, 8, -16, -8, }, +{6: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{9: 16, 0, 16, 16, -16, 0, 0, 16, 0, -16, -16, 0, 0, 0, -16, 0, }, +{a: 16, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, }, +{c: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{7: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{b: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, , , x, , x, x, x, x, , , , x, }, +{6: , x, , x, , x, x, x, x, , x, x, , x, x, x, }, +{9: , x, , , , , x, , x, x, x, , x, x, , x, }, +{a: , x, , x, , x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , x, , , , , x, , x, x, x, , , , , x, }, +{e: , x, , , , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0010,0010,1,}, +{0010,1001,0,}, +{0010,1011,1,}, +{0100,0111,1,}, +{0100,1001,0,}, +{0100,1110,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1010,1001,1,}, +{1010,1011,0,}, +{1100,0111,1,}, +{1100,1001,1,}, +{1100,1110,0,}, +{1110,0101,1,}, +{1110,1001,1,}, +{1110,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_255.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_255.txt new file mode 100644 index 0000000..5481e88 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_255.txt @@ -0,0 +1,502 @@ +255 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0a,0x0d,0x09,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 4, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 2, 2, }, +{c: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, }, +{7: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 2, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:1, 4:5, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 16, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 16, 0, 4, 2, 0, 4, 2, 2, 8, 4, 0, 2, 4, 0, 0, 0, }, +{4: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 16, 4, 4, 4, 16, 0, 8, 8, 4, 4, 4, 4, 0, 8, 8, 4, }, +{3: 16, 4, 0, 2, 0, 4, 2, 2, 4, 8, 0, 2, 4, 0, 0, 0, }, +{5: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 16, 0, 4, 2, 0, 4, 2, 2, 8, 4, 0, 2, 4, 0, 0, 0, }, +{9: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{a: 16, 4, 0, 0, 0, 4, 0, 0, 4, 8, 2, 0, 4, 2, 2, 2, }, +{c: 16, 4, 4, 8, 16, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 8, }, +{7: 16, 4, 0, 2, 0, 4, 2, 2, 4, 8, 0, 2, 4, 0, 0, 0, }, +{b: 16, 0, 4, 0, 0, 4, 0, 0, 8, 4, 2, 0, 4, 2, 2, 2, }, +{d: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 16, 4, 0, 0, 0, 4, 0, 0, 4, 8, 2, 0, 4, 2, 2, 2, }, +{f: 16, 0, 4, 0, 0, 4, 0, 0, 8, 4, 2, 0, 4, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:32, 4:80, 8:16, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 8, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{6: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{c: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, 4, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +{e: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{f: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:2, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -16, }, +{2: 16, 0, -8, 0, 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{4: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{8: 16, 8, 8, 0, -16, 0, 8, 8, -8, -8, 0, 16, 0, -8, -8, -16, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{6: 16, 0, -8, 0, 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{9: 16, 0, 0, 16, -16, -16, 0, 0, 0, 0, -16, -16, 16, 0, 0, 16, }, +{a: 16, 0, -8, 0, -16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{c: 16, 8, 8, 0, -16, 16, 8, 8, -8, -8, 0, 0, -16, -8, -8, 0, }, +{7: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{b: 16, -8, 0, 0, -16, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, -8, 0, -16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{f: 16, -8, 0, 0, -16, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, , , , x, , x, x, , x, , x, , x, }, +{6: , x, , , , , , x, x, , , x, , , x, x, }, +{9: , x, x, , , , x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, , , x, , x, x, x, , x, x, x, x, }, +{c: , , , , , , , , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , , x, , x, , x, , x, x, , x, }, +{d: , , , , , , , , x, x, , , , x, , x, }, +{e: , , , , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0011,0101,1,}, +{0011,1001,1,}, +{0011,1100,0,}, +{0100,0100,1,}, +{0100,1001,0,}, +{0100,1101,1,}, +{0111,0001,1,}, +{0111,1000,0,}, +{0111,1001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0101,1,}, +{1011,1001,0,}, +{1011,1100,1,}, +{1100,0100,1,}, +{1100,1001,1,}, +{1100,1101,0,}, +{1111,0001,1,}, +{1111,1000,1,}, +{1111,1001,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x03,0x08,0x0b,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +255 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x0d,0x0a,0x08,0x0b,0x0c,0x09,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 0, 2, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 2, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{7: 0, 4, 2, 4, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 4, 2, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:1, 4:5, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 4, 4, 4, 0, 16, 4, 4, 4, 0, 0, 4, 0, }, +{2: 16, 4, 4, 0, 4, 0, 4, 4, 16, 0, 4, 0, 4, 0, 0, 4, }, +{4: 16, 4, 2, 4, 4, 2, 0, 2, 0, 0, 8, 2, 0, 4, 0, 0, }, +{8: 16, 16, 0, 16, 16, 0, 16, 0, 16, 0, 16, 0, 0, 16, 0, 0, }, +{3: 16, 0, 4, 0, 0, 4, 0, 4, 16, 4, 0, 4, 4, 0, 4, 4, }, +{5: 16, 0, 2, 4, 8, 2, 4, 2, 0, 0, 4, 2, 0, 4, 0, 0, }, +{6: 16, 0, 2, 4, 8, 2, 4, 2, 0, 0, 4, 2, 0, 4, 0, 0, }, +{9: 16, 4, 8, 0, 4, 4, 4, 8, 16, 4, 4, 4, 8, 0, 4, 8, }, +{a: 16, 4, 4, 0, 4, 8, 4, 4, 16, 8, 4, 8, 4, 0, 8, 4, }, +{c: 16, 4, 0, 4, 4, 0, 0, 0, 0, 2, 8, 0, 2, 4, 2, 2, }, +{7: 16, 4, 2, 4, 4, 2, 0, 2, 0, 0, 8, 2, 0, 4, 0, 0, }, +{b: 16, 0, 4, 0, 0, 4, 0, 4, 16, 4, 0, 4, 4, 0, 4, 4, }, +{d: 16, 0, 0, 4, 8, 0, 4, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{e: 16, 0, 0, 4, 8, 0, 4, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{f: 16, 4, 0, 4, 4, 0, 0, 0, 0, 2, 8, 0, 2, 4, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:32, 4:80, 8:16, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, 8, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, }, +{5: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, }, +{7: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:2, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{8: 16, 16, 16, 0, -16, 16, 0, 0, -16, -16, 0, 0, -16, 0, 0, 0, }, +{3: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, -8, 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -8, 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{9: 16, -16, 0, 8, -16, 0, -8, 8, 16, 0, -8, -8, 0, 8, -8, 8, }, +{a: 16, 0, 0, 8, -16, -16, -8, 8, 0, 0, -8, -8, 16, 8, -8, 8, }, +{c: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, 0, 0, 0, 16, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, -8, }, +{b: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, -8, }, +{e: 16, 0, 0, 0, -16, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, -8, }, +{f: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , , , x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, x, , , , x, x, x, x, , x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{9: , , , x, , , x, , x, x, x, , x, x, , x, }, +{a: , , , x, , , x, , x, x, x, , x, x, x, x, }, +{c: , , , x, , , x, , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , x, , , , x, , x, x, , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , x, , , x, , x, x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0001,0001,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{0010,0011,1,}, +{0010,1000,0,}, +{0010,1011,1,}, +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,1000,1,}, +{1001,1001,0,}, +{1010,0011,1,}, +{1010,1000,1,}, +{1010,1011,0,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x01,0x08,0x09,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x07,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x01,0x08,0x09,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_256.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_256.txt new file mode 100644 index 0000000..d8ad01f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_256.txt @@ -0,0 +1,502 @@ +256 Sbox: +LUT = { +0x06,0x00,0x01,0x02,0x03,0x05,0x04,0x07,0x0c,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 4:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 8, 0, 16, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{9: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 16, 8, 0, 16, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:32, 4:32, 8:32, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, -8, -8, 0, -8, 0, 0, 8, -8, -8, 0, 8, }, +{2: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{4: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 16, 8, -8, 0, -8, 0, 0, -8, 8, -8, 0, -8, }, +{5: 16, -8, 0, 0, 16, -8, -8, 0, -8, 0, 0, 8, -8, -8, 0, 8, }, +{6: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{9: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, 0, 16, 8, -8, 0, -8, 0, 0, -8, 8, -8, 0, -8, }, +{b: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -16, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, , x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, , , x, x, x, , , x, }, +{5: , , , , , x, x, x, , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, , , x, , x, x, , x, , x, x, , x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, , x, , , x, , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{0110,0100,1,}, +{0110,1010,1,}, +{0110,1110,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1100,1000,1,}, +{1100,1100,0,}, +{1110,0100,1,}, +{1110,1010,0,}, +{1110,1110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 11, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x02,0x08,0x0a,}}, +{{0x09,0x02,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x02,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +256 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x06,0x05,0x00,0x07,0x0c,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 2, }, +{3: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 4, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 2, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 4:2, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 16, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 0, 16, 16, 16, 0, 0, 16, 0, 16, 16, 0, 0, 0, 16, 0, }, +{4: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{3: 16, 8, 0, 16, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 8, 16, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{a: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{7: 16, 0, 8, 16, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{d: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{e: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{f: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:32, 4:32, 8:32, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 0, 8, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -16, 0, 16, -16, 0, 0, 16, -16, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 0, -8, 16, 16, -8, -8, 0, 0, -8, -8, 16, -8, -8, -8, }, +{8: 16, 0, 0, 0, -16, 0, 0, 8, 0, 0, 0, 8, 0, 0, -8, -8, }, +{3: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 16, -8, 16, 0, -8, -8, 0, 16, -8, -8, 0, -8, -8, -8, }, +{6: 16, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{9: 16, 0, 0, 0, -16, 0, 0, 8, 0, 0, 0, 8, 0, 0, -8, -8, }, +{a: 16, 0, 0, 8, -16, 0, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{7: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{b: 16, 0, 0, 8, -16, 0, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{e: 16, 0, 0, -8, -16, 0, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{f: 16, 0, 0, -8, -16, 0, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{2: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , x, x, x, , , x, }, +{5: , , , , , , x, x, , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, , x, , x, x, , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x02,0x08,0x0a,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_257.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_257.txt new file mode 100644 index 0000000..7329641 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_257.txt @@ -0,0 +1,502 @@ +257 Sbox: +LUT = { +0x06,0x00,0x01,0x02,0x03,0x05,0x04,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 0, 4, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{3: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 4, 2, 0, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 4, 2, }, +{7: 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 4, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 0, 16, 0, 0, 0, 16, 0, 16, 0, 16, 16, 16, 0, 16, 0, }, +{4: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{3: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 8, 8, 8, 0, 16, 16, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 0, 8, 0, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{a: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{c: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 0, 2, 8, 2, }, +{7: 16, 8, 8, 8, 0, 0, 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 8, 2, 0, 2, }, +{d: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 0, 2, 8, 2, }, +{e: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 0, 2, 8, 2, }, +{f: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 0, 2, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:32, 4:32, 8:32, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 8, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:2, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{2: 16, 0, -16, 0, 16, 0, 16, 0, 0, -16, 0, -16, 0, 16, 0, -16, }, +{4: 16, -8, 16, -8, 16, -8, 0, -8, -8, 16, -8, 0, -8, 0, -8, 0, }, +{8: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{5: 16, -8, 0, -8, 16, -8, 0, -8, -8, 0, -8, 16, -8, 0, -8, 16, }, +{6: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 8, -16, 0, 0, 0, 8, 0, -8, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{c: 16, 8, 0, -8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -16, }, +{b: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 8, 0, -8, -16, 0, 0, 0, -8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, , x, , x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, x, x, , x, x, x, x, , x, }, +{5: , , , , , x, x, x, , , , x, , x, , x, }, +{6: , x, , x, , x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , , x, x, x, x, , x, , x, x, , x, }, +{a: , x, , x, , x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, , x, , x, x, x, x, , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , x, x, x, x, , x, , x, x, , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , x, , x, , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1111,0010,1,}, +{1111,0101,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +257 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x06,0x05,0x00,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:183, 2:32, 4:36, 8:4, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:1, 4:4, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 0, 16, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 8, 0, 16, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 8, 0, 8, 0, 8, 16, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:32, 4:32, 8:32, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:150, 4:64, 8:40, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:2, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 8, -8, 0, -8, 0, 0, -8, 8, -8, 0, -8, }, +{2: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{4: 16, -8, 0, 0, 16, 8, -8, 0, -8, 0, 0, -8, 8, -8, 0, -8, }, +{8: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 16, -8, 0, 0, 16, -8, -8, 0, -8, 0, 0, 8, -8, -8, 0, 8, }, +{5: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{6: 16, -8, 0, 0, 16, -8, -8, 0, -8, 0, 0, 8, -8, -8, 0, 8, }, +{9: 16, 0, 0, 0, -16, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{a: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{7: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, , x, , x, x, x, x, , x, }, +{5: , , , , , , x, x, , , , x, , x, , x, }, +{6: , x, , x, , x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, , , x, x, x, , x, , x, x, , x, }, +{a: , x, , x, , x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , x, , , , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 33 */ +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0100,0101,1,}, +{0100,1011,0,}, +{0100,1110,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +{1100,0101,1,}, +{1100,1011,1,}, +{1100,1110,0,}, +{1110,0101,1,}, +{1110,1001,1,}, +{1110,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 11, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_258.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_258.txt new file mode 100644 index 0000000..d7622f9 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_258.txt @@ -0,0 +1,550 @@ +258 Sbox: +LUT = { +0x06,0x05,0x01,0x02,0x03,0x00,0x04,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + x1 + x2 + + + + + + x1x3 + x2x3; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + + x1 + x2 + x3 + + + + + x1x3 + ; deg = 2, term_n = 5, related_n = 3 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + x2x3; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3; deg = 2, term_n = 6, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + + + + + x1x3 + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + + + + x1x3 + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:1, 2:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{7: 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:177, 2:64, 8:14, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 2:1, 8:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{c: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:64, 16:80, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{7: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{e: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{f: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:198, 8:56, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 0, -16, 0, 16, 0, 16, 0, 0, -16, 0, -16, 0, 16, 0, -16, }, +{4: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 16, 0, 0, 0, 16, 16, -16, -16, 0, 0, 0, 0, 16, -16, -16, 0, }, +{5: 16, 0, 0, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, 0, 16, }, +{6: 16, 16, -16, 0, 16, -16, 0, 0, 16, -16, 0, 0, -16, 0, 0, 0, }, +{9: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, -16, 0, 0, 16, 0, 0, 16, -16, 0, 0, -16, 0, 0, 16, -16, }, +{b: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, x, x, , x, , x, x, , x, x, }, +{4: , x, , x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, x, x, , , , x, x, , , x, }, +{5: , , , , , x, x, x, , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , x, , , x, x, x, x, , , , x, x, , x, }, +{a: , x, , x, , x, x, x, , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , x, x, x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0001,1,}, +{0001,0110,0,}, +{0001,0111,1,}, +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0011,0011,0,}, +{0011,0101,1,}, +{0011,0110,1,}, +{0100,0001,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0111,0,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0110,0,}, +{1001,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1011,0011,0,}, +{1011,0101,1,}, +{1011,0110,1,}, +{1100,0001,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0111,0,}, +{1111,0010,1,}, +{1111,0101,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x0e,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +258 Inverse Sbox: +LUT = { +0x05,0x02,0x03,0x04,0x06,0x01,0x00,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3; deg = 2, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 4, related_n = 4 + + y1 + y2 + = 1 + + + x2 + x3 + + + + + x1x3 + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = + x0 + + + + + + + + x1x3 + x2x3; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + + + + + x1x3 + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = + x0 + + + x3 + + + + + x1x3 + x2x3; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:1, 2:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +Diff: 8, DDT_spectrum: {0:177, 2:64, 8:14, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:12, 2:1, 8:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{3: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{a: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{c: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{d: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{e: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +{f: 16, 0, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:64, 16:80, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{9: 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:198, 8:56, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 16, -16, 0, 0, -16, 0, 0, 16, -16, }, +{2: 16, 16, -16, 0, 16, -16, 0, 0, 16, -16, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 0, 0, 16, 16, -16, -16, 0, 0, 0, 0, 16, -16, -16, 0, }, +{8: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, 0, 16, }, +{9: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 16, 0, -16, 0, 16, 0, 16, 0, 0, -16, 0, -16, 0, 16, 0, -16, }, +{b: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, , x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, x, , , , , x, x, , , x, }, +{5: , , , , , , x, x, , , , x, , x, , x, }, +{6: , , , , , x, x, x, , , , x, , , x, x, }, +{9: , , x, x, , , x, x, x, , , , x, x, , x, }, +{a: , , , x, , x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, , x, x, x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , x, , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , , , x, x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0011,0,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0101,0011,1,}, +{0101,0100,1,}, +{0101,0111,0,}, +{0110,0001,0,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0111,0001,1,}, +{0111,0110,0,}, +{0111,0111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +{1100,0011,0,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1101,0011,1,}, +{1101,0100,1,}, +{1101,0111,0,}, +{1110,0001,0,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1111,0001,1,}, +{1111,0110,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x05,0x08,0x0d,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x05,0x08,0x0d,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0b,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_259.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_259.txt new file mode 100644 index 0000000..8ee0ecd --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_259.txt @@ -0,0 +1,470 @@ +259 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 6, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 6, 2, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 4, 6, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 4, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 0, 4, 6, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 0, 2, 4, 4, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 4, 2, 0, 6, 0, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 4, 6, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 4, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:178, 2:45, 4:21, 6:11, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:2, 4:1, 6:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 0, 8, 8, 0, 0, 8, 8, 0, 0, 8, 2, 2, 0, }, +{2: 16, 10, 10, 4, 0, 8, 4, 4, 0, 0, 0, 4, 0, 2, 2, 0, }, +{4: 16, 0, 8, 6, 10, 0, 0, 4, 0, 8, 4, 2, 2, 0, 4, 0, }, +{8: 16, 4, 0, 8, 6, 0, 4, 2, 10, 0, 4, 2, 0, 8, 0, 0, }, +{3: 16, 8, 8, 0, 0, 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, 8, 0, 8, 0, 6, 2, 2, 10, 0, 4, 0, 4, 0, 4, }, +{6: 16, 0, 8, 10, 0, 0, 0, 8, 6, 2, 0, 2, 4, 4, 0, 4, }, +{9: 16, 4, 0, 2, 4, 0, 2, 4, 8, 2, 0, 0, 2, 0, 0, 4, }, +{a: 16, 4, 0, 4, 0, 0, 8, 2, 0, 6, 0, 2, 10, 0, 8, 4, }, +{c: 16, 0, 0, 4, 4, 8, 0, 0, 0, 0, 10, 4, 4, 2, 2, 10, }, +{7: 16, 0, 8, 0, 2, 0, 10, 2, 4, 0, 4, 8, 6, 0, 4, 0, }, +{b: 16, 4, 0, 2, 2, 0, 2, 0, 2, 4, 4, 4, 8, 0, 0, 0, }, +{d: 16, 2, 2, 0, 4, 0, 8, 0, 0, 0, 2, 0, 4, 4, 4, 2, }, +{e: 16, 2, 2, 8, 0, 0, 0, 0, 4, 4, 2, 0, 0, 4, 4, 2, }, +{f: 16, 0, 0, 0, 0, 8, 4, 4, 4, 4, 10, 0, 0, 2, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:36, 4:46, 6:6, 8:28, 10:14, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 8, 0, 4, 4, }, +{2: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 8, 0, 8, 4, 4, }, +{e: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 8, LAT1_spectrum: {4:9, 8:7, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 8, -16, 0, 0, 0, 0, 16, -8, -8, 0, 0, -16, }, +{2: 16, 0, -8, 8, 8, -8, 0, -8, 0, -8, 16, 0, 0, 0, -8, -8, }, +{4: 16, 8, 0, 0, 0, 8, 0, -8, 0, 8, -16, -8, 8, -8, 0, -8, }, +{8: 16, 8, 8, 0, 0, 8, 0, 8, 0, -8, -16, 0, 0, -8, -8, -8, }, +{3: 16, -8, 0, 0, 0, 8, -8, 0, -8, 0, 16, -8, -8, -8, 0, 8, }, +{5: 16, 0, 8, 0, 0, -8, 8, 0, -8, 0, -16, 8, -8, 0, -8, 8, }, +{6: 16, 0, 0, 0, 0, -8, -8, 8, 8, -8, -16, -8, 8, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, -8, 0, 8, 0, -16, 0, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, 0, -8, 8, -8, -8, 8, -16, 0, 0, 0, 8, 8, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, -8, -8, 16, 0, 0, 0, 0, 8, }, +{7: 16, -8, -8, 0, 0, 8, 0, 0, 0, 0, -16, 8, -8, 8, 8, -8, }, +{b: 16, -8, 0, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 8, 0, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 0, 0, 0, 16, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, , x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , , x, x, x, , x, , , x, x, , , x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , , , x, x, , x, , , x, , , , x, , x, }, +{e: , , x, x, x, , x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0011,0001,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 2, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x02,0x08,}, {0x0c,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x01,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x0c,}}, +{{0x09,0x06,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +259 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x08,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 6, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 6, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 2, 6, 4, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 4, 0, 0, 2, 2, 2, 6, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{b: 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 6, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 4, 4, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 6, }, +}; +Diff: 6, DDT_spectrum: {0:178, 2:45, 4:21, 6:11, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:8, 2:2, 4:1, 6:5, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 0, 4, 8, 0, 0, 4, 4, 0, 0, 4, 2, 2, 0, }, +{2: 16, 10, 10, 8, 0, 8, 8, 8, 0, 0, 0, 8, 0, 2, 2, 0, }, +{4: 16, 0, 4, 6, 8, 0, 0, 10, 2, 4, 4, 0, 2, 0, 8, 0, }, +{8: 16, 8, 0, 10, 6, 0, 8, 0, 4, 0, 4, 2, 2, 4, 0, 0, }, +{3: 16, 8, 8, 0, 0, 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, 4, 0, 4, 0, 6, 0, 2, 8, 0, 10, 2, 8, 0, 4, }, +{6: 16, 0, 4, 4, 2, 0, 2, 8, 4, 2, 0, 2, 0, 0, 0, 4, }, +{9: 16, 8, 0, 0, 10, 0, 2, 6, 8, 0, 0, 4, 2, 0, 4, 4, }, +{a: 16, 8, 0, 8, 0, 0, 10, 2, 2, 6, 0, 0, 4, 0, 4, 4, }, +{c: 16, 0, 0, 4, 4, 8, 0, 0, 0, 0, 10, 4, 4, 2, 2, 10, }, +{7: 16, 0, 4, 2, 2, 0, 4, 2, 0, 2, 4, 8, 4, 0, 0, 0, }, +{b: 16, 8, 0, 2, 0, 0, 0, 4, 2, 10, 4, 6, 8, 4, 0, 0, }, +{d: 16, 2, 2, 0, 8, 0, 4, 4, 0, 0, 2, 0, 0, 4, 4, 2, }, +{e: 16, 2, 2, 4, 0, 0, 0, 0, 0, 8, 2, 4, 0, 4, 4, 2, }, +{f: 16, 0, 0, 0, 0, 8, 4, 4, 4, 4, 10, 0, 0, 2, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:94, 2:36, 4:46, 6:6, 8:28, 10:14, 16:32, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{b: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 8, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 8, LAT1_spectrum: {4:9, 8:7, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -8, 0, -8, }, +{2: 16, 0, 0, 8, 8, -16, 0, 0, 0, 0, 16, -8, -8, 0, 0, -16, }, +{4: 16, 8, 8, 0, 0, 8, -8, 0, 8, 0, -16, 0, 0, -8, -8, -8, }, +{8: 16, 0, 8, 0, 0, 8, 8, 0, -8, 0, -16, 8, -8, 0, -8, -8, }, +{3: 16, 0, -8, 0, 0, 8, 0, -8, 0, -8, 16, -8, -8, 0, -8, 8, }, +{5: 16, -8, 0, 0, 0, -8, 8, -8, -8, 8, -16, 0, 0, 8, 0, 8, }, +{6: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -16, 0, 0, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, -8, 8, 8, -8, -16, 8, -8, 0, 0, 8, }, +{a: 16, 8, 0, 0, 0, -8, 0, -8, 0, 8, -16, -8, 8, -8, 0, 8, }, +{c: 16, 0, 0, -8, -8, 8, -8, -8, -8, -8, 16, 0, 0, 0, 0, 8, }, +{7: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{b: 16, -8, -8, 0, 0, 8, 0, 0, 0, 0, -16, -8, 8, 8, 8, -8, }, +{d: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, }, +{e: 16, 0, 0, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 0, 0, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 0, 0, 0, 16, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, , x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , x, , x, x, , x, , , x, x, , , x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , x, , x, x, , x, , , x, , , , x, , x, }, +{e: , , , x, x, , x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0011,0010,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 21, 2, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x05,0x09,0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x0c,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_260.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_260.txt new file mode 100644 index 0000000..b76ce32 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_260.txt @@ -0,0 +1,470 @@ +260 Sbox: +LUT = { +0x02,0x00,0x01,0x04,0x03,0x05,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 4, 2, 0, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 6, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 0, 2, 2, 4, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 2, 6, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 2, 0, 4, }, +{7: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 4, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 0, 0, 0, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:50, 4:18, 6:10, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 6:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 2, 8, 8, 0, 10, 2, 8, 0, 8, 0, 0, 8, 0, 0, }, +{2: 16, 0, 10, 10, 4, 2, 2, 8, 0, 4, 4, 0, 0, 0, 4, 0, }, +{4: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 4, 8, 0, 6, 4, 0, 0, 10, 4, 0, 0, 8, 0, 2, 2, }, +{3: 16, 2, 0, 10, 4, 10, 0, 2, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 16, 8, 2, 8, 0, 2, 8, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 16, 2, 10, 10, 0, 0, 0, 8, 4, 0, 0, 2, 4, 4, 0, 4, }, +{9: 16, 4, 0, 0, 4, 0, 0, 0, 8, 2, 2, 4, 2, 2, 4, 0, }, +{a: 16, 0, 8, 0, 10, 0, 4, 0, 0, 8, 0, 4, 2, 6, 2, 4, }, +{c: 16, 4, 8, 0, 0, 4, 0, 0, 0, 2, 6, 0, 2, 10, 4, 8, }, +{7: 16, 0, 0, 10, 0, 8, 2, 2, 4, 4, 0, 10, 0, 4, 4, 0, }, +{b: 16, 0, 0, 0, 8, 4, 4, 0, 2, 2, 2, 0, 4, 4, 0, 2, }, +{d: 16, 4, 0, 0, 2, 0, 0, 0, 2, 4, 4, 4, 0, 8, 2, 2, }, +{e: 16, 0, 8, 0, 0, 0, 4, 0, 6, 2, 10, 4, 4, 0, 8, 2, }, +{f: 16, 0, 0, 0, 2, 4, 4, 0, 4, 0, 8, 0, 2, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:38, 4:44, 6:4, 8:27, 10:18, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +{e: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:5, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 16, -16, 0, 0, -8, 8, 0, 0, -16, 0, 0, 0, }, +{2: 16, 8, -8, 0, 16, -8, 0, -8, 8, -8, 0, 0, -8, 0, -8, 0, }, +{4: 16, 0, 8, -8, 16, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 8, 0, 8, 0, 0, -8, 8, -8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 16, 8, -8, 0, -8, -8, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 0, 0, 16, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, 0, }, +{6: 16, 8, -8, 0, 16, -8, 0, 0, 8, -8, 0, -8, -8, 0, 0, -8, }, +{9: 16, 0, 0, 0, -16, -8, -8, 0, 0, 0, 0, 0, 8, 8, 0, 0, }, +{a: 16, 0, 0, 0, -16, -8, 8, -8, 0, 0, 0, 8, 8, -8, 8, -8, }, +{c: 16, 0, 0, -8, -16, 8, 0, -8, 0, 0, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, }, +{b: 16, 0, 0, 8, -16, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, -8, 8, 0, 0, 0, 0, 0, 8, -8, 0, 0, }, +{e: 16, 0, 0, 0, -16, -8, -8, 8, 0, 0, 0, -8, 8, 8, -8, 8, }, +{f: 16, 0, 0, -8, -16, 8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , , x, x, x, , , x, }, +{5: , , , x, , x, x, , , , , x, , x, , x, }, +{6: , , x, x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , , x, , x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0011,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 3, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x03,0x08,0x0b,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x02,0x08,0x0a,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x03,0x08,0x0b,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +260 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x03,0x05,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 8, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, 0, 4, 2, 0, 2, }, +{3: 0, 0, 2, 2, 0, 6, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 6, 2, 2, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 4, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 2, 6, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 2, 0, 2, 4, }, +{7: 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 2, 0, 4, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 0, 4, 0, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:50, 4:18, 6:10, 8:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:3, 6:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 10, 4, 2, 8, 2, 4, 0, 4, 0, 0, 4, 0, 0, }, +{2: 16, 2, 10, 8, 8, 0, 2, 10, 0, 8, 8, 0, 0, 0, 8, 0, }, +{4: 16, 8, 10, 8, 0, 10, 8, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 8, 4, 0, 6, 4, 0, 0, 4, 10, 0, 0, 8, 2, 0, 2, }, +{3: 16, 0, 2, 10, 4, 10, 2, 0, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 16, 10, 2, 10, 0, 0, 8, 0, 0, 4, 0, 2, 4, 0, 4, 4, }, +{6: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 16, 8, 0, 0, 10, 0, 0, 4, 8, 0, 0, 4, 2, 2, 6, 4, }, +{a: 16, 0, 4, 0, 4, 0, 0, 0, 2, 8, 2, 4, 2, 4, 2, 0, }, +{c: 16, 8, 4, 0, 0, 4, 0, 0, 2, 0, 6, 0, 2, 4, 10, 8, }, +{7: 16, 0, 0, 10, 0, 8, 2, 2, 4, 4, 0, 10, 0, 4, 4, 0, }, +{b: 16, 0, 0, 0, 8, 4, 0, 4, 2, 2, 2, 0, 4, 0, 4, 2, }, +{d: 16, 8, 0, 0, 0, 0, 0, 4, 2, 6, 10, 4, 4, 8, 0, 2, }, +{e: 16, 0, 4, 0, 2, 0, 0, 0, 4, 2, 4, 4, 0, 2, 8, 2, }, +{f: 16, 0, 0, 0, 2, 4, 0, 4, 0, 4, 8, 0, 2, 2, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:94, 2:38, 4:44, 6:4, 8:27, 10:18, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 12, 4, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:5, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 16, -8, -8, 0, -8, 8, 0, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 0, 16, -16, 0, 0, 8, -8, 0, 0, -16, 0, 0, 0, }, +{4: 16, 8, 0, -8, 16, 8, -8, -8, 8, 0, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 8, 8, 0, 0, 0, -8, 8, -8, -8, 0, -8, }, +{3: 16, -8, -8, 0, 16, 8, 0, -8, -8, -8, 0, 0, 8, 0, -8, 0, }, +{5: 16, -8, 8, 0, 16, -8, 0, 0, -8, 8, 0, -8, -8, 0, 0, -8, }, +{6: 16, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 0, 0, -16, -8, -8, 8, 0, 0, 0, 8, 8, 8, -8, -8, }, +{a: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -16, 8, -8, 0, 0, 0, 8, -8, -8, 8, 0, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 0, -8, -8, -8, 0, 8, 0, 0, 0, }, +{b: 16, 0, 0, 8, -16, 8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, -8, 8, -8, 0, 0, 0, -8, 8, -8, 8, 8, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, -8, -16, 8, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , , x, x, x, , , x, }, +{5: , x, , x, , x, x, , , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, , x, , x, x, , x, }, +{a: , x, x, x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0011,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 3, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x05,0x08,0x0d,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_261.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_261.txt new file mode 100644 index 0000000..0a7c1ac --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_261.txt @@ -0,0 +1,482 @@ +261 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 6, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 4, 0, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 2, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, 4, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 2, 2, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 2, 4, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 4, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:181, 2:40, 4:24, 6:8, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 4:3, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 10, 8, 2, 8, 2, 8, 0, 8, 0, 0, 8, 0, 0, }, +{2: 16, 0, 16, 0, 0, 0, 16, 0, 8, 0, 8, 16, 8, 0, 8, 0, }, +{4: 16, 8, 8, 8, 0, 0, 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 4, 4, 4, 4, 0, 0, 4, 10, 0, 0, 0, 6, 6, 0, 6, }, +{3: 16, 2, 0, 2, 0, 10, 8, 10, 8, 8, 8, 0, 0, 0, 0, 8, }, +{5: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 0, 8, 0, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 4, 4, 4, 6, 4, 0, 0, 10, 6, 0, 0, 6, 4, 0, 0, }, +{a: 16, 0, 4, 0, 0, 4, 0, 0, 8, 4, 2, 0, 4, 2, 2, 2, }, +{c: 16, 4, 4, 4, 4, 4, 0, 0, 0, 0, 10, 0, 0, 6, 6, 6, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 4, 8, 2, 2, 0, 4, 0, 2, 4, }, +{d: 16, 4, 4, 4, 6, 0, 0, 4, 0, 6, 10, 0, 0, 4, 6, 0, }, +{e: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{f: 16, 0, 4, 0, 2, 4, 0, 0, 2, 2, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:24, 4:36, 6:12, 8:32, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:94, 8:28, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:3, 8:1, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 16, 0, -16, 0, 0, 8, 0, -8, 0, -16, 0, -8, }, +{2: 16, 0, -8, 0, 16, -8, 16, -8, 0, -8, 0, -8, -8, 16, -8, -8, }, +{4: 16, -8, 8, -8, 16, 0, 0, 0, -8, 8, -8, -8, 0, 0, 0, -8, }, +{8: 16, -8, 8, 8, -16, 0, 0, 8, 8, -8, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, -8, 0, 16, 0, -16, 0, 0, -8, 0, 8, 0, -16, 0, 8, }, +{5: 16, -8, 8, -8, 16, -8, 0, -8, -8, 8, -8, 8, -8, 0, -8, 8, }, +{6: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, -16, -8, 0, 0, 8, -8, -8, 0, 8, 0, 0, 0, }, +{a: 16, 0, -8, 0, -16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{c: 16, 8, 8, -8, -16, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, }, +{7: 16, 0, -8, 0, 16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, -8, }, +{b: 16, 0, -8, 0, -16, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, }, +{d: 16, 8, 8, -8, -16, 0, 0, -8, -8, -8, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, 0, -16, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, 0, -16, 0, 0, 8, 0, 8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{5: , , x, , , x, x, , , , , x, , x, , x, }, +{6: , x, , x, , x, x, x, x, , x, x, , x, x, x, }, +{9: , , x, , , x, x, , x, , x, , x, x, , x, }, +{a: , x, x, x, , x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, , x, , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, , , x, x, , x, , x, , x, x, , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , x, , x, , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0010,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x02,}, {0x05,0x08,0x0d,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +261 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0d,0x09,0x0a,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 6, 0, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 6, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 0, 0, }, +{7: 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 4, 0, 2, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:181, 2:40, 4:24, 6:8, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 4:3, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 8, 4, 2, 10, 0, 4, 0, 4, 2, 0, 4, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 10, 0, 8, 4, 2, 10, 0, 4, 0, 4, 2, 0, 4, 0, 0, }, +{8: 16, 8, 0, 0, 4, 0, 0, 0, 6, 0, 4, 0, 2, 6, 0, 2, }, +{3: 16, 2, 0, 0, 0, 10, 10, 8, 4, 4, 4, 2, 0, 0, 0, 4, }, +{5: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 2, 0, 0, 4, 10, 10, 8, 0, 0, 0, 2, 4, 4, 4, 0, }, +{9: 16, 8, 8, 0, 10, 8, 0, 0, 10, 8, 0, 0, 8, 0, 2, 2, }, +{a: 16, 0, 0, 0, 0, 8, 0, 0, 6, 4, 0, 0, 2, 6, 4, 2, }, +{c: 16, 8, 8, 0, 0, 8, 0, 0, 0, 2, 10, 0, 2, 10, 8, 8, }, +{7: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 0, 0, 4, 0, 2, 2, }, +{d: 16, 8, 0, 0, 6, 0, 0, 0, 4, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 4, 4, }, +{f: 16, 0, 0, 0, 6, 8, 0, 0, 0, 2, 6, 0, 4, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:24, 4:36, 6:12, 8:32, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:94, 8:28, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:3, 8:1, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 16, 0, -8, 0, -8, 8, 0, -8, 0, -8, 0, -8, }, +{2: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{4: 16, -8, 8, 0, 16, 0, -8, 0, -8, 8, 0, -8, 0, -8, 0, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{3: 16, -8, -8, 0, 16, 0, -8, 0, -8, -8, 0, 8, 0, -8, 0, 8, }, +{5: 16, 0, 8, -8, 16, -8, 8, -16, 0, 8, -8, 0, -8, 8, -16, 0, }, +{6: 16, -8, -8, 0, 16, 0, -8, 0, -8, -8, 0, 8, 0, -8, 0, 8, }, +{9: 16, 0, 8, 8, -16, 0, 0, 16, 0, -8, -8, 0, 0, 0, -16, 0, }, +{a: 16, 0, -8, 0, -16, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, -16, 0, 0, -16, 0, -8, 8, 0, 0, 0, 16, 0, }, +{7: 16, 8, -8, -8, 16, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, -8, }, +{b: 16, 0, -8, 8, -16, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, }, +{d: 16, 0, 8, 0, -16, -8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -16, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, 0, -16, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, , x, , x, x, x, x, , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , x, , x, , x, x, x, x, , x, x, , x, x, x, }, +{9: , x, x, x, , , x, , x, , x, , x, x, , x, }, +{a: , x, , x, , x, x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , x, x, , x, , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , x, x, , x, , x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0010,0010,1,}, +{0110,0101,1,}, +{0110,1001,0,}, +{0110,1100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1110,0101,1,}, +{1110,1001,1,}, +{1110,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_262.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_262.txt new file mode 100644 index 0000000..bc14f90 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_262.txt @@ -0,0 +1,482 @@ +262 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0e,0x09,0x0a,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 0, 2, 0, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 2, 2, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 0, 0, }, +{7: 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:181, 2:40, 4:24, 6:8, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:1, 4:4, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 2, 0, 2, 0, 10, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 2, 0, 2, 0, 10, 8, 10, 4, 4, 4, 0, 0, 0, 0, 4, }, +{5: 16, 2, 0, 2, 4, 10, 8, 10, 0, 0, 0, 0, 4, 4, 4, 0, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, 2, 8, 0, 0, 4, 6, 0, 0, 0, 6, 4, 2, }, +{a: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 0, 0, 10, 0, 2, 2, }, +{c: 16, 8, 8, 0, 2, 8, 0, 0, 2, 0, 10, 0, 0, 10, 8, 8, }, +{7: 16, 10, 0, 2, 0, 2, 0, 10, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 16, 8, 0, 0, 2, 0, 0, 0, 0, 6, 4, 0, 4, 6, 0, 2, }, +{d: 16, 8, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 6, 4, 2, 0, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 6, 0, 6, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:24, 4:36, 6:12, 8:32, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:94, 8:28, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{2: 16, 8, 0, 0, 16, -8, 8, -16, 8, 0, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 0, -8, 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 0, 16, 0, -8, -8, -8, 0, 0, 8, 0, -8, -8, 8, }, +{5: 16, -8, 0, 0, 16, 0, -8, -8, -8, 0, 0, 8, 0, -8, -8, 8, }, +{6: 16, 8, -16, -8, 16, -8, 0, 8, 8, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, -16, 8, -16, 0, 0, -8, 0, 16, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 16, -8, -16, 0, 0, -8, 0, -16, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, 0, 16, 0, -8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{b: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, , x, x, x, , x, x, x, , x, x, x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, x, , x, x, x, x, }, +{a: , x, , , , x, , x, , x, x, , x, , x, x, }, +{c: , x, , x, , x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, , x, , x, x, , x, , x, x, }, +{d: , , , x, , x, , x, , x, x, , , x, x, x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0010,0110,1,}, +{0010,1010,1,}, +{0010,1100,0,}, +{0110,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1010,1010,0,}, +{1010,1100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 5, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +262 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0e,0x09,0x0a,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +{3: 0, 2, 0, 0, 0, 6, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 2, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 2, 2, 2, }, +{7: 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:181, 2:40, 4:24, 6:8, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:1, 4:4, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 0, 0, 2, 2, 8, 0, 8, 8, 10, 8, 8, 0, 0, }, +{2: 16, 0, 16, 16, 8, 0, 0, 16, 0, 8, 8, 0, 0, 0, 8, 0, }, +{4: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{3: 16, 2, 0, 0, 0, 10, 10, 8, 8, 8, 8, 2, 0, 0, 0, 8, }, +{5: 16, 0, 8, 8, 0, 8, 8, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 4, 4, 0, 0, 4, 8, 2, 0, 0, 2, 2, 2, }, +{a: 16, 4, 4, 0, 6, 4, 0, 0, 6, 10, 0, 4, 6, 4, 0, 0, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 8, 8, 8, 0, 0, 0, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 0, 4, 0, 0, 10, 0, 4, 4, 6, 0, 6, }, +{d: 16, 4, 4, 0, 0, 0, 4, 0, 6, 0, 10, 4, 6, 4, 6, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{f: 16, 0, 4, 0, 2, 4, 0, 0, 2, 2, 8, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:24, 4:36, 6:12, 8:32, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:94, 8:28, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 16, -8, 0, 16, -8, 0, -8, 16, -8, 0, -8, -8, 0, -8, -8, }, +{4: 16, 0, 0, 0, 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{8: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{3: 16, -16, 0, 0, 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, -8, 8, }, +{5: 16, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{6: 16, 0, -8, -8, 16, -8, -8, 8, 0, -8, -8, 8, -8, -8, 8, 8, }, +{9: 16, 0, 8, 0, -16, 0, 0, 8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -16, -8, 8, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -16, 8, -8, -8, 0, 0, 8, 0, -8, 8, 8, 0, }, +{7: 16, 0, 0, -8, 16, 0, -8, 8, 0, 0, -8, -8, 0, -8, 8, -8, }, +{b: 16, 0, -8, 8, -16, 0, 8, -8, 0, 8, -8, 0, 0, -8, 8, 0, }, +{d: 16, 0, 8, -8, -16, 0, -8, -8, 0, -8, 8, 0, 0, 8, 8, 0, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, 0, -16, 0, 0, 8, 0, 8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, , , x, x, , x, x, x, , x, x, x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, x, x, , x, x, x, x, }, +{a: , , x, x, , x, , x, , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, , , , , x, , x, x, , x, , x, x, }, +{d: , , , , , , , x, , x, x, , , x, x, x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x01,0x08,0x09,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_263.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_263.txt new file mode 100644 index 0000000..39d60eb --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_263.txt @@ -0,0 +1,482 @@ +263 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0e,0x08,0x0a,0x0b,0x0c,0x0d,0x09,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 2, 2, 0, 4, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 0, 0, 0, 4, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 2, 2, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 0, }, +{7: 0, 6, 0, 2, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 4, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:181, 2:40, 4:24, 6:8, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 2, 2, 0, 0, 0, 8, 0, 4, 4, 10, 4, 4, 0, 0, }, +{2: 16, 0, 4, 4, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 16, 0, 2, 4, 8, 2, 4, 2, 0, 0, 4, 2, 0, 4, 0, 0, }, +{8: 16, 0, 4, 4, 8, 4, 4, 4, 0, 6, 4, 4, 6, 4, 6, 6, }, +{3: 16, 2, 2, 2, 0, 4, 4, 0, 8, 4, 4, 2, 0, 0, 0, 0, }, +{5: 16, 2, 4, 2, 0, 2, 4, 2, 8, 0, 4, 0, 4, 0, 0, 0, }, +{6: 16, 8, 2, 0, 8, 2, 0, 10, 8, 0, 0, 10, 0, 0, 8, 8, }, +{9: 16, 0, 0, 0, 0, 4, 4, 4, 10, 6, 6, 4, 0, 0, 4, 6, }, +{a: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 0, 0, 10, 0, 2, 2, }, +{c: 16, 8, 0, 8, 16, 0, 16, 0, 8, 0, 8, 0, 0, 16, 0, 0, }, +{7: 16, 10, 0, 2, 0, 2, 0, 10, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 16, 8, 0, 0, 0, 0, 0, 0, 2, 6, 6, 0, 4, 4, 0, 2, }, +{d: 16, 8, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 6, 4, 2, 0, }, +{e: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 0, 4, 0, 0, 0, 4, 4, 10, 0, 6, 4, 6, 0, 6, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:24, 4:58, 6:14, 8:22, 10:10, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{d: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:94, 8:28, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:2, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, -8, -8, 8, 0, 0, 0, -8, -8, -8, 8, -8, }, +{2: 16, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{4: 16, 0, 0, -8, 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{8: 16, 8, 0, 8, -16, 8, 8, 8, -8, 0, -8, 8, -8, -8, -8, -8, }, +{3: 16, -8, 0, 0, 16, 0, 0, -8, -8, 0, 0, 0, 0, 0, -8, 0, }, +{5: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{6: 16, 0, -16, -8, 16, 0, 0, 8, 0, -16, -8, 0, 0, 0, 8, 0, }, +{9: 16, 0, 0, 0, -16, -8, -8, 8, 0, 0, 0, -8, 8, 8, -8, 8, }, +{a: 16, 0, -16, 8, -16, 0, 0, -8, 0, 16, -8, 0, 0, 0, 8, 0, }, +{c: 16, 8, 16, -8, -16, 8, 0, -8, -8, -16, 8, 0, -8, 0, 8, 0, }, +{7: 16, -8, 0, 0, 16, 0, -8, 8, -8, 0, 0, -8, 0, -8, 8, -8, }, +{b: 16, -8, 0, 0, -16, 0, 0, -8, 8, 0, 0, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, 0, -8, -16, 0, 8, 8, 0, 0, 8, 8, 0, -8, -8, -8, }, +{f: 16, -8, 0, 0, -16, 0, -8, 8, 8, 0, 0, -8, 0, 8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, , , x, x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{5: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{6: , x, , , , , , x, x, , , x, , , x, x, }, +{9: , x, x, x, , , , x, x, x, x, , x, x, x, x, }, +{a: , x, , , , , , x, x, x, x, , x, , x, x, }, +{c: , , , x, , , , x, x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , , x, x, x, x, , x, , x, x, }, +{d: , , , x, , , , x, x, x, x, , , x, x, x, }, +{e: , , , , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0010,0110,1,}, +{0010,1010,1,}, +{0010,1100,0,}, +{0110,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1010,1010,0,}, +{1010,1100,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x03,0x08,0x0b,}}, +{{0x03,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x01,0x08,0x09,}}, +{{0x01,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +263 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x09,0x0e,0x0a,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, }, +{2: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, }, +{3: 0, 0, 4, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 6, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 8, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 4, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:181, 2:40, 4:24, 6:8, 8:2, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:3, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 0, 0, 2, 2, 8, 0, 8, 8, 10, 8, 8, 0, 0, }, +{2: 16, 2, 4, 2, 4, 2, 4, 2, 0, 8, 0, 0, 0, 0, 0, 4, }, +{4: 16, 2, 4, 4, 4, 2, 2, 0, 0, 0, 8, 2, 0, 0, 4, 0, }, +{8: 16, 0, 16, 8, 8, 0, 0, 8, 0, 8, 16, 0, 0, 0, 16, 0, }, +{3: 16, 0, 4, 2, 4, 4, 2, 2, 4, 8, 0, 2, 0, 0, 0, 0, }, +{5: 16, 0, 4, 4, 4, 4, 4, 0, 4, 0, 16, 0, 0, 0, 4, 4, }, +{6: 16, 8, 0, 2, 4, 0, 2, 10, 4, 0, 0, 10, 0, 0, 4, 4, }, +{9: 16, 0, 0, 0, 0, 8, 8, 8, 10, 8, 8, 0, 2, 2, 0, 10, }, +{a: 16, 4, 4, 0, 6, 4, 0, 0, 6, 10, 0, 4, 6, 4, 0, 0, }, +{c: 16, 4, 4, 4, 4, 4, 4, 0, 6, 0, 8, 4, 6, 6, 4, 6, }, +{7: 16, 10, 0, 2, 4, 2, 0, 10, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 16, 4, 4, 0, 6, 0, 4, 0, 0, 10, 0, 4, 4, 6, 0, 6, }, +{d: 16, 4, 4, 4, 4, 0, 0, 0, 0, 0, 16, 4, 4, 4, 4, 0, }, +{e: 16, 0, 0, 0, 6, 0, 0, 8, 4, 2, 0, 0, 0, 2, 4, 6, }, +{f: 16, 0, 0, 0, 6, 0, 0, 8, 6, 2, 0, 0, 2, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 2:24, 4:58, 6:14, 8:22, 10:10, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{4: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:94, 8:28, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:2, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, 8, -8, }, +{2: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{4: 16, 0, 0, 0, 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{8: 16, 16, 8, 0, -16, 8, 0, 8, -16, -8, 0, 8, -8, 0, -8, -8, }, +{3: 16, 0, -8, 0, 16, 0, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, }, +{5: 16, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -8, 16, -8, -8, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{9: 16, -16, 0, 0, -16, 0, 0, 8, 16, 0, 0, -8, 0, 0, -8, 8, }, +{a: 16, 0, 0, 8, -16, -8, 8, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 8, -8, -16, 8, -8, -8, 0, -8, 8, -8, -8, 8, 8, 8, }, +{7: 16, 0, -8, -8, 16, 0, -8, 8, 0, -8, -8, 0, 0, -8, 8, 0, }, +{b: 16, 0, -8, 8, -16, 0, 8, -8, 0, 8, -8, 0, 0, -8, 8, 0, }, +{d: 16, 0, 0, -8, -16, 0, -8, -8, 0, 0, 8, 8, 0, 8, 8, -8, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, 0, -16, 0, 0, 8, 0, 8, 0, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , , x, x, x, , , x, x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, , , x, x, , x, x, x, , x, x, x, }, +{6: , x, x, x, , , , x, x, x, x, x, , , , x, }, +{9: , , x, x, , , , x, x, x, x, , x, x, x, x, }, +{a: , , x, x, , , , x, x, x, x, , x, , x, x, }, +{c: , , , x, , , , x, x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, , , , , x, , x, x, , x, , x, x, }, +{d: , , , , , , , x, , x, x, , , x, x, x, }, +{e: , , , x, , , , x, x, x, x, , , , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0001,0001,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,1000,1,}, +{1001,1001,0,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x01,0x08,0x09,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_264.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_264.txt new file mode 100644 index 0000000..1cd6a02 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_264.txt @@ -0,0 +1,470 @@ +264 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0b,0x08,0x0a,0x09,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 4, 6, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 2, 4, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 2, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 8, 0, 2, 0, 2, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 2, 2, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 6, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:48, 4:24, 6:4, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 2, 4, 8, 0, 0, 4, 4, 0, 2, 4, 0, 0, 0, }, +{2: 16, 8, 10, 2, 4, 10, 2, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{4: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 16, 0, 0, }, +{8: 16, 4, 4, 0, 8, 4, 4, 4, 4, 6, 0, 4, 6, 4, 6, 6, }, +{3: 16, 10, 8, 0, 4, 10, 2, 0, 4, 4, 0, 2, 4, 0, 0, 0, }, +{5: 16, 2, 2, 2, 0, 0, 4, 4, 4, 4, 8, 2, 0, 0, 0, 0, }, +{6: 16, 0, 2, 2, 4, 2, 2, 4, 4, 0, 0, 4, 0, 0, 0, 8, }, +{9: 16, 4, 4, 4, 6, 4, 4, 4, 8, 4, 6, 0, 6, 4, 0, 6, }, +{a: 16, 4, 4, 4, 4, 4, 0, 4, 6, 8, 6, 4, 6, 4, 6, 0, }, +{c: 16, 0, 0, 0, 6, 0, 8, 0, 6, 0, 4, 0, 0, 4, 2, 2, }, +{7: 16, 2, 0, 4, 4, 2, 2, 4, 0, 4, 0, 2, 0, 0, 8, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 4, 6, 6, 0, 0, 10, 4, 0, 0, }, +{d: 16, 0, 0, 8, 0, 0, 0, 0, 6, 6, 2, 0, 0, 4, 4, 2, }, +{e: 16, 0, 0, 0, 6, 0, 0, 0, 0, 6, 2, 8, 0, 4, 2, 4, }, +{f: 16, 0, 0, 0, 4, 0, 0, 16, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:24, 4:75, 6:21, 8:12, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{9: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{b: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +{d: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, -8, }, +{2: 16, 0, 0, 8, 16, -8, 0, -8, 0, 0, 8, -8, -8, 0, -8, -8, }, +{4: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{8: 16, 8, 0, 8, -16, 8, 8, 8, -8, 0, -8, 8, -8, -8, -8, -8, }, +{3: 16, -8, -8, 8, 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, -8, 0, }, +{5: 16, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +{6: 16, 0, -8, -8, 16, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, -16, 0, -8, 8, 8, -8, -8, -8, 0, 8, -8, 8, }, +{a: 16, 8, -8, 8, -16, -8, 0, -8, -8, 8, -8, -8, 8, 0, 8, 8, }, +{c: 16, 0, 8, -8, -16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, -8, 0, 8, -16, 0, 0, -8, 8, 0, -8, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, -8, -16, -8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{e: 16, 0, 0, -8, -16, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, -8, -8, -16, 8, -8, 0, 0, 8, 8, 0, -8, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , , , x, x, , , x, }, +{5: , x, x, , , x, x, , , x, , x, x, x, , x, }, +{6: , x, x, , , x, , x, x, x, , x, x, , x, x, }, +{9: , x, x, x, , x, , , x, x, , , x, x, , x, }, +{a: , , x, x, , x, , , x, x, , , x, , x, x, }, +{c: , x, x, , , x, , , x, x, x, , x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, , , , x, , , , x, , , x, x, , x, }, +{e: , , x, , , x, , , x, x, , , x, , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0100,0100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1100,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 1, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x05,0x08,0x0d,}}, +{{0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +264 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x09,0x0b,0x0a,0x08,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 4, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 4, 2, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 2, 2, 0, 2, 2, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 0, 8, 0, 0, 2, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, 4, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 6, 0, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, 4, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:176, 2:48, 4:24, 6:4, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:8, 2:3, 4:2, 6:2, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 0, 4, 10, 2, 0, 4, 4, 0, 2, 4, 0, 0, 0, }, +{2: 16, 10, 10, 0, 4, 8, 2, 2, 4, 4, 0, 0, 4, 0, 0, 0, }, +{4: 16, 2, 2, 4, 0, 0, 2, 2, 4, 4, 0, 4, 0, 8, 0, 0, }, +{8: 16, 4, 4, 4, 8, 4, 0, 4, 6, 4, 6, 4, 6, 0, 6, 4, }, +{3: 16, 8, 10, 0, 4, 10, 0, 2, 4, 4, 0, 2, 4, 0, 0, 0, }, +{5: 16, 0, 2, 4, 4, 2, 4, 2, 4, 0, 8, 2, 0, 0, 0, 0, }, +{6: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 16, }, +{9: 16, 4, 4, 4, 4, 4, 4, 4, 8, 6, 6, 0, 6, 6, 0, 4, }, +{a: 16, 4, 4, 4, 6, 4, 4, 0, 4, 8, 0, 4, 6, 6, 6, 4, }, +{c: 16, 0, 0, 0, 0, 0, 8, 0, 6, 6, 4, 0, 0, 2, 2, 4, }, +{7: 16, 2, 0, 4, 4, 2, 2, 4, 0, 4, 0, 2, 0, 0, 8, 0, }, +{b: 16, 4, 4, 4, 6, 4, 0, 0, 6, 6, 0, 0, 10, 0, 0, 4, }, +{d: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 0, 0, 6, 0, 0, 0, 0, 6, 2, 8, 0, 4, 2, 4, }, +{f: 16, 0, 0, 0, 6, 0, 0, 8, 6, 0, 2, 0, 0, 2, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:24, 4:75, 6:21, 8:12, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, -8, 0, 0, -8, 0, 8, -8, -8, 0, 0, -8, }, +{2: 16, 0, -8, 8, 16, -8, 0, -8, 0, -8, 8, 0, -8, 0, -8, 0, }, +{4: 16, 0, 0, -8, 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, -8, }, +{8: 16, 8, 8, 8, -16, 8, 0, 8, -8, -8, -8, 8, -8, 0, -8, -8, }, +{3: 16, -8, -8, 8, 16, 0, -8, 0, -8, -8, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{9: 16, -8, 8, 8, -16, -8, -8, 0, 8, -8, -8, -8, 8, 8, 0, 8, }, +{a: 16, 8, -8, 8, -16, -8, 8, -8, -8, 8, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 8, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, -8, -8, 8, -16, 8, 0, 0, 8, 8, -8, 0, -8, 0, 0, 0, }, +{d: 16, 0, 0, -8, -16, 0, -8, -8, 0, 0, 8, 8, 0, 8, 8, -8, }, +{e: 16, 0, 0, -8, -16, 0, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, }, +{f: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{6: , x, x, , , , , x, x, , , x, , , x, x, }, +{9: , x, , x, , x, , , x, x, , , x, x, , x, }, +{a: , , x, x, , , , , x, x, , , x, , x, x, }, +{c: , x, x, x, , x, , , x, x, x, , x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , x, , x, , x, , , x, x, , , x, x, , x, }, +{e: , , x, , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0100,0110,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1100,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 1, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x04,}, {0x05,0x08,0x0d,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x05,0x08,0x0d,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,0x08,0x0a,}}, +{{0x03,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_265.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_265.txt new file mode 100644 index 0000000..e243b23 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_265.txt @@ -0,0 +1,474 @@ +265 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 2, }, +{3: 0, 2, 0, 4, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 2, 0, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 2, 2, 4, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 0, 2, 6, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, 0, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 6, }, +}; +Diff: 8, DDT_spectrum: {0:182, 2:44, 4:12, 6:16, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 2, 2, 0, 0, 0, 8, 0, 4, 4, 10, 4, 4, 0, 0, }, +{2: 16, 0, 10, 2, 0, 2, 10, 0, 8, 0, 8, 8, 8, 0, 8, 0, }, +{4: 16, 0, 0, 10, 0, 8, 2, 2, 4, 4, 0, 10, 0, 4, 4, 0, }, +{8: 16, 0, 0, 0, 6, 4, 8, 4, 2, 0, 0, 0, 8, 4, 10, 2, }, +{3: 16, 2, 0, 8, 4, 10, 2, 0, 0, 0, 4, 10, 4, 0, 0, 4, }, +{5: 16, 2, 10, 0, 8, 0, 10, 2, 0, 8, 0, 8, 0, 8, 0, 8, }, +{6: 16, 8, 2, 0, 4, 2, 0, 10, 4, 0, 0, 10, 0, 0, 4, 4, }, +{9: 16, 0, 8, 4, 0, 0, 0, 4, 6, 2, 0, 0, 4, 10, 2, 8, }, +{a: 16, 4, 0, 4, 0, 0, 8, 0, 0, 6, 2, 0, 10, 2, 8, 4, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 8, 4, 10, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 0, 4, 4, 0, 8, 0, 8, 2, 10, 0, 2, 6, 0, 0, }, +{e: 16, 0, 8, 4, 8, 0, 0, 4, 2, 10, 4, 0, 0, 2, 6, 0, }, +{f: 16, 0, 0, 0, 2, 4, 8, 4, 10, 4, 8, 0, 0, 0, 2, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:28, 4:40, 6:8, 8:33, 10:24, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{a: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:122, 4:108, 8:20, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, -8, -8, 8, 0, 0, 0, -8, -8, -8, 8, -8, }, +{2: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{4: 16, 0, 0, -8, 16, 8, -8, -8, 0, 0, -8, 0, 8, -8, -8, 0, }, +{8: 16, 0, 0, 8, -16, 8, 0, 8, 0, 0, -8, 8, -8, 0, -8, -8, }, +{3: 16, -8, 0, 0, 16, 8, -8, -8, -8, 0, 0, 0, 8, -8, -8, 0, }, +{5: 16, 0, 0, 0, 16, -16, 8, -8, 0, 0, 0, 0, -16, 8, -8, 0, }, +{6: 16, 0, -8, 0, 16, -8, -8, 8, 0, -8, 0, 0, -8, -8, 8, 0, }, +{9: 16, -8, 0, 0, -16, -8, 0, 8, 8, 0, 0, -8, 8, 0, -8, 8, }, +{a: 16, 8, -8, 0, -16, -8, 0, -8, -8, 8, 0, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -16, 8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, -8, 8, 0, -16, -8, 0, -8, 8, -8, 0, 0, 8, 0, 8, 0, }, +{e: 16, 8, 0, 0, -16, -8, 0, 8, -8, 0, 0, 8, 8, 0, -8, -8, }, +{f: 16, 0, 0, -8, -16, 8, 0, 8, 0, 0, 8, -8, -8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , , , x, , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 19 */ +{0011,0101,1,}, +{0110,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0101,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x04,}, {0x01,0x08,0x09,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x03,0x08,0x0b,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x03,0x08,0x0b,}}, +{{0x09,0x06,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +265 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 6, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 2, }, +{3: 0, 0, 2, 4, 0, 6, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 2, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 4, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 2, 0, 4, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 2, 0, 6, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 6, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 6, }, +}; +Diff: 8, DDT_spectrum: {0:182, 2:44, 4:12, 6:16, 8:1, 16:1, }; +Diff1: 6, DDT1_spectrum: {0:9, 2:3, 6:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 0, 0, 2, 2, 8, 0, 4, 4, 10, 4, 4, 0, 0, }, +{2: 16, 2, 10, 0, 0, 0, 10, 2, 8, 0, 8, 8, 8, 0, 8, 0, }, +{4: 16, 2, 2, 10, 0, 8, 0, 0, 4, 4, 0, 10, 0, 4, 4, 0, }, +{8: 16, 0, 0, 0, 6, 4, 8, 4, 0, 0, 2, 0, 10, 4, 8, 2, }, +{3: 16, 0, 2, 8, 4, 10, 0, 2, 0, 0, 4, 10, 4, 0, 0, 4, }, +{5: 16, 0, 10, 2, 8, 2, 10, 0, 0, 8, 0, 8, 0, 8, 0, 8, }, +{6: 16, 8, 0, 2, 4, 0, 2, 10, 4, 0, 0, 10, 0, 0, 4, 4, }, +{9: 16, 0, 8, 4, 2, 0, 0, 4, 6, 0, 0, 0, 4, 8, 2, 10, }, +{a: 16, 4, 0, 4, 0, 0, 8, 0, 2, 6, 0, 0, 8, 2, 10, 4, }, +{c: 16, 4, 8, 0, 0, 4, 0, 0, 0, 2, 6, 0, 2, 10, 4, 8, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 8, 0, 8, 4, 0, 0, 4, 10, 2, 0, 6, 2, 0, 0, }, +{d: 16, 4, 0, 4, 4, 0, 8, 0, 10, 2, 8, 0, 0, 6, 2, 0, }, +{e: 16, 0, 8, 4, 10, 0, 0, 4, 2, 8, 4, 0, 0, 0, 6, 2, }, +{f: 16, 0, 0, 0, 2, 4, 8, 4, 8, 4, 10, 0, 2, 0, 0, 6, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:92, 2:28, 4:40, 6:8, 8:33, 10:24, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 12, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:122, 4:108, 8:20, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, -8, -8, 8, -8, 0, 0, 0, -8, -8, 8, 0, }, +{2: 16, 0, 0, 0, 16, -16, 8, -8, 0, 0, 0, 0, -16, 8, -8, 0, }, +{4: 16, 0, 0, 0, 16, 8, -8, -8, 0, 0, 0, -8, 8, -8, -8, -8, }, +{8: 16, 8, 0, 0, -16, 8, 0, 8, -8, 0, 0, 8, -8, 0, -8, -8, }, +{3: 16, 0, -8, 0, 16, 8, -8, -8, 0, -8, 0, 0, 8, -8, -8, 0, }, +{5: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{6: 16, 0, 0, -8, 16, -8, -8, 8, 0, 0, -8, 0, -8, -8, 8, 0, }, +{9: 16, -8, 8, 0, -16, -8, 0, 8, 8, -8, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -16, -8, 0, -8, 0, 8, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 0, -8, -16, 8, 0, -8, 0, 0, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, 0, 8, -16, 8, 0, -8, 0, 0, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, -8, -16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 8, 0, }, +{e: 16, 8, -8, 0, -16, -8, 0, 8, -8, 8, 0, 0, 8, 0, -8, 0, }, +{f: 16, -8, 0, 0, -16, 8, 0, 8, 8, 0, 0, -8, -8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , , x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 19 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x01,0x08,0x09,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_266.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_266.txt new file mode 100644 index 0000000..f85c401 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_266.txt @@ -0,0 +1,486 @@ +266 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x05,0x04,0x06,0x07,0x0e,0x09,0x0a,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 4, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 4, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 0, 0, 4, 2, 0, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 6, 0, 2, 4, 2, 0, }, +{7: 0, 4, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 6, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:188, 2:28, 4:30, 6:4, 8:5, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 4:5, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 0, 4, 8, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 16, 0, 8, 16, 4, 8, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 16, 4, 0, 8, 8, 0, 4, 0, 6, 0, 10, 0, 2, 4, 2, 0, }, +{3: 16, 8, 8, 0, 0, 16, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 0, 16, 16, 16, 8, 8, 8, 0, 0, 0, 0, 8, }, +{6: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 4, 0, 0, 4, 0, 4, 0, 8, 2, 4, 0, 2, 0, 2, 2, }, +{a: 16, 4, 0, 8, 2, 0, 4, 0, 0, 6, 0, 0, 8, 2, 4, 10, }, +{c: 16, 4, 0, 8, 4, 0, 4, 0, 10, 0, 6, 0, 2, 8, 2, 0, }, +{7: 16, 8, 0, 0, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 0, 0, 2, 0, 4, 0, 2, 8, 2, 0, 4, 2, 0, 4, }, +{d: 16, 4, 0, 0, 0, 0, 4, 0, 4, 2, 8, 0, 2, 4, 2, 2, }, +{e: 16, 4, 0, 8, 2, 0, 4, 0, 0, 10, 0, 0, 4, 2, 8, 6, }, +{f: 16, 4, 0, 0, 2, 0, 4, 0, 2, 4, 2, 0, 0, 2, 4, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:24, 4:44, 6:4, 8:40, 10:4, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{6: 0, 4, 4, 0, 0, 0, 4, 12, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{a: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, -8, 0, 8, -8, 0, 8, -16, -8, 0, 8, -16, }, +{2: 16, 0, -8, 8, 16, 8, -8, -16, 0, -8, 8, 0, 8, -8, -16, 0, }, +{4: 16, 8, 0, -8, 16, 8, 0, -8, 8, 0, -8, -16, 8, 0, -8, -16, }, +{8: 16, 0, 8, 8, -16, 0, -8, 8, 0, -8, -8, 0, 0, 8, -8, 0, }, +{3: 16, -8, 0, 8, 16, -8, 0, -8, -8, 0, 8, 0, -8, 0, -8, 0, }, +{5: 16, -8, 0, -8, 16, -8, 0, -8, -8, 0, -8, 16, -8, 0, -8, 16, }, +{6: 16, 8, -8, -16, 16, 0, -8, 8, 8, -8, -16, 0, 0, -8, 8, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -16, 0, 8, -8, 0, 8, -8, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -8, -16, 0, -8, -8, 0, -8, 8, 0, 0, 8, 8, 0, }, +{7: 16, -8, 0, -8, 16, -8, 0, 8, -8, 0, -8, 0, -8, 0, 8, 0, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -16, 0, 8, 8, 0, 8, 8, 0, 0, -8, -8, 0, }, +{f: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , x, x, x, , , x, x, , x, x, x, , x, x, x, }, +{6: , , , , , , x, x, , , , x, , , x, x, }, +{9: , x, x, x, , , , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, , , x, x, , x, x, , x, , x, x, }, +{c: , x, , x, , , x, x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , x, , x, x, , x, , x, x, }, +{d: , x, , x, , , , x, , x, x, , , x, x, x, }, +{e: , , , , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0100,0110,1,}, +{0110,0010,1,}, +{0111,0001,1,}, +{0111,0100,1,}, +{0111,0101,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1100,0110,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +{1111,0100,1,}, +{1111,0101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,}, {0x07,0x08,0x0f,}}, +{{0x09,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +266 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x04,0x06,0x07,0x0e,0x09,0x0a,0x0b,0x0c,0x0d,0x08,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 4, 4, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 0, 8, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, 4, }, +}; +Diff: 8, DDT_spectrum: {0:188, 2:28, 4:30, 6:4, 8:5, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 4:5, 8:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 0, 4, 8, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 16, 8, 16, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 16, 0, 16, 16, 8, 0, 0, 16, 0, 8, 8, 0, 0, 0, 8, 0, }, +{8: 16, 4, 0, 4, 8, 0, 0, 0, 4, 2, 4, 0, 2, 0, 2, 2, }, +{3: 16, 8, 8, 8, 0, 16, 16, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 0, 8, 0, 4, 8, 16, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 4, 0, 4, 6, 0, 8, 0, 8, 0, 10, 0, 2, 4, 0, 2, }, +{a: 16, 4, 0, 4, 0, 0, 8, 0, 2, 6, 0, 0, 8, 2, 10, 4, }, +{c: 16, 4, 0, 4, 10, 0, 8, 0, 4, 0, 6, 0, 2, 8, 0, 2, }, +{7: 16, 8, 8, 8, 0, 0, 0, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 0, 2, 8, 2, 0, 4, 2, 4, 0, }, +{d: 16, 4, 0, 4, 4, 0, 0, 0, 0, 2, 8, 0, 2, 4, 2, 2, }, +{e: 16, 4, 0, 4, 2, 0, 0, 0, 2, 4, 2, 0, 0, 2, 8, 4, }, +{f: 16, 4, 0, 4, 0, 0, 8, 0, 2, 10, 0, 0, 4, 2, 6, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:24, 4:44, 6:4, 8:40, 10:4, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{b: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{d: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:9, 4:3, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 16, 0, -8, 8, -16, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 0, 0, 8, 16, 0, -8, -8, 0, 0, 8, -8, 0, -8, -8, -8, }, +{4: 16, 16, 0, -8, 16, 0, -8, -8, 16, 0, -8, -8, 0, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, 0, -8, 8, 16, -8, 8, -16, 0, -8, 8, 0, -8, 8, -16, 0, }, +{5: 16, -16, 0, -8, 16, 0, 8, -8, -16, 0, -8, 8, 0, 8, -8, 8, }, +{6: 16, 0, -8, -16, 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 8, -16, 8, 0, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -16, -8, 0, -8, 0, 8, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, 0, -8, 16, 0, -8, 8, 0, 0, -8, -8, 0, -8, 8, -8, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -16, -8, 0, 8, 0, 8, 8, 0, 8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, , x, x, x, x, , x, x, }, +{4: , , x, x, , , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, x, x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{5: , , x, x, , , x, x, , x, x, x, , x, x, x, }, +{6: , , x, , , , x, x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, x, x, , x, x, x, x, }, +{a: , x, x, x, , , x, x, , x, x, , x, , x, x, }, +{c: , , x, x, , , x, x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , x, , x, x, , x, , x, x, }, +{d: , , , x, , , , x, , x, x, , , x, x, x, }, +{e: , , x, , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0001,0001,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0100,0110,1,}, +{0110,0011,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0100,0,}, +{1001,0101,1,}, +{1100,0110,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x08,}, {0x08,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x01,0x08,0x09,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x01,0x08,0x09,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,}, {0x08,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x01,0x08,0x09,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_267.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_267.txt new file mode 100644 index 0000000..b0a078d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_267.txt @@ -0,0 +1,486 @@ +267 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 6, 0, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 4, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 4, }, +{7: 0, 2, 0, 2, 0, 6, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 4, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:188, 2:28, 4:30, 6:4, 8:5, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 6:1, 8:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 10, 4, 2, 8, 2, 4, 0, 4, 0, 0, 4, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 8, 16, 0, 8, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 0, }, +{3: 16, 2, 0, 10, 4, 10, 0, 2, 0, 0, 4, 8, 4, 0, 0, 4, }, +{5: 16, 10, 0, 10, 4, 2, 8, 2, 4, 0, 4, 0, 0, 4, 0, 0, }, +{6: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{9: 16, 8, 0, 0, 6, 0, 0, 0, 4, 2, 6, 0, 0, 4, 2, 0, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{7: 16, 2, 0, 10, 4, 10, 0, 2, 0, 0, 4, 8, 4, 0, 0, 4, }, +{b: 16, 0, 0, 0, 6, 8, 0, 0, 0, 2, 6, 0, 4, 0, 2, 4, }, +{d: 16, 8, 0, 0, 6, 0, 0, 0, 4, 2, 6, 0, 0, 4, 2, 0, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 0, 0, 6, 8, 0, 0, 0, 2, 6, 0, 4, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:16, 4:56, 6:8, 8:28, 10:8, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 16, -8, -8, 0, -8, 8, 0, 0, -8, -8, 0, 0, }, +{2: 16, 8, -8, 0, 16, -16, 8, -8, 8, -8, 0, 0, -16, 8, -8, 0, }, +{4: 16, 0, 8, -16, 16, 8, 0, -8, 0, 8, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 16, -16, 8, 0, 8, 0, -8, -16, 8, -8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 16, 8, -8, 0, -8, -8, 0, 0, 8, -8, 0, 0, }, +{5: 16, -8, 8, 0, 16, -8, -8, 0, -8, 8, 0, 0, -8, -8, 0, 0, }, +{6: 16, 8, -16, 0, 16, -8, 8, 0, 8, -16, 0, -8, -8, 8, 0, -8, }, +{9: 16, 0, 8, 0, -16, -8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, }, +{a: 16, 0, -8, 0, -16, -8, 0, -8, 0, 8, 0, 8, 8, 0, 8, -8, }, +{c: 16, 0, 8, -16, -16, 8, 0, -8, 0, -8, 16, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, 0, 16, 8, -8, 0, -8, -8, 0, 0, 8, -8, 0, 0, }, +{b: 16, 0, -8, 0, -16, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, }, +{d: 16, 0, 8, 0, -16, -8, 0, 0, 0, -8, 0, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +{f: 16, 0, -8, 0, -16, 8, 0, 0, 0, 8, 0, 0, -8, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , , x, x, x, , , x, }, +{5: , , x, , , x, x, , , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, , , x, , , x, , x, , x, x, , x, }, +{a: , x, x, , , x, , , , x, x, , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , , , , x, , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1100,0100,1,}, +{1100,1000,1,}, +{1100,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +267 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0c,0x09,0x0a,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 6, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, }, +{3: 0, 2, 0, 0, 0, 6, 2, 0, 0, 0, 0, 6, 0, 0, 0, 0, }, +{5: 0, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 4, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 8, 0, 2, 2, 0, 2, }, +{7: 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 2, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:188, 2:28, 4:30, 6:4, 8:5, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 6:1, 8:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 8, 8, 2, 10, 0, 8, 0, 8, 2, 0, 8, 0, 0, }, +{2: 16, 0, 16, 16, 16, 0, 0, 16, 0, 16, 16, 0, 0, 0, 16, 0, }, +{4: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 8, 4, 4, 4, 6, 4, 0, 4, 6, 6, 4, 6, }, +{3: 16, 2, 0, 8, 8, 10, 2, 0, 0, 0, 8, 10, 8, 0, 0, 8, }, +{5: 16, 8, 8, 16, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 16, 0, 4, 0, 8, 0, 0, 4, 2, 4, 0, 0, 2, 2, 4, 2, }, +{c: 16, 4, 4, 0, 0, 4, 4, 4, 6, 4, 8, 4, 6, 6, 4, 6, }, +{7: 16, 0, 8, 16, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 16, 0, 0, 4, 4, 0, }, +{e: 16, 0, 4, 0, 0, 0, 0, 4, 2, 4, 8, 0, 2, 2, 4, 2, }, +{f: 16, 0, 4, 0, 0, 4, 0, 4, 0, 4, 16, 4, 4, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:16, 4:56, 6:8, 8:28, 10:8, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 0, 0, 4, 8, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 16, -8, 0, 0, -16, 8, 0, 0, -8, 0, 0, 0, }, +{2: 16, 16, -16, 0, 16, -16, 0, 0, 16, -16, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 8, -8, 16, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, -16, 8, 8, 8, 0, -8, -8, 8, -8, -8, -8, -8, }, +{3: 16, -16, -8, 0, 16, 8, 0, 0, -16, -8, 0, 0, 8, 0, 0, 0, }, +{5: 16, 0, 8, 0, 16, -8, 0, -8, 0, 8, 0, -8, -8, 0, -8, -8, }, +{6: 16, 0, -8, 0, 16, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, 0, }, +{9: 16, 0, 8, 0, -16, -8, 0, 8, 0, -8, 0, 8, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -16, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 8, -8, -16, 8, -8, -8, 0, -8, 8, -8, -8, 8, 8, 8, }, +{7: 16, 0, -8, -8, 16, 8, -8, 0, 0, -8, -8, 0, 8, -8, 0, 0, }, +{b: 16, 0, -8, 8, -16, 8, 8, 0, 0, 8, -8, 0, -8, -8, 0, 0, }, +{d: 16, 0, 8, 0, -16, -8, 0, -8, 0, -8, 0, -8, 8, 0, 8, 8, }, +{e: 16, 0, -8, 0, -16, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{f: 16, 0, -8, -8, -16, 8, -8, 0, 0, 8, 8, 0, -8, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , x, x, x, x, , x, }, +{2: , , x, x, , x, , x, , x, x, x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , x, x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , x, , x, x, , x, }, +{a: , , , x, , x, , , , x, x, , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 13, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_268.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_268.txt new file mode 100644 index 0000000..37406a5 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_268.txt @@ -0,0 +1,486 @@ +268 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 2, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 4, }, +{3: 0, 2, 0, 6, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:188, 2:28, 4:30, 6:4, 8:5, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 2, 0, 2, 0, 10, 0, 8, 8, 8, 8, 8, 0, 0, }, +{2: 16, 0, 16, 0, 0, 0, 16, 0, 16, 0, 16, 16, 16, 0, 16, 0, }, +{4: 16, 0, 8, 8, 0, 8, 8, 0, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 16, 0, 4, 4, }, +{3: 16, 2, 0, 10, 8, 10, 0, 2, 0, 0, 8, 8, 8, 0, 0, 8, }, +{5: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 8, 0, 0, 0, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{a: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 16, 4, 4, 0, }, +{c: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 8, 0, 0, 6, 4, 6, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 0, 0, 8, 6, 4, 6, }, +{d: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 16, 0, 0, 4, 4, 0, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{f: 16, 0, 4, 4, 4, 4, 4, 0, 4, 0, 16, 0, 0, 0, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:16, 4:56, 6:8, 8:28, 10:8, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 8, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 8, 8, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{a: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{c: 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, }, +{7: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:5, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, -8, -16, 8, 0, 0, 0, 0, -8, -16, 8, 0, }, +{2: 16, 0, 0, 0, 16, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, }, +{4: 16, -8, 0, -8, 16, 8, 0, -8, -8, 0, -8, 0, 8, 0, -8, 0, }, +{8: 16, -8, 0, 8, -16, 8, 0, 8, 8, 0, -8, 0, -8, 0, -8, 0, }, +{3: 16, 0, 0, 0, 16, 8, -16, -8, 0, 0, 0, 0, 8, -16, -8, 0, }, +{5: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{6: 16, 0, -8, 0, 16, -8, 0, 8, 0, -8, 0, -8, -8, 0, 8, -8, }, +{9: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 0, -16, -8, 0, -8, 0, 8, 0, 8, 8, 0, 8, -8, }, +{c: 16, 8, 8, -8, -16, 8, 0, -8, -8, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, -8, -8, 8, -16, 8, 0, -8, 8, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, 0, -16, -8, 0, -8, 0, -8, 0, -8, 8, 0, 8, 8, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 8, 0, -8, -16, 8, 0, 8, -8, 0, 8, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , , x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , x, x, x, x, x, x, , x, x, x, }, +{d: , x, , x, , , x, x, x, x, x, x, x, , x, x, }, +{e: , x, x, x, , , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0011,0010,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 19, 13, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x05,0x08,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +268 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +{3: 0, 2, 0, 4, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 6, 0, 0, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 8, DDT_spectrum: {0:188, 2:28, 4:30, 6:4, 8:5, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 2:1, 4:2, 6:1, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 0, 0, 0, 2, 2, 8, 0, 4, 4, 10, 4, 4, 0, 0, }, +{2: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 2, 0, 8, 4, 10, 2, 0, 0, 0, 4, 10, 4, 0, 0, 4, }, +{8: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 6, 0, 6, 0, 2, 4, }, +{3: 16, 2, 0, 8, 4, 10, 2, 0, 0, 0, 4, 10, 4, 0, 0, 4, }, +{5: 16, 0, 16, 8, 4, 0, 8, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 10, 0, 0, 0, 2, 2, 8, 0, 4, 4, 10, 4, 4, 0, 0, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 8, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 6, 4, 2, 0, }, +{c: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 16, 0, 16, 8, 0, 0, 8, 16, 0, 0, 8, 0, 0, 0, }, +{d: 16, 8, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 6, 4, 2, 0, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 0, 0, 4, 8, 0, 0, 2, 0, 6, 0, 6, 0, 2, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:16, 4:56, 6:8, 8:28, 10:8, 16:44, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{a: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 8, }, +{7: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:5, 8:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, -8, -8, 8, -8, 0, 0, 0, -8, -8, 8, 0, }, +{2: 16, 8, -8, 0, 16, -16, 8, -8, 8, -8, 0, 0, -16, 8, -8, 0, }, +{4: 16, -8, 0, 0, 16, 8, -8, -8, -8, 0, 0, 0, 8, -8, -8, 0, }, +{8: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{3: 16, -8, 0, 0, 16, 8, -8, -8, -8, 0, 0, 0, 8, -8, -8, 0, }, +{5: 16, 8, 0, 0, 16, -8, 8, -16, 8, 0, 0, -8, -8, 8, -16, -8, }, +{6: 16, -8, 0, 0, 16, -8, -8, 8, -8, 0, 0, 0, -8, -8, 8, 0, }, +{9: 16, 0, 8, 0, -16, -8, 0, 8, 0, -8, 0, 8, 8, 0, -8, -8, }, +{a: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, -16, -16, 8, 0, -8, 0, -8, 16, -8, -8, 0, 8, 8, }, +{7: 16, 0, -8, -16, 16, 8, 0, 8, 0, -8, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 16, -16, 8, 0, -8, 0, 8, -16, 8, -8, 0, 8, -8, }, +{d: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +{f: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, , , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , x, x, , , , x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0011,0010,1,}, +{0100,0111,1,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1100,0111,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_269.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_269.txt new file mode 100644 index 0000000..8f781f3 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_269.txt @@ -0,0 +1,478 @@ +269 Sbox: +LUT = { +0x01,0x00,0x04,0x06,0x02,0x05,0x03,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 2, 4, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 4, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 2, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 4, 2, 0, }, +{d: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 2, 0, 8, 0, 0, 0, 0, 4, 2, 0, 4, 4, 4, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{3: 16, 8, 8, 2, 0, 8, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 16, 0, 10, 2, 4, 2, 10, 0, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 16, 0, 10, 8, 0, 2, 0, 10, 4, 0, 0, 2, 4, 4, 0, 4, }, +{9: 16, 0, 4, 0, 2, 0, 0, 4, 8, 2, 2, 0, 4, 0, 2, 4, }, +{a: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{c: 16, 4, 4, 0, 2, 0, 0, 0, 2, 2, 8, 0, 2, 4, 4, 0, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 4, 4, 2, 2, 0, 8, 4, 2, 0, }, +{d: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 16, 0, 4, }, +{e: 16, 4, 4, 0, 2, 0, 0, 0, 2, 2, 4, 0, 2, 0, 8, 4, }, +{f: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:42, 4:60, 8:21, 10:10, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, 0, 8, -8, -8, 0, -8, 0, 0, 8, -8, 0, }, +{6: 16, 8, -8, -8, 16, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 0, 0, -16, 0, 0, 8, 0, 0, 0, -8, 0, 0, -8, 8, }, +{a: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 8, }, +{c: 16, 0, 8, 0, -16, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{e: 16, 0, -8, 0, -16, 0, 0, 8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, , , , x, x, , , x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , x, , x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0011,0010,1,}, +{0011,1101,0,}, +{0011,1111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1011,1101,1,}, +{1011,1111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x03,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +269 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x06,0x02,0x05,0x03,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 2, 4, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 2, 0, 0, 0, 2, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 4, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 2, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 4, 4, 2, 0, }, +{d: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 4:2, 6:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 2, 0, 8, 0, 0, 0, 0, 4, 2, 0, 4, 4, 4, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{3: 16, 8, 8, 2, 0, 8, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 16, 0, 10, 2, 4, 2, 10, 0, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 16, 0, 10, 8, 0, 2, 0, 10, 4, 0, 0, 2, 4, 4, 0, 4, }, +{9: 16, 0, 4, 0, 2, 0, 0, 4, 8, 2, 2, 0, 4, 0, 2, 4, }, +{a: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{c: 16, 4, 4, 0, 2, 0, 0, 0, 2, 2, 8, 0, 2, 4, 4, 0, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 0, 4, 4, 2, 2, 0, 8, 4, 2, 0, }, +{d: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 16, 0, 4, }, +{e: 16, 4, 4, 0, 2, 0, 0, 0, 2, 2, 4, 0, 2, 0, 8, 4, }, +{f: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:42, 4:60, 8:21, 10:10, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, 0, 8, -8, -8, 0, -8, 0, 0, 8, -8, 0, }, +{6: 16, 8, -8, -8, 16, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 0, 0, -16, 0, 0, 8, 0, 0, 0, -8, 0, 0, -8, 8, }, +{a: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 8, }, +{c: 16, 0, 8, 0, -16, 0, 0, -8, 0, -8, 0, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, 8, 0, 0, 8, -8, }, +{d: 16, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{e: 16, 0, -8, 0, -16, 0, 0, 8, 0, 8, 0, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, , , , x, x, , , x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , x, , x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0011,0010,1,}, +{0011,1101,0,}, +{0011,1111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1011,1101,1,}, +{1011,1111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x02,0x08,0x0a,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x03,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_270.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_270.txt new file mode 100644 index 0000000..0b31d5f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_270.txt @@ -0,0 +1,478 @@ +270 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0d,0x08,0x09,0x0b,0x0c,0x0a,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 10, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 2, 0, 0, 4, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 4, 2, 0, 0, 2, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 6, }, +{7: 0, 2, 2, 2, 0, 4, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 2, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 4, 6, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 4, 2, 2, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 4, 0, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:7, 2:3, 4:5, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 2, 8, 0, 2, 2, 4, 4, 0, 2, 0, 0, 0, 0, }, +{2: 16, 0, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 16, 0, 4, 4, }, +{4: 16, 2, 2, 4, 8, 0, 2, 2, 0, 0, 4, 4, 0, 0, 0, 4, }, +{8: 16, 8, 4, 4, 10, 4, 4, 8, 10, 4, 4, 8, 4, 4, 10, 10, }, +{3: 16, 4, 0, 2, 4, 4, 2, 2, 8, 4, 0, 2, 0, 0, 0, 0, }, +{5: 16, 2, 2, 2, 8, 0, 4, 4, 0, 0, 0, 2, 0, 4, 4, 0, }, +{6: 16, 2, 2, 0, 4, 4, 2, 2, 0, 0, 4, 4, 0, 0, 0, 8, }, +{9: 16, 4, 8, 0, 10, 4, 0, 0, 6, 8, 2, 0, 4, 2, 0, 0, }, +{a: 16, 0, 0, 0, 4, 16, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 0, 8, 10, 4, 0, 0, 0, 2, 8, 4, 4, 2, 0, 6, }, +{7: 16, 2, 2, 2, 4, 4, 0, 4, 0, 0, 0, 2, 0, 4, 8, 0, }, +{b: 16, 4, 4, 0, 4, 0, 0, 0, 8, 0, 2, 0, 4, 2, 2, 2, }, +{d: 16, 0, 0, 0, 10, 4, 8, 4, 0, 2, 2, 0, 4, 8, 6, 0, }, +{e: 16, 0, 0, 4, 4, 0, 0, 0, 2, 2, 0, 4, 4, 2, 2, 8, }, +{f: 16, 0, 0, 0, 4, 0, 4, 4, 2, 2, 2, 0, 4, 0, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:42, 4:69, 6:3, 8:18, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 0, 8, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:4, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{2: 16, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{4: 16, 0, 0, -8, 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, -8, }, +{8: 16, 8, 8, 8, -16, 8, 8, 16, -8, -8, -8, 8, -8, -8, -16, -8, }, +{3: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +{6: 16, -8, -8, 0, 16, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 8, -16, -8, 0, 0, 0, -8, -8, -8, 8, 0, 0, 8, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, -8, -16, 8, 8, 0, 0, 0, 8, -8, -8, -8, 0, 8, }, +{7: 16, 0, -8, 0, 16, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, 0, }, +{b: 16, -8, 0, 0, -16, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{d: 16, 8, 0, -8, -16, -8, 0, 0, -8, 0, 8, 8, 8, 0, 0, -8, }, +{e: 16, -8, -8, 0, -16, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, -8, 0, -16, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{5: , x, x, , , , x, , x, x, , x, , x, , x, }, +{6: , x, x, x, , , x, x, , x, x, x, , x, x, x, }, +{9: , x, , , , , x, , x, x, x, , x, x, , x, }, +{a: , x, x, x, , , x, , x, x, x, , x, x, x, x, }, +{c: , x, x, x, , , x, , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, x, x, , x, x, , x, }, +{d: , , , , , , , , x, x, , , , x, , x, }, +{e: , x, x, x, , , x, , , x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x08,0x0a,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0e,}, {0x01,0x08,0x09,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +270 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x09,0x0a,0x0d,0x0b,0x0c,0x08,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 2, 0, 4, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 4, 4, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{4: 0, 2, 4, 4, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 10, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 2, 4, 2, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 2, 0, 0, 2, 2, 2, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 2, 2, 0, 2, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 4, 2, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:48, 4:29, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:7, 2:3, 4:5, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 2, 8, 4, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{2: 16, 4, 4, 2, 4, 0, 2, 2, 8, 0, 0, 2, 4, 0, 0, 0, }, +{4: 16, 2, 4, 4, 4, 2, 2, 0, 0, 0, 8, 2, 0, 0, 4, 0, }, +{8: 16, 8, 4, 8, 10, 4, 8, 4, 10, 4, 10, 4, 4, 10, 4, 4, }, +{3: 16, 0, 4, 0, 4, 4, 0, 4, 4, 16, 4, 4, 0, 4, 0, 0, }, +{5: 16, 2, 4, 2, 4, 2, 4, 2, 0, 0, 0, 0, 0, 8, 0, 4, }, +{6: 16, 2, 0, 2, 8, 2, 4, 2, 0, 0, 0, 4, 0, 4, 0, 4, }, +{9: 16, 4, 4, 0, 10, 8, 0, 0, 6, 4, 0, 0, 8, 0, 2, 2, }, +{a: 16, 4, 0, 0, 4, 4, 0, 0, 8, 4, 2, 0, 0, 2, 2, 2, }, +{c: 16, 0, 0, 4, 4, 0, 0, 4, 2, 4, 8, 0, 2, 2, 0, 2, }, +{7: 16, 2, 0, 4, 8, 2, 2, 4, 0, 0, 4, 2, 0, 0, 4, 0, }, +{b: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 0, 0, 4, 0, 4, 0, 2, 4, 2, 4, 2, 8, 2, 0, }, +{e: 16, 0, 4, 0, 10, 0, 4, 0, 0, 4, 0, 8, 2, 6, 2, 8, }, +{f: 16, 0, 4, 4, 10, 0, 0, 8, 0, 4, 6, 0, 2, 0, 8, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:42, 4:69, 6:3, 8:18, 10:7, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{2: 0, 4, 8, 8, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 8, 4, 0, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 8, 4, 4, 4, 0, 4, }, +{c: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 8, 4, }, +{7: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:96, 8:32, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:4, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, 0, -8, 0, -8, 0, 0, 0, 0, -8, 0, 0, }, +{2: 16, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{4: 16, 0, 0, 0, 16, 0, 0, -8, 0, 0, 0, -8, 0, 0, -8, -8, }, +{8: 16, 8, 16, 8, -16, 8, 8, 8, -8, -16, -8, 8, -8, -8, -8, -8, }, +{3: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 16, -8, 0, -8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{6: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{9: 16, -8, 0, 8, -16, 0, -8, 8, 8, 0, -8, 0, 0, 8, -8, 0, }, +{a: 16, 0, 0, 0, -16, -8, 0, 0, 0, 0, 0, -8, 8, 0, 0, 8, }, +{c: 16, 0, 0, 0, -16, 0, 0, -8, 0, 0, 0, -8, 0, 0, 8, 8, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{e: 16, -8, 0, -8, -16, 0, 8, 0, 8, 0, 8, 8, 0, -8, 0, -8, }, +{f: 16, 8, 0, -8, -16, 8, -8, 0, -8, 0, 8, 0, -8, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , x, , x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, x, , x, , x, x, x, x, , x, }, +{5: , x, x, x, , , x, , x, x, x, x, , , , x, }, +{6: , x, x, x, , , x, x, , x, x, x, , x, x, x, }, +{9: , x, , , , , x, , x, x, x, , x, x, , x, }, +{a: , x, , x, , , x, , x, x, x, , x, x, x, x, }, +{c: , x, , x, , , x, , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , , x, , x, , x, , x, x, , x, }, +{d: , x, , , , , x, , x, x, x, , , , , x, }, +{e: , x, , x, , , x, , , x, x, , , x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0010,0011,1,}, +{0010,1000,0,}, +{0010,1011,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0011,1,}, +{1010,1000,1,}, +{1010,1011,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x02,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x08,}, {0x02,0x08,0x0a,}}, +{{0x07,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x02,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_271.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_271.txt new file mode 100644 index 0000000..1902510 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_271.txt @@ -0,0 +1,470 @@ +271 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x08,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 0, }, +{8: 0, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 2, 0, 4, 2, 4, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 0, 2, 2, 4, 4, 0, 2, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 4, 4, 0, 0, 0, }, +{b: 0, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 4, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:180, 2:36, 4:35, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:3, 4:3, 6:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 0, 4, 8, 0, 0, 4, 4, 0, 0, 4, 2, 2, 0, }, +{2: 16, 10, 10, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 10, 10, 8, }, +{4: 16, 0, 4, 4, 2, 0, 2, 8, 0, 2, 0, 2, 4, 4, 0, 0, }, +{8: 16, 4, 4, 4, 4, 0, 0, 0, 16, 0, 0, 4, 4, 4, 4, 0, }, +{3: 16, 8, 8, 0, 0, 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, 4, 2, 2, 0, 4, 2, 4, 2, 0, 8, 0, 0, 4, 0, }, +{6: 16, 0, 4, 8, 2, 0, 2, 4, 4, 2, 0, 2, 0, 4, 0, 0, }, +{9: 16, 4, 4, 2, 8, 0, 2, 2, 4, 4, 0, 2, 0, 0, 0, 0, }, +{a: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 16, 4, 4, 0, }, +{c: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 16, }, +{7: 16, 0, 4, 2, 2, 0, 8, 2, 0, 2, 0, 4, 4, 0, 4, 0, }, +{b: 16, 4, 4, 2, 4, 0, 2, 2, 0, 8, 0, 2, 4, 0, 0, 0, }, +{d: 16, 2, 10, 0, 0, 0, 4, 0, 4, 0, 8, 4, 4, 2, 10, 0, }, +{e: 16, 2, 10, 4, 0, 0, 0, 4, 4, 0, 0, 0, 4, 10, 2, 8, }, +{f: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:30, 4:60, 8:24, 10:10, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 0, 4, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 8, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 8, LAT1_spectrum: {4:11, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 16, -8, -8, 8, -8, -16, }, +{4: 16, 0, 0, 0, 0, 8, 0, -8, 0, 8, -16, 0, 0, 0, 0, -8, }, +{8: 16, 0, 8, 0, 0, 8, 0, 8, 0, -8, -16, -8, 8, 0, -8, -8, }, +{3: 16, -8, 0, 0, 0, 8, -8, 0, -8, 0, 16, -8, -8, -8, 0, 8, }, +{5: 16, 0, 8, 0, 0, -8, 0, 0, 0, 0, -16, 0, 0, 0, -8, 8, }, +{6: 16, 0, 0, 0, 0, -8, 0, 8, 0, -8, -16, 0, 0, 0, 0, 8, }, +{9: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, -8, 8, 0, 0, 8, }, +{a: 16, 0, -8, 0, 0, -8, 0, -8, 0, 8, -16, 8, -8, 0, 8, 8, }, +{c: 16, -8, 0, -8, -8, 8, 0, -8, 0, -8, 16, 0, 0, -8, 0, 8, }, +{7: 16, 0, -8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, 8, -8, }, +{b: 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, -16, 8, -8, 0, 0, -8, }, +{d: 16, 8, 0, -8, -8, -8, -8, 0, -8, 0, 16, 0, 0, 8, 0, -8, }, +{e: 16, -8, 0, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, -8, 0, -8, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, -8, 0, 16, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, x, x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , x, , x, x, x, x, , , x, , , , x, , x, }, +{e: , x, x, x, x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0011,0010,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 4, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x0c,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +271 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x08,0x0a,0x06,0x07,0x04,0x09,0x05,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{2: 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, }, +{4: 0, 0, 0, 4, 4, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 4, 0, 2, 2, 0, 0, 0, 2, 4, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 0, 0, 4, 2, 2, 4, 0, 0, 2, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 4, 2, 4, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 0, 2, 2, 4, 4, 0, 2, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 2, 4, 0, 0, 2, 2, 0, 0, 4, 2, 0, 0, 0, }, +{b: 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 2, 6, 0, }, +{e: 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 4, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:180, 2:36, 4:35, 6:3, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:3, 4:3, 6:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 0, 4, 8, 0, 0, 4, 4, 0, 0, 4, 2, 2, 0, }, +{2: 16, 10, 10, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 10, 10, 8, }, +{4: 16, 0, 4, 4, 4, 0, 2, 8, 2, 0, 0, 2, 2, 0, 4, 0, }, +{8: 16, 4, 4, 2, 4, 0, 2, 2, 8, 0, 0, 2, 4, 0, 0, 0, }, +{3: 16, 8, 8, 0, 0, 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, }, +{5: 16, 0, 4, 2, 0, 0, 4, 2, 2, 4, 0, 8, 2, 4, 0, 0, }, +{6: 16, 0, 4, 8, 0, 0, 2, 4, 2, 4, 0, 2, 2, 0, 4, 0, }, +{9: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 16, 4, 4, 2, 0, 0, 2, 2, 4, 4, 0, 2, 8, 0, 0, 0, }, +{c: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, 0, 16, }, +{7: 16, 0, 4, 2, 4, 0, 8, 2, 2, 0, 0, 4, 2, 4, 0, 0, }, +{b: 16, 4, 4, 4, 4, 0, 0, 0, 0, 16, 0, 4, 4, 4, 4, 0, }, +{d: 16, 2, 10, 4, 4, 0, 0, 4, 0, 4, 8, 0, 0, 2, 10, 0, }, +{e: 16, 2, 10, 0, 4, 0, 4, 0, 0, 4, 0, 4, 0, 10, 2, 8, }, +{f: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:30, 4:60, 8:24, 10:10, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{4: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{8: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{b: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 0, 4, 4, 4, 4, 0, 8, 0, 8, 0, 0, 4, 4, 4, 4, 0, }, +{e: 0, 4, 0, 4, 4, 4, 0, 4, 0, 4, 0, 0, 8, 4, 8, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:118, 4:110, 8:24, 12:2, 16:2, }; +Lin1: 8, LAT1_spectrum: {4:11, 8:5, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 8, -16, 8, -8, 8, -8, 16, -8, -8, 8, -8, -16, }, +{4: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 0, 0, 0, 8, 0, 0, 0, 0, -16, 8, -8, 0, 0, -8, }, +{3: 16, -8, 0, 0, 0, 8, -8, 0, -8, 0, 16, -8, -8, -8, 0, 8, }, +{5: 16, 0, 0, 0, 0, -8, 0, -8, 0, 8, -16, 0, 0, 0, 0, 8, }, +{6: 16, 0, -8, 0, 0, -8, 0, 0, 0, 0, -16, 0, 0, 0, 8, 8, }, +{9: 16, 0, 8, 0, 0, -8, 0, 8, 0, -8, -16, 8, -8, 0, -8, 8, }, +{a: 16, 0, 0, 0, 0, -8, 0, 0, 0, 0, -16, -8, 8, 0, 0, 8, }, +{c: 16, -8, 0, -8, -8, 8, 0, -8, 0, -8, 16, 0, 0, -8, 0, 8, }, +{7: 16, 0, 0, 0, 0, 8, 0, 8, 0, -8, -16, 0, 0, 0, 0, -8, }, +{b: 16, 0, -8, 0, 0, 8, 0, -8, 0, 8, -16, -8, 8, 0, 8, -8, }, +{d: 16, 8, 0, -8, -8, -8, -8, 0, -8, 0, 16, 0, 0, 8, 0, -8, }, +{e: 16, -8, 0, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, -8, 0, -8, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, -8, 0, 16, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, x, , x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, x, , , x, , x, x, , , x, }, +{5: , x, x, x, x, , x, , , x, , x, , x, , x, }, +{6: , x, x, x, x, x, x, x, , x, , x, , , x, x, }, +{9: , x, x, x, x, , x, , x, x, , , x, x, , x, }, +{a: , x, x, x, x, x, x, , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, x, , , x, x, , , x, x, x, }, +{7: , x, x, , , , x, , , x, , x, , , , x, }, +{b: , x, x, , , , x, , , x, , , x, , , x, }, +{d: , x, , x, x, , x, , , x, , , , x, , x, }, +{e: , x, x, x, x, x, x, , , x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 17 */ +{0011,0010,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 17, 4, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x0c,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x0c,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x09,0x0a,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x0c,}}, +{{0x03,0x04,}, {0x0c,}}, +{{0x09,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x05,0x09,0x0c,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x0c,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x0c,}}, +{{0x05,0x06,}, {0x0c,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_272.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_272.txt new file mode 100644 index 0000000..b798fbc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_272.txt @@ -0,0 +1,486 @@ +272 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 2, 2, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 10, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 6, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 2, 4, 0, 2, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 4, 0, 0, 2, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 4, }, +}; +Diff: 10, DDT_spectrum: {0:184, 2:40, 4:17, 6:11, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 2, 4, 8, 0, 0, 4, 4, 0, 2, 4, 0, 0, 0, }, +{2: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 0, 8, 10, 8, 0, 2, 10, 0, 8, 8, 2, 0, 0, 8, 0, }, +{8: 16, 8, 4, 4, 16, 4, 4, 8, 8, 4, 4, 0, 4, 4, 8, 0, }, +{3: 16, 10, 8, 0, 8, 10, 2, 0, 8, 8, 0, 2, 8, 0, 0, 0, }, +{5: 16, 2, 10, 0, 4, 0, 10, 2, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 16, 0, 10, 8, 4, 2, 0, 10, 0, 4, 4, 2, 0, 0, 4, 0, }, +{9: 16, 8, 4, 0, 4, 4, 0, 0, 6, 8, 0, 0, 10, 2, 0, 2, }, +{a: 16, 8, 4, 4, 4, 4, 4, 8, 4, 16, 8, 0, 8, 0, 4, 4, }, +{c: 16, 0, 4, 4, 8, 0, 0, 8, 0, 4, 6, 0, 0, 2, 10, 2, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 4, 0, 8, 4, 0, 0, 10, 4, 0, 0, 6, 2, 0, 2, }, +{d: 16, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 8, 2, 4, }, +{e: 16, 0, 4, 4, 4, 0, 0, 8, 0, 8, 10, 0, 0, 2, 6, 2, }, +{f: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:78, 2:30, 4:56, 6:4, 8:37, 10:18, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:1, 12:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, 0, -8, 0, -8, 0, 8, -8, 0, -8, 0, -8, }, +{2: 16, 8, -8, 8, 16, -8, 8, -16, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 8, 0, -16, 16, 0, -8, 0, 8, 0, -16, 0, 0, -8, 0, 0, }, +{8: 16, 8, 8, 8, -16, 0, 0, 16, -8, -8, -8, 8, 0, 0, -16, -8, }, +{3: 16, -16, 0, 8, 16, 0, -8, 0, -16, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, -8, 8, 0, -8, 0, -8, 0, -8, 8, 0, 0, }, +{6: 16, 8, -8, -8, 16, 0, -8, 0, 8, -8, -8, 0, 0, -8, 0, 0, }, +{9: 16, -8, 0, 8, -16, -8, 0, 0, 8, 0, -8, -8, 8, 0, 0, 8, }, +{a: 16, 8, -8, 8, -16, 0, 0, -16, -8, 8, -8, -8, 0, 0, 16, 8, }, +{c: 16, 8, 8, -8, -16, 8, 0, 0, -8, -8, 8, 0, -8, 0, 0, 0, }, +{7: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{b: 16, -8, 0, 8, -16, 8, 0, 0, 8, 0, -8, 8, -8, 0, 0, -8, }, +{d: 16, -8, 0, -8, -16, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, -8, -8, -16, -8, 0, 0, -8, 8, 8, 0, 8, 0, 0, 0, }, +{f: 16, -8, 0, -8, -16, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , , , x, x, , , x, }, +{5: , x, x, , , , x, , , x, , x, , x, , x, }, +{6: , x, , , , , , x, , , , x, , , x, x, }, +{9: , x, x, x, , , , , x, x, , , x, x, , x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, , , , , , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, , , , , , , , x, , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0001,0011,1,}, +{0100,0100,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0011,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 8, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +272 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 6, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, }, +{3: 0, 4, 2, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 0, 6, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 0, 0, 2, 2, 2, }, +{7: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 4, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 4, }, +}; +Diff: 10, DDT_spectrum: {0:184, 2:40, 4:17, 6:11, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 0, 8, 10, 2, 0, 8, 8, 0, 2, 8, 0, 0, 0, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 2, 10, 10, 4, 0, 0, 8, 0, 4, 4, 2, 0, 0, 4, 0, }, +{8: 16, 4, 4, 8, 16, 8, 4, 4, 4, 4, 8, 0, 8, 4, 4, 0, }, +{3: 16, 8, 10, 0, 4, 10, 0, 2, 4, 4, 0, 2, 4, 0, 0, 0, }, +{5: 16, 0, 10, 2, 4, 2, 10, 0, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 16, 0, 8, 10, 8, 0, 2, 10, 0, 8, 8, 2, 0, 0, 8, 0, }, +{9: 16, 4, 4, 0, 8, 8, 0, 0, 6, 4, 0, 0, 10, 2, 0, 2, }, +{a: 16, 4, 4, 8, 4, 8, 4, 4, 8, 16, 4, 0, 4, 0, 8, 4, }, +{c: 16, 0, 4, 8, 4, 0, 0, 4, 0, 8, 6, 0, 0, 2, 10, 2, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 4, 8, 0, 0, 10, 8, 0, 0, 6, 2, 0, 2, }, +{d: 16, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 8, 2, 4, }, +{e: 16, 0, 4, 8, 8, 0, 0, 4, 0, 4, 10, 0, 0, 2, 6, 2, }, +{f: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:78, 2:30, 4:56, 6:4, 8:37, 10:18, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{b: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:1, 12:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 16, 0, -8, 0, -16, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 8, 0, -8, 16, 0, -8, 0, 8, 0, -8, -8, 0, -8, 0, -8, }, +{8: 16, 8, 8, 8, -16, 16, 0, 0, -8, -8, -8, 8, -16, 0, 0, -8, }, +{3: 16, -8, -8, 8, 16, 0, -8, 0, -8, -8, 8, 0, 0, -8, 0, 0, }, +{5: 16, -8, 0, -8, 16, 0, 8, -8, -8, 0, -8, 0, 0, 8, -8, 0, }, +{6: 16, 8, 0, -16, 16, 0, -8, 0, 8, 0, -16, 0, 0, -8, 0, 0, }, +{9: 16, -8, 8, 8, -16, 0, 0, 8, 8, -8, -8, 0, 0, 0, -8, 0, }, +{a: 16, 8, -8, 8, -16, -16, 0, 0, -8, 8, -8, -8, 16, 0, 0, 8, }, +{c: 16, 8, 0, -8, -16, 0, 0, -8, -8, 0, 8, -8, 0, 0, 8, 8, }, +{7: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{b: 16, -8, -8, 8, -16, 0, 0, -8, 8, 8, -8, 0, 0, 0, 8, 0, }, +{d: 16, -8, 0, -8, -16, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{e: 16, 8, 0, -8, -16, 0, 0, 8, -8, 0, 8, 8, 0, 0, -8, -8, }, +{f: 16, -8, 0, -8, -16, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , x, x, , , , , x, , , , x, , , x, x, }, +{9: , , , x, , , , , x, x, , , x, x, , x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, x, x, , , , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0001,0001,1,}, +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{0100,0110,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +{1100,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 8, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x03,0x08,0x0b,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_273.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_273.txt new file mode 100644 index 0000000..468f1bc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_273.txt @@ -0,0 +1,486 @@ +273 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x04,0x06,0x07,0x05,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, }, +{2: 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 0, 10, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 6, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 0, 4, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 4, 2, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 4, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 2, 0, 0, 2, 0, 6, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 2, 2, }, +{7: 0, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 6, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:184, 2:40, 4:17, 6:11, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:1, 4:1, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{2: 16, 8, 10, 8, 0, 10, 8, 8, 0, 0, 0, 8, 0, 0, 2, 2, }, +{4: 16, 4, 4, 10, 4, 8, 4, 4, 10, 10, 4, 10, 4, 8, 8, 4, }, +{8: 16, 4, 0, 10, 6, 0, 4, 0, 8, 0, 4, 2, 2, 8, 0, 0, }, +{3: 16, 8, 10, 4, 0, 10, 4, 4, 0, 0, 0, 4, 0, 0, 2, 2, }, +{5: 16, 4, 4, 4, 8, 8, 16, 8, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 16, 4, 4, 10, 0, 8, 4, 6, 2, 0, 0, 8, 2, 0, 0, 0, }, +{9: 16, 4, 0, 4, 10, 0, 8, 0, 6, 2, 4, 0, 2, 8, 0, 0, }, +{a: 16, 4, 0, 10, 2, 0, 4, 2, 0, 6, 0, 0, 8, 0, 4, 8, }, +{c: 16, 8, 0, 8, 8, 0, 8, 0, 8, 0, 10, 0, 0, 10, 2, 2, }, +{7: 16, 4, 4, 4, 0, 8, 8, 10, 0, 2, 0, 6, 2, 0, 0, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 2, 2, 8, 0, 2, 4, 0, 4, 0, }, +{d: 16, 8, 0, 4, 4, 0, 4, 0, 4, 0, 10, 0, 0, 10, 2, 2, }, +{e: 16, 0, 2, 8, 0, 2, 0, 0, 0, 4, 2, 0, 4, 2, 4, 4, }, +{f: 16, 0, 2, 4, 0, 2, 4, 0, 0, 8, 2, 0, 0, 2, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:76, 2:30, 4:59, 6:5, 8:36, 10:17, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 0, 12, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{8: 0, 4, 0, 4, 12, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 8, 8, -8, -8, 0, -8, 0, 16, -16, -16, 0, 8, -8, }, +{2: 16, 0, -16, 8, 8, 0, 0, -8, 0, -8, 16, 0, 0, 0, -16, 0, }, +{4: 16, 8, 8, -8, 8, 8, -8, -8, 8, 8, -16, -16, 16, -8, -8, -8, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, 0, -8, -16, 0, 0, 0, -8, -8, }, +{3: 16, -8, -8, 8, 8, 0, -8, 0, -8, 0, 16, 0, 0, -8, -8, 0, }, +{5: 16, 0, 8, -8, 8, -8, 8, 0, -8, 0, -16, 16, -16, 0, -8, 8, }, +{6: 16, 0, -8, -8, 8, 0, -8, 8, 8, -8, -16, 0, 0, 0, 8, 0, }, +{9: 16, -8, 8, 8, -8, -8, 0, 0, 0, 0, -16, 0, 0, 8, -8, 8, }, +{a: 16, 8, -8, 8, -8, 0, 0, -8, 0, 8, -16, 0, 0, -8, 8, 0, }, +{c: 16, 0, 8, -16, -16, 0, 0, -8, 0, -8, 16, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -8, 8, 0, 8, 0, -8, 0, -16, 0, 0, 8, 8, 0, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0, }, +{d: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, -8, 8, -8, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , x, , x, x, x, x, , , , , x, x, , , x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, , x, x, , , , x, , , x, x, }, +{9: , x, x, x, x, , x, , x, , , , x, x, , x, }, +{a: , x, , x, x, , x, , , x, , , x, , x, x, }, +{c: , x, x, , , , x, , , , x, , , x, x, x, }, +{7: , x, , x, x, , x, , , , , x, , , , x, }, +{b: , x, , x, x, , x, , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0010,0010,1,}, +{0100,1100,1,}, +{0111,0001,1,}, +{0111,0100,1,}, +{0111,0101,0,}, +{1000,1100,1,}, +{1011,0001,1,}, +{1011,0100,0,}, +{1011,0101,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 8, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x03,0x08,}, {0x0c,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x06,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0a,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0a,}, {0x0c,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +273 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x08,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 4, 6, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{4: 0, 0, 0, 10, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 4, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 6, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 6, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 2, 4, 0, 0, 2, 6, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 0, 2, 6, 0, 2, 4, 0, 0, 0, }, +{c: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 2, 2, }, +{e: 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:184, 2:40, 4:17, 6:11, 8:2, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 2:1, 4:1, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{2: 16, 8, 10, 4, 0, 10, 4, 4, 0, 0, 0, 4, 0, 0, 2, 2, }, +{4: 16, 4, 8, 10, 10, 4, 4, 10, 4, 10, 8, 4, 4, 4, 8, 4, }, +{8: 16, 4, 0, 4, 6, 0, 8, 0, 10, 2, 8, 0, 2, 4, 0, 0, }, +{3: 16, 8, 10, 8, 0, 10, 8, 8, 0, 0, 0, 8, 0, 0, 2, 2, }, +{5: 16, 4, 8, 4, 4, 4, 16, 4, 8, 4, 8, 8, 0, 4, 0, 4, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 2, 0, 10, 2, 0, 0, 0, }, +{9: 16, 4, 0, 10, 8, 0, 4, 2, 6, 0, 8, 0, 2, 4, 0, 0, }, +{a: 16, 4, 0, 10, 0, 0, 4, 0, 2, 6, 0, 2, 8, 0, 4, 8, }, +{c: 16, 8, 0, 4, 4, 0, 4, 0, 4, 0, 10, 0, 0, 10, 2, 2, }, +{7: 16, 4, 8, 10, 2, 4, 4, 8, 0, 0, 0, 6, 2, 0, 0, 0, }, +{b: 16, 4, 0, 4, 2, 0, 0, 2, 2, 8, 0, 2, 4, 0, 4, 0, }, +{d: 16, 8, 0, 8, 8, 0, 8, 0, 8, 0, 10, 0, 0, 10, 2, 2, }, +{e: 16, 0, 2, 8, 0, 2, 0, 0, 0, 4, 2, 0, 4, 2, 4, 4, }, +{f: 16, 0, 2, 4, 0, 2, 4, 0, 0, 8, 2, 0, 0, 2, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:76, 2:30, 4:59, 6:5, 8:36, 10:17, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 0, 0, 4, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 8, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{5: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{b: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 0, 8, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:7, 4:5, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -16, 8, -8, }, +{2: 16, 0, -8, 8, 8, -8, 0, 0, 0, 0, 16, -8, -8, 0, -8, -8, }, +{4: 16, 16, 8, -8, 8, 8, -8, -8, 8, 8, -16, -8, 8, -16, -8, -8, }, +{8: 16, 0, 8, 8, -8, 0, 8, 0, -8, 0, -16, 8, -8, 0, -8, 0, }, +{3: 16, 0, -16, 8, 8, 0, 0, -8, 0, -8, 16, 0, 0, 0, -16, 0, }, +{5: 16, -16, 8, -8, 8, -8, 8, 0, -8, 0, -16, 0, 0, 16, -8, 8, }, +{6: 16, 0, -8, -8, 8, -8, 0, 0, 0, 0, -16, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 8, -8, 0, -8, 8, 8, -8, -16, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 8, -8, 0, 0, -8, 0, 8, -16, -8, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -8, 0, -8, 0, -8, 0, 16, -8, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 8, 8, 0, 8, 0, -8, -16, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 0, 0, 0, 0, 0, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -16, -16, 0, 0, -8, 0, -8, 16, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -8, -8, 0, 0, 0, 0, 0, 16, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, x, x, , x, , x, x, , x, x, }, +{4: , , x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , x, , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , x, x, x, , x, x, , , , x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, x, x, x, , x, , , x, , , x, , x, x, }, +{c: , , x, x, x, , x, , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , , x, x, x, , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0001,0001,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0010,0011,1,}, +{0100,1101,1,}, +{1000,1101,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0100,1,}, +{1101,0101,0,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 8, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x02,0x08,}, {0x0c,}}, +{{0x06,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x01,0x06,0x07,0x0a,0x0b,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x07,0x0b,0x0c,}}, +{{0x0a,0x0c,}, {0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x0b,0x0c,}, {0x0c,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x0c,}}, +{{0x0d,0x02,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_274.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_274.txt new file mode 100644 index 0000000..2f2b54e --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_274.txt @@ -0,0 +1,478 @@ +274 Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 0, 2, 2, 8, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 4, 0, 0, }, +{9: 0, 0, 2, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 4, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:188, 2:32, 4:23, 6:7, 8:4, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 4, 4, 4, 4, 8, 4, 10, 10, 10, 8, 8, 4, 4, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 4, 6, 10, 0, 6, 6, 4, 0, 0, 0, 4, 4, 0, 0, 4, }, +{8: 16, 4, 6, 0, 10, 6, 0, 4, 6, 4, 0, 0, 4, 0, 4, 0, }, +{3: 16, 4, 4, 6, 6, 8, 6, 4, 6, 4, 4, 4, 4, 0, 0, 4, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 8, 4, 4, 4, 4, 4, 16, 4, 0, 0, 8, 8, 8, 4, 4, }, +{9: 16, 4, 6, 0, 6, 6, 0, 4, 10, 4, 0, 0, 4, 0, 0, 4, }, +{a: 16, 10, 4, 0, 4, 4, 0, 0, 4, 10, 2, 2, 8, 0, 0, 0, }, +{c: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{7: 16, 10, 4, 4, 0, 4, 4, 8, 0, 2, 2, 10, 0, 0, 0, 0, }, +{b: 16, 8, 4, 4, 4, 4, 4, 8, 4, 8, 0, 0, 16, 8, 4, 4, }, +{d: 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 16, 0, 0, }, +{e: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 16, 4, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:72, 2:6, 4:88, 6:20, 8:20, 10:14, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:106, 8:16, 12:6, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 8, -16, 8, 8, -16, -8, -8, 16, -8, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 8, 8, 0, -8, 0, -8, -16, 0, }, +{8: 16, 8, 0, 8, -8, 0, 0, 8, -8, -8, 0, 8, 0, 0, -16, -8, }, +{3: 16, -8, 0, 8, 8, 8, -8, -8, -8, -8, 0, 8, 8, -8, -16, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, -8, -16, 8, -8, 0, 8, 8, -16, -8, 8, 0, -8, 16, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, -8, 0, -8, 0, 0, -16, 8, }, +{a: 16, 0, -8, 8, -8, 0, 0, -8, -8, 8, -8, -8, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 16, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, -8, -8, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, -8, 8, -16, 0, 0, -16, 8, 8, -8, 8, 0, 0, 16, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, -8, 8, -8, 0, 8, -8, 0, 16, 0, }, +{e: 16, 0, 0, -8, -8, 0, 8, 8, -8, 8, 0, 8, -8, 0, -16, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 8, 8, 8, 0, -8, 8, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0100,0110,1,}, +{0110,1011,1,}, +{0111,0001,1,}, +{1000,1011,1,}, +{1001,0001,1,}, +{1010,0110,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0e,}}, +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x03,0x04,0x08,}, {0x0e,}}, +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x05,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x01,0x02,0x0c,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +274 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x08,0x02,0x05,0x06,0x07,0x03,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, }, +{2: 0, 0, 8, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{8: 0, 0, 2, 0, 6, 2, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 0, 2, 2, 8, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 4, 0, 0, }, +{9: 0, 0, 2, 0, 2, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 2, 0, 0, 0, 0, 0, 0, 0, 6, 2, 2, 4, 0, 0, 0, }, +{c: 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 6, 2, 0, 4, 0, 0, }, +{7: 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 2, 6, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:188, 2:32, 4:23, 6:7, 8:4, 10:1, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 6:2, 8:1, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 4, 4, 4, 4, 4, 8, 4, 10, 10, 10, 8, 8, 4, 4, }, +{2: 16, 4, 8, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 0, 4, 0, }, +{4: 16, 4, 6, 10, 0, 6, 6, 4, 0, 0, 0, 4, 4, 0, 0, 4, }, +{8: 16, 4, 6, 0, 10, 6, 0, 4, 6, 4, 0, 0, 4, 0, 4, 0, }, +{3: 16, 4, 4, 6, 6, 8, 6, 4, 6, 4, 4, 4, 4, 0, 0, 4, }, +{5: 16, 4, 6, 6, 0, 6, 10, 4, 0, 0, 0, 4, 4, 0, 4, 0, }, +{6: 16, 8, 4, 4, 4, 4, 4, 16, 4, 0, 0, 8, 8, 8, 4, 4, }, +{9: 16, 4, 6, 0, 6, 6, 0, 4, 10, 4, 0, 0, 4, 0, 0, 4, }, +{a: 16, 10, 4, 0, 4, 4, 0, 0, 4, 10, 2, 2, 8, 0, 0, 0, }, +{c: 16, 10, 4, 0, 0, 4, 0, 0, 0, 2, 10, 2, 0, 8, 4, 4, }, +{7: 16, 10, 4, 4, 0, 4, 4, 8, 0, 2, 2, 10, 0, 0, 0, 0, }, +{b: 16, 8, 4, 4, 4, 4, 4, 8, 4, 8, 0, 0, 16, 8, 4, 4, }, +{d: 16, 8, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 16, 0, 0, }, +{e: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 16, 4, }, +{f: 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:72, 2:6, 4:88, 6:20, 8:20, 10:14, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 4, 4, 8, 4, 4, 0, 4, 4, 0, 4, 0, 0, }, +{2: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 4, 4, 0, 12, 0, 4, 4, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 4, 4, 0, 4, 0, 4, 12, 0, 0, 4, 0, 4, 0, 0, 4, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 8, 4, 4, 4, 0, 4, 0, 4, 8, 0, 0, 4, 0, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 0, 4, 4, 8, 4, 4, 4, 4, 0, 4, 4, 0, 0, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 4, 0, 4, 4, 0, 4, 4, 0, 4, 4, 8, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:126, 4:106, 8:16, 12:6, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:4, 4:8, 8:2, 12:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -8, -8, 8, -16, 8, 8, -16, -8, -8, 16, -8, }, +{2: 16, 8, 0, 8, 8, -8, 8, -8, 8, -8, 0, -8, -8, 8, -16, -8, }, +{4: 16, 0, 0, -8, 8, 8, 0, -8, 8, 8, 0, -8, 0, -8, -16, 0, }, +{8: 16, 8, 0, 8, -8, 0, 0, 8, -8, -8, 0, 8, 0, 0, -16, -8, }, +{3: 16, -8, 0, 8, 8, 8, -8, -8, -8, -8, 0, 8, 8, -8, -16, 8, }, +{5: 16, 0, 0, -8, 8, -8, 0, -8, -8, 8, 0, 8, 0, 8, -16, 0, }, +{6: 16, 0, -8, -16, 8, -8, 0, 8, 8, -16, -8, 8, 0, -8, 16, 0, }, +{9: 16, -8, 0, 8, -8, 0, 0, 8, 8, -8, 0, -8, 0, 0, -16, 8, }, +{a: 16, 0, -8, 8, -8, 0, 0, -8, -8, 8, -8, -8, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -8, 0, 0, -8, -8, -8, 8, -8, 0, 0, 16, 0, }, +{7: 16, 0, -8, -8, 8, 0, 0, 8, -8, -8, -8, -8, 0, 0, 16, 0, }, +{b: 16, -8, -8, 8, -16, 0, 0, -16, 8, 8, -8, 8, 0, 0, 16, -8, }, +{d: 16, 0, 0, -8, -8, 0, -8, -8, 8, -8, 0, 8, -8, 0, 16, 0, }, +{e: 16, 0, 0, -8, -8, 0, 8, 8, -8, 8, 0, 8, -8, 0, -16, 0, }, +{f: 16, 0, 0, -8, -8, 0, -8, 8, 8, 8, 0, -8, 8, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, x, x, , , , , x, , x, , x, }, +{6: , x, x, , x, x, , x, , , , x, , , x, x, }, +{9: , x, x, x, x, x, , , x, , , , x, x, , x, }, +{a: , , x, x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, x, x, x, , , , , x, , , x, x, x, }, +{7: , x, x, , x, x, , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, , x, x, x, , , , , , , , x, , x, }, +{e: , , x, , x, x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 21 */ +{0100,0110,1,}, +{0110,1011,1,}, +{0111,0001,1,}, +{1000,1011,1,}, +{1001,0001,1,}, +{1010,0110,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 25, 4, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0e,}}, +{{0x01,0x04,0x08,}, {0x0e,}}, +{{0x03,0x04,0x08,}, {0x0e,}}, +{{0x01,0x02,0x08,}, {0x0e,}}, +{{0x05,0x02,0x08,}, {0x0e,}}, +{{0x01,0x06,0x08,}, {0x0e,}}, +{{0x05,0x06,0x08,}, {0x0e,}}, +{{0x01,0x02,0x04,}, {0x0e,}}, +{{0x09,0x02,0x04,}, {0x0e,}}, +{{0x01,0x0a,0x04,}, {0x0e,}}, +{{0x09,0x0a,0x04,}, {0x0e,}}, +{{0x01,0x02,0x0c,}, {0x0e,}}, +{{0x09,0x02,0x0c,}, {0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x0e,}}, +{{0x04,0x08,}, {0x0e,}}, +{{0x02,0x08,}, {0x01,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x0a,0x0e,}}, +{{0x02,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x0a,0x04,}, {0x0e,}}, +{{0x02,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x0a,0x0e,}}, +{{0x01,0x04,}, {0x07,0x09,0x0e,}}, +{{0x03,0x04,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x0e,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x09,0x0b,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x05,0x0b,0x0e,}}, +{{0x09,0x0c,}, {0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x07,0x09,0x0e,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x0e,}}, +{{0x07,0x08,}, {0x0e,}}, +{{0x01,0x02,}, {0x07,0x09,0x0e,}}, +{{0x05,0x02,}, {0x03,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x0e,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,0x09,0x0a,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x09,0x06,}, {0x04,0x0a,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x0e,}}, +{{0x09,0x0a,}, {0x01,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x07,0x09,0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x0e,}}, +{{0x0d,0x0e,}, {0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_275.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_275.txt new file mode 100644 index 0000000..6fbdc49 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_275.txt @@ -0,0 +1,482 @@ +275 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x08,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 8, 2, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 8, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 2, 0, 8, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 0, 8, 2, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 0, 0, 2, 0, 8, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 2, 2, 0, 8, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 6, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 6, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 6, }, +}; +Diff: 10, DDT_spectrum: {0:187, 2:42, 4:11, 6:5, 8:9, 10:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:1, 8:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{2: 16, 8, 16, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{4: 16, 4, 4, 8, 6, 4, 6, 4, 4, 6, 4, 6, 0, 4, 4, 0, }, +{8: 16, 4, 4, 6, 8, 4, 4, 6, 6, 4, 4, 0, 6, 4, 4, 0, }, +{3: 16, 8, 8, 4, 4, 16, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{5: 16, 4, 4, 4, 6, 4, 8, 6, 6, 4, 4, 6, 0, 4, 0, 4, }, +{6: 16, 4, 4, 6, 4, 4, 4, 8, 6, 6, 4, 6, 0, 0, 4, 4, }, +{9: 16, 4, 4, 6, 4, 4, 6, 4, 8, 6, 4, 0, 6, 4, 0, 4, }, +{a: 16, 4, 4, 4, 6, 4, 6, 6, 4, 8, 4, 0, 6, 0, 4, 4, }, +{c: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 8, 0, 4, 4, 0, 4, 0, 4, 0, 10, 0, 0, 10, 2, 2, }, +{e: 16, 0, 8, 4, 4, 0, 0, 4, 0, 4, 10, 0, 0, 2, 10, 2, }, +{f: 16, 0, 0, 0, 0, 8, 4, 4, 4, 4, 10, 0, 0, 2, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:48, 2:6, 4:102, 6:30, 8:24, 10:12, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{6: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{9: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{a: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:104, 8:12, 12:8, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 12:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 8, -16, 0, 0, 0, 0, 16, -8, -8, -8, 8, -16, }, +{2: 16, 8, -16, 8, 8, -8, 0, -8, 0, -8, 16, 0, 0, 8, -16, -8, }, +{4: 16, 8, 8, -8, 8, 8, 0, -8, 0, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, 8, 8, 8, -8, 8, 0, 8, 0, -8, -16, 8, -8, -8, -8, -8, }, +{3: 16, -16, -8, 8, 8, 8, -8, 0, -8, 0, 16, 0, 0, -16, -8, 8, }, +{5: 16, -8, 8, -8, 8, -8, 8, 0, -8, 0, -16, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, -8, 8, 8, -8, -16, 0, 0, -8, 8, 8, }, +{9: 16, -8, 8, 8, -8, -8, -8, 0, 8, 0, -16, -8, 8, 8, -8, 8, }, +{a: 16, 8, -8, 8, -8, -8, 8, -8, -8, 8, -16, 0, 0, -8, 8, 8, }, +{c: 16, 8, 8, -16, -16, 8, -8, -8, -8, -8, 16, -8, -8, 8, 8, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{d: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, -8, 8, -8, }, +{e: 16, 8, -8, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 8, -8, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 0, 0, 0, 16, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , x, x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, , x, x, , , x, , , , x, , , x, x, }, +{9: , x, x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, , x, x, , , , , x, , , x, , x, x, }, +{c: , x, x, , , , , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0001,1,}, +{0100,1100,1,}, +{1000,1100,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x05,0x09,0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x03,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +275 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x08,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 8, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 8, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 0, 0, 8, 0, 2, 2, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 2, 0, 2, 8, 0, 2, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 2, 0, 0, 0, 2, 2, 8, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 6, 4, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 4, 6, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 2, 2, 6, }, +}; +Diff: 10, DDT_spectrum: {0:187, 2:42, 4:11, 6:5, 8:9, 10:1, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:9, 2:2, 4:1, 8:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{2: 16, 8, 16, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 0, 8, 0, }, +{4: 16, 4, 4, 8, 6, 4, 4, 6, 6, 4, 4, 6, 0, 4, 4, 0, }, +{8: 16, 4, 4, 6, 8, 4, 6, 4, 4, 6, 4, 0, 6, 4, 4, 0, }, +{3: 16, 8, 8, 4, 4, 16, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{5: 16, 4, 4, 6, 4, 4, 8, 4, 6, 6, 4, 6, 0, 4, 0, 4, }, +{6: 16, 4, 4, 4, 6, 4, 6, 8, 4, 6, 4, 6, 0, 0, 4, 4, }, +{9: 16, 4, 4, 4, 6, 4, 6, 6, 8, 4, 4, 0, 6, 4, 0, 4, }, +{a: 16, 4, 4, 6, 4, 4, 4, 6, 6, 8, 4, 0, 6, 0, 4, 4, }, +{c: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{7: 16, 4, 4, 6, 0, 4, 6, 6, 0, 0, 4, 10, 4, 0, 0, 0, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 8, 0, 4, 4, 0, 4, 0, 4, 0, 10, 0, 0, 10, 2, 2, }, +{e: 16, 0, 8, 4, 4, 0, 0, 4, 0, 4, 10, 0, 0, 2, 10, 2, }, +{f: 16, 0, 0, 0, 0, 8, 4, 4, 4, 4, 10, 0, 0, 2, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:48, 2:6, 4:102, 6:30, 8:24, 10:12, 16:34, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 4, 4, 4, 0, 8, 0, 0, 8, 0, 4, 4, 4, 4, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 4, 4, 4, 4, 0, 0, 8, 8, 0, 0, 4, 4, 4, 4, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 4, 4, 4, 8, 4, 0, 4, 0, 8, 0, 4, 0, 4, }, +{b: 0, 4, 0, 4, 4, 4, 0, 4, 8, 4, 0, 0, 8, 4, 0, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:104, 8:12, 12:8, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:9, 4:3, 12:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -16, 8, -8, }, +{2: 16, 8, -8, 8, 8, -16, 0, 0, 0, 0, 16, -8, -8, 8, -8, -16, }, +{4: 16, 8, 8, -8, 8, 8, -8, 0, 8, 0, -16, -8, 8, -8, -8, -8, }, +{8: 16, 8, 8, 8, -8, 8, 8, 0, -8, 0, -16, 8, -8, -8, -8, -8, }, +{3: 16, -8, -16, 8, 8, 8, 0, -8, 0, -8, 16, 0, 0, -8, -16, 8, }, +{5: 16, -8, 8, -8, 8, -8, 8, -8, -8, 8, -16, 0, 0, 8, -8, 8, }, +{6: 16, 8, -8, -8, 8, -8, 0, 8, 0, -8, -16, 8, -8, -8, 8, 8, }, +{9: 16, -8, 8, 8, -8, -8, -8, 8, 8, -8, -16, 0, 0, 8, -8, 8, }, +{a: 16, 8, -8, 8, -8, -8, 0, -8, 0, 8, -16, -8, 8, -8, 8, 8, }, +{c: 16, 8, 8, -16, -16, 8, -8, -8, -8, -8, 16, -8, -8, 8, 8, 8, }, +{7: 16, -8, -8, -8, 8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{b: 16, -8, -8, 8, -8, 8, 0, 0, 0, 0, -16, 0, 0, 8, 8, -8, }, +{d: 16, -8, 8, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, -8, 8, -8, }, +{e: 16, 8, -8, -8, -8, -8, 0, 0, 0, 0, 16, 0, 0, 8, -8, -8, }, +{f: 16, -8, -8, -8, -8, 8, 0, 0, 0, 0, 16, 0, 0, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , x, x, x, x, , , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , x, x, x, x, , , , , x, , , x, , x, x, }, +{c: , x, x, , , , , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0001,0001,1,}, +{0010,0011,1,}, +{0011,0010,1,}, +{0100,1100,1,}, +{1000,1100,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1110,0011,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 4, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x0c,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x0c,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x0c,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x04,}, {0x03,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x05,0x09,0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x02,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0a,}, {0x02,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x0c,}}, +{{0x09,0x0e,}, {0x0c,}}, +{{0x0d,0x0e,}, {0x02,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_276.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_276.txt new file mode 100644 index 0000000..63f6cbc --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_276.txt @@ -0,0 +1,474 @@ +276 Sbox: +LUT = { +0x04,0x06,0x01,0x02,0x03,0x05,0x00,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 10, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +{3: 0, 0, 0, 2, 0, 8, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 10, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 2, 2, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:58, 4:16, 8:5, 10:2, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 4:1, 8:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 10, 8, 0, 10, 8, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{2: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{3: 16, 8, 8, 10, 0, 8, 10, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{5: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 10, 10, 10, 0, 8, 8, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{a: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 8, 2, 4, 0, 4, 2, 0, 2, }, +{d: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{f: 16, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 8, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:32, 4:48, 8:29, 10:28, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:122, 4:108, 8:20, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, -8, -8, 8, -8, 0, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, -8, 8, 16, -8, 8, -16, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 16, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 0, 16, 8, -8, -8, -8, -8, 0, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 16, -16, 8, -8, -8, 8, -8, 8, -16, 8, -8, 8, }, +{6: 16, 8, -8, -8, 16, -8, -8, 8, 8, -8, -8, 0, -8, -8, 8, 0, }, +{9: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{c: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , , , x, , x, , , , x, x, , , x, }, +{5: , , , x, , x, x, x, , , , x, , x, , x, }, +{6: , , x, x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, , x, , , , , x, , , x, }, +{d: , , , x, , x, , x, , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 19 */ +{0011,0101,1,}, +{0110,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0101,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +276 Inverse Sbox: +LUT = { +0x06,0x02,0x03,0x04,0x00,0x05,0x01,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 8, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +{3: 0, 2, 2, 2, 0, 8, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 4, 0, 4, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 4, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 10, DDT_spectrum: {0:174, 2:58, 4:16, 8:5, 10:2, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 4:1, 8:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 10, 0, 8, 10, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 8, 10, 8, 0, 10, 8, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{3: 16, 10, 10, 10, 0, 8, 8, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{5: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{a: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 8, 2, 4, 0, 4, 2, 0, 2, }, +{d: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{f: 16, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 8, 2, 4, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:88, 2:32, 4:48, 8:29, 10:28, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 12, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:122, 4:108, 8:20, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 16, -8, -8, 8, -8, 8, 0, -8, -8, -8, 8, -8, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 8, 0, -8, 16, 8, -8, -8, 8, 0, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 8, 16, 8, -8, -8, -8, -8, 8, 0, 8, -8, -8, 0, }, +{5: 16, -8, 8, -8, 16, -8, 8, -16, -8, 8, -8, 8, -8, 8, -16, 8, }, +{6: 16, 0, -8, -8, 16, -8, -8, 8, 0, -8, -8, 8, -8, -8, 8, 8, }, +{9: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{a: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{c: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, 0, 0, -16, 8, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, }, +{d: 16, 0, 0, 0, -16, -8, 0, -8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{e: 16, 0, 0, 0, -16, -8, 0, 8, 0, 0, 0, 0, 8, 0, -8, 0, }, +{f: 16, 0, 0, 0, -16, 8, 0, 8, 0, 0, 0, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, , , , x, x, , , x, }, +{5: , x, , , , , x, x, , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , , , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , , , x, , , , , x, , , x, }, +{d: , x, , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 19 */ +{0011,0010,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 15, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_277.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_277.txt new file mode 100644 index 0000000..3cf85b1 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_277.txt @@ -0,0 +1,486 @@ +277 Sbox: +LUT = { +0x04,0x00,0x01,0x06,0x02,0x05,0x03,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 8, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{3: 0, 2, 2, 0, 0, 8, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 10, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 4, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 4, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{d: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 10, DDT_spectrum: {0:180, 2:46, 4:22, 8:5, 10:2, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:3, 4:2, 8:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 10, 10, 8, 0, 8, 10, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{3: 16, 10, 10, 8, 0, 8, 10, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 4, 0, 8, 2, 4, 0, 4, 2, 0, 2, }, +{a: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{7: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 8, 2, 4, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:88, 2:32, 4:48, 8:32, 10:16, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 0, 16, 0, -8, 8, -8, 8, 0, -16, 0, -8, 8, -16, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 8, 8, -8, 16, 0, -8, -8, 8, 8, -8, -8, 0, -8, -8, -8, }, +{8: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, }, +{3: 16, -8, -8, 8, 16, 0, -8, -8, -8, -8, 8, 8, 0, -8, -8, 8, }, +{5: 16, -8, 8, -8, 16, -16, 8, -8, -8, 8, -8, 8, -16, 8, -8, 8, }, +{6: 16, 0, -16, -8, 16, 0, -8, 8, 0, -16, -8, 8, 0, -8, 8, 8, }, +{9: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 8, }, +{c: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 16, 16, 0, 0, -8, -8, -8, -8, 16, 0, 0, -8, }, +{b: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, , , , x, x, , , x, }, +{5: , x, x, , , , x, , , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0011,0101,1,}, +{0011,0111,0,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +277 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x06,0x00,0x05,0x03,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 2, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 10, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 2, 0, 2, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 4, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 4, 0, 0, 2, 0, 2, }, +{7: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{d: 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 2, 4, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 4, 2, 4, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 2, 0, 2, 4, }, +}; +Diff: 10, DDT_spectrum: {0:180, 2:46, 4:22, 8:5, 10:2, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:3, 4:2, 8:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 10, 10, 0, 10, 10, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 4, 0, 8, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 0, }, +{3: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 8, 10, 10, 0, 10, 10, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 4, 0, 2, 0, 4, 0, 8, 2, 4, 0, 4, 2, 0, 2, }, +{a: 16, 0, 4, 0, 4, 0, 4, 0, 2, 8, 2, 0, 2, 0, 2, 4, }, +{c: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 8, 0, 0, 2, 4, 2, }, +{7: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 4, 0, 2, 0, 4, 0, 4, 2, 0, 0, 8, 2, 4, 2, }, +{d: 16, 0, 4, 0, 4, 0, 4, 0, 2, 0, 2, 0, 2, 8, 2, 4, }, +{e: 16, 0, 4, 0, 2, 0, 4, 0, 0, 2, 4, 0, 4, 2, 8, 2, }, +{f: 16, 0, 4, 0, 0, 0, 4, 0, 2, 4, 2, 0, 2, 4, 2, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:88, 2:32, 4:48, 8:32, 10:16, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:134, 4:92, 8:24, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -8, -8, 0, -8, 8, 8, -8, -8, -8, 0, -8, }, +{2: 16, 8, -8, 8, 16, -8, 8, -16, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 16, 8, -8, 0, 0, 8, -8, -16, 8, -8, 0, -16, }, +{8: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, }, +{3: 16, -8, -16, 0, 16, 8, -8, 0, -8, -16, 0, 8, 8, -8, 0, 8, }, +{5: 16, -8, 8, -8, 16, -8, 8, -16, -8, 8, -8, 8, -8, 8, -16, 8, }, +{6: 16, 8, -8, -8, 16, -8, -8, 0, 8, -8, -8, 8, -8, -8, 0, 8, }, +{9: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{a: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 8, }, +{c: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, 8, }, +{7: 16, -8, -8, -8, 16, 0, 0, 16, -8, -8, -8, -8, 0, 0, 16, -8, }, +{b: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{d: 16, 0, 8, 0, -16, 0, 0, 0, 0, -8, 0, 8, 0, 0, 0, -8, }, +{e: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, -8, }, +{f: 16, 0, -8, 0, -16, 0, 0, 0, 0, 8, 0, -8, 0, 0, 0, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , , , x, , x, , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , , x, x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, , x, , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 25 */ +{0010,0011,1,}, +{0110,0010,1,}, +{0110,0101,1,}, +{0110,0111,0,}, +{0111,0100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0011,1,}, +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +{1111,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 7, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x08,0x0f,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x08,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x08,}}, +{{0x03,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x08,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x08,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_278.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_278.txt new file mode 100644 index 0000000..d6c7a98 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_278.txt @@ -0,0 +1,490 @@ +278 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x09,0x08,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 6, 0, 0, 6, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, }, +{3: 0, 2, 4, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 4, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 10, 2, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 0, 6, 2, 0, 4, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 6, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 6, 4, }, +}; +Diff: 10, DDT_spectrum: {0:186, 2:42, 4:9, 6:15, 10:3, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:2, 10:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 10, 4, 8, 8, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{2: 16, 8, 10, 2, 8, 10, 2, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{4: 16, 8, 0, 10, 8, 0, 10, 2, 8, 0, 8, 2, 0, 8, 0, 0, }, +{8: 16, 4, 4, 4, 10, 8, 8, 8, 4, 4, 4, 4, 10, 10, 10, 4, }, +{3: 16, 10, 8, 0, 4, 10, 2, 0, 4, 4, 0, 2, 4, 0, 0, 0, }, +{5: 16, 10, 2, 8, 4, 0, 10, 2, 4, 0, 4, 0, 0, 4, 0, 0, }, +{6: 16, 8, 2, 0, 8, 2, 0, 10, 8, 0, 0, 10, 0, 0, 8, 8, }, +{9: 16, 4, 4, 4, 4, 8, 8, 8, 10, 10, 10, 4, 4, 4, 4, 10, }, +{a: 16, 4, 4, 0, 10, 8, 0, 0, 4, 6, 2, 0, 8, 0, 2, 0, }, +{c: 16, 4, 0, 4, 10, 0, 8, 0, 4, 0, 6, 0, 2, 8, 0, 2, }, +{7: 16, 10, 0, 2, 4, 2, 0, 10, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 16, 4, 4, 0, 4, 8, 0, 0, 10, 8, 0, 0, 6, 2, 0, 2, }, +{d: 16, 4, 0, 4, 4, 0, 8, 0, 10, 2, 8, 0, 0, 6, 2, 0, }, +{e: 16, 4, 0, 0, 10, 0, 0, 8, 4, 2, 0, 4, 0, 2, 8, 6, }, +{f: 16, 4, 0, 0, 4, 0, 0, 8, 10, 0, 2, 4, 2, 0, 6, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:72, 2:24, 4:54, 6:6, 8:39, 10:30, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 8, 0, 4, 4, 0, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +{b: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, 4, 8, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 8, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:138, 4:90, 8:20, 12:6, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:1, 12:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -8, -8, 8, -8, 8, 8, -16, -8, -8, 8, -16, }, +{2: 16, 0, -8, 8, 16, 0, 0, -16, 0, -8, 8, 0, 0, 0, -16, 0, }, +{4: 16, 0, 8, -16, 16, 0, 0, -8, 0, 8, -16, 0, 0, 0, -8, 0, }, +{8: 16, 8, 8, 8, -16, 8, 8, 8, -8, -8, -8, 16, -8, -8, -8, -16, }, +{3: 16, -8, -8, 8, 16, 0, 0, -8, -8, -8, 8, 0, 0, 0, -8, 0, }, +{5: 16, 0, 8, -8, 16, -8, 0, -8, 0, 8, -8, 0, -8, 0, -8, 0, }, +{6: 16, 0, -16, -8, 16, 0, 0, 8, 0, -16, -8, 0, 0, 0, 8, 0, }, +{9: 16, -8, 8, 8, -16, -8, -8, 8, 8, -8, -8, -16, 8, 8, -8, 16, }, +{a: 16, 8, -8, 8, -16, 0, 0, -8, -8, 8, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -8, 16, 0, -8, 8, 0, -8, -8, 0, 0, -8, 8, 0, }, +{b: 16, -8, -8, 8, -16, 0, 0, -8, 8, 8, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -8, -16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 8, 0, }, +{e: 16, 0, -8, -8, -16, 0, 8, 8, 0, 8, 8, 0, 0, -8, -8, 0, }, +{f: 16, 0, -8, -8, -16, 0, -8, 8, 0, 8, 8, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , , , x, x, , , x, }, +{5: , x, x, , , , x, , , , , x, , x, , x, }, +{6: , x, , , , , , x, x, , , x, , , x, x, }, +{9: , x, x, x, , , , , x, , , , x, x, , x, }, +{a: , , x, x, , , , , x, x, , , x, , x, x, }, +{c: , x, x, , , , , , x, , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 27 */ +{0010,0110,1,}, +{0100,0100,1,}, +{0110,0010,1,}, +{0111,0001,1,}, +{0111,1000,0,}, +{0111,1001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +{1111,1000,1,}, +{1111,1001,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 10, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x08,0x0a,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +278 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x09,0x08,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 6, 0, 0, 4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 6, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 10, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 0, }, +{3: 0, 0, 6, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 6, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 6, 0, 0, 0, 6, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 2, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 6, 0, 0, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 6, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 6, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 6, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 6, 4, }, +}; +Diff: 10, DDT_spectrum: {0:186, 2:42, 4:9, 6:15, 10:3, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:2, 10:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 8, 4, 10, 10, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{2: 16, 10, 10, 0, 4, 8, 2, 2, 4, 4, 0, 0, 4, 0, 0, 0, }, +{4: 16, 10, 2, 10, 4, 0, 8, 0, 4, 0, 4, 2, 0, 4, 0, 0, }, +{8: 16, 4, 8, 8, 10, 4, 4, 8, 4, 10, 10, 4, 4, 4, 10, 4, }, +{3: 16, 8, 10, 0, 8, 10, 0, 2, 8, 8, 0, 2, 8, 0, 0, 0, }, +{5: 16, 8, 2, 10, 8, 2, 10, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{6: 16, 8, 0, 2, 8, 0, 2, 10, 8, 0, 0, 10, 0, 0, 8, 8, }, +{9: 16, 4, 8, 8, 4, 4, 4, 8, 10, 4, 4, 4, 10, 10, 4, 10, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 10, 6, 0, 0, 8, 2, 2, 0, }, +{c: 16, 4, 0, 8, 4, 0, 4, 0, 10, 2, 6, 0, 0, 8, 0, 2, }, +{7: 16, 10, 0, 2, 4, 2, 0, 10, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 0, 8, 10, 0, 4, 0, 4, 0, 8, 0, 2, 6, 2, 0, }, +{e: 16, 4, 0, 0, 10, 0, 0, 8, 4, 2, 0, 4, 0, 2, 8, 6, }, +{f: 16, 4, 0, 0, 4, 0, 0, 8, 10, 0, 2, 4, 2, 0, 6, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:72, 2:24, 4:54, 6:6, 8:39, 10:30, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 0, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:138, 4:90, 8:20, 12:6, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:1, 12:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 16, -8, -8, 8, -16, 8, 8, -8, -8, -8, 8, -8, }, +{2: 16, 0, -8, 8, 16, -8, 0, -8, 0, -8, 8, 0, -8, 0, -8, 0, }, +{4: 16, 0, 8, -8, 16, 0, 0, -8, 0, 8, -8, -8, 0, 0, -8, -8, }, +{8: 16, 16, 8, 8, -16, 8, 8, 8, -16, -8, -8, 8, -8, -8, -8, -8, }, +{3: 16, 0, -16, 8, 16, 0, 0, -8, 0, -16, 8, 0, 0, 0, -8, 0, }, +{5: 16, 0, 8, -8, 16, 0, 0, -16, 0, 8, -8, 0, 0, 0, -16, 0, }, +{6: 16, 0, -8, -16, 16, 0, 0, 8, 0, -8, -16, 0, 0, 0, 8, 0, }, +{9: 16, -16, 8, 8, -16, -8, -8, 8, 16, -8, -8, -8, 8, 8, -8, 8, }, +{a: 16, 0, -8, 8, -16, -8, 0, -8, 0, 8, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -16, 0, 0, -8, 0, -8, 8, -8, 0, 0, 8, 8, }, +{7: 16, 0, -8, -8, 16, 0, -8, 8, 0, -8, -8, 0, 0, -8, 8, 0, }, +{b: 16, 0, -8, 8, -16, 8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -16, 0, 0, -8, 0, -8, 8, 8, 0, 0, 8, -8, }, +{e: 16, 0, -8, -8, -16, 0, 8, 8, 0, 8, 8, 0, 0, -8, -8, 0, }, +{f: 16, 0, -8, -8, -16, 0, -8, 8, 0, 8, 8, 0, 0, 8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, , x, x, , x, x, x, }, +{8: , , x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , x, x, , , , , x, x, , , x, , , x, x, }, +{9: , , x, x, , , , , x, , , , x, x, , x, }, +{a: , , x, x, , , , , x, x, , , x, , x, x, }, +{c: , , x, x, , , , , x, , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , x, , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 27 */ +{0001,0001,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{0010,0011,1,}, +{0100,0110,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,1000,1,}, +{1001,1001,0,}, +{1010,0011,1,}, +{1100,0110,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 29, 10, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x06,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x01,0x08,0x09,}}, +{{0x0d,0x02,}, {0x08,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_279.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_279.txt new file mode 100644 index 0000000..1f1c54b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_279.txt @@ -0,0 +1,482 @@ +279 Sbox: +LUT = { +0x01,0x00,0x04,0x06,0x02,0x05,0x03,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 0, 2, 0, 8, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 0, }, +{d: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:192, 2:24, 4:32, 8:3, 10:4, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 4:1, 8:1, 10:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 10, 4, 8, 8, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 16, 8, 8, 10, 0, 8, 10, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{5: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 8, 10, 8, 4, 10, 8, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 4, 4, 0, 4, 0, 4, 4, 16, 0, 4, 0, 4, 0, 0, 4, }, +{a: 16, 4, 4, 0, 4, 0, 4, 4, 0, 16, 4, 0, 4, 0, 0, 4, }, +{c: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 16, 0, 0, 4, 4, 0, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 16, 4, 4, 0, }, +{d: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 16, 0, 4, }, +{e: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 16, 4, }, +{f: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:72, 4:96, 8:21, 10:28, 16:39, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:104, 8:12, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -8, -8, 8, -8, 8, 8, -16, -8, -8, 8, -16, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 8, -8, 16, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 8, 0, -16, -8, 0, 8, 0, -8, 0, 8, 8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 16, 8, -8, -8, -8, -8, 0, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 16, -8, 8, -16, -8, 8, -8, 8, -8, 8, -16, 8, }, +{6: 16, 8, -16, -8, 16, -8, -8, 8, 8, -16, -8, 8, -8, -8, 8, 8, }, +{9: 16, 0, 8, 0, -16, 8, 0, 8, 0, -8, 0, -8, -8, 0, -8, 8, }, +{a: 16, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, -8, -8, 0, 8, 8, }, +{c: 16, 0, 8, 0, -16, -8, 0, -8, 0, -8, 0, -8, 8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 0, -16, -8, 0, -8, 0, 8, 0, 8, 8, 0, 8, -8, }, +{d: 16, 0, 8, 0, -16, 8, 0, -8, 0, -8, 0, 8, -8, 0, 8, -8, }, +{e: 16, 0, -8, 0, -16, 8, 0, 8, 0, 8, 0, 8, -8, 0, -8, -8, }, +{f: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0110,0101,1,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1110,0101,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +279 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x06,0x02,0x05,0x03,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, }, +{3: 0, 0, 0, 2, 0, 8, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 0, }, +{d: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:192, 2:24, 4:32, 8:3, 10:4, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:8, 2:4, 4:1, 8:1, 10:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 10, 4, 8, 8, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{3: 16, 8, 8, 10, 0, 8, 10, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{5: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 8, 10, 8, 4, 10, 8, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 4, 4, 0, 4, 0, 4, 4, 16, 0, 4, 0, 4, 0, 0, 4, }, +{a: 16, 4, 4, 0, 4, 0, 4, 4, 0, 16, 4, 0, 4, 0, 0, 4, }, +{c: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 16, 0, 0, 4, 4, 0, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 16, 4, 4, 0, }, +{d: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 16, 0, 4, }, +{e: 16, 4, 4, 0, 4, 0, 4, 4, 0, 0, 4, 0, 4, 0, 16, 4, }, +{f: 16, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:72, 4:96, 8:21, 10:28, 16:39, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 4, 4, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, 4, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:104, 8:12, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -8, -8, 8, -8, 8, 8, -16, -8, -8, 8, -16, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 8, -8, 16, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 8, 0, -16, -8, 0, 8, 0, -8, 0, 8, 8, 0, -8, -8, }, +{3: 16, -8, -8, 0, 16, 8, -8, -8, -8, -8, 0, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 16, -8, 8, -16, -8, 8, -8, 8, -8, 8, -16, 8, }, +{6: 16, 8, -16, -8, 16, -8, -8, 8, 8, -16, -8, 8, -8, -8, 8, 8, }, +{9: 16, 0, 8, 0, -16, 8, 0, 8, 0, -8, 0, -8, -8, 0, -8, 8, }, +{a: 16, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, -8, -8, 0, 8, 8, }, +{c: 16, 0, 8, 0, -16, -8, 0, -8, 0, -8, 0, -8, 8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 0, -16, -8, 0, -8, 0, 8, 0, 8, 8, 0, 8, -8, }, +{d: 16, 0, 8, 0, -16, 8, 0, -8, 0, -8, 0, 8, -8, 0, 8, -8, }, +{e: 16, 0, -8, 0, -16, 8, 0, 8, 0, 8, 0, 8, -8, 0, -8, -8, }, +{f: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, x, , , x, , x, , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, x, x, , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, , , x, , x, , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0110,0101,1,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1110,0101,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x08,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x08,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x08,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_280.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_280.txt new file mode 100644 index 0000000..e550684 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_280.txt @@ -0,0 +1,482 @@ +280 Sbox: +LUT = { +0x02,0x00,0x01,0x04,0x03,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 10, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, }, +{3: 0, 2, 0, 2, 0, 10, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 0, 0, 2, 8, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 2, 2, 0, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, 0, 4, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 10, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 6, }, +}; +Diff: 10, DDT_spectrum: {0:184, 2:48, 4:8, 6:8, 8:3, 10:4, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:1, 8:1, 10:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 10, 4, 0, 0, 6, 6, 0, 4, 6, 0, 0, 4, }, +{3: 16, 10, 8, 10, 4, 10, 8, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 16, 8, 10, 8, 0, 10, 8, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{6: 16, 10, 10, 10, 0, 8, 8, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{9: 16, 4, 4, 0, 6, 4, 0, 0, 10, 6, 0, 4, 6, 0, 4, 0, }, +{a: 16, 4, 4, 0, 6, 4, 0, 0, 6, 10, 0, 4, 6, 4, 0, 0, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 4, 4, 0, 0, 4, 0, 0, 0, 4, 6, 4, 0, 10, 6, 6, }, +{e: 16, 4, 4, 0, 0, 4, 0, 0, 4, 0, 6, 4, 0, 6, 10, 6, }, +{f: 16, 4, 4, 0, 4, 4, 0, 0, 0, 0, 6, 4, 0, 6, 6, 10, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:72, 4:72, 6:24, 8:21, 10:36, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{2: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 0, 0, 4, 12, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 4, 0, 0, 0, 4, 12, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 0, 8, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 0, }, +{a: 0, 0, 8, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:104, 8:12, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:5, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -16, -8, 8, -8, 8, 8, -8, -16, -8, 8, -8, }, +{2: 16, 8, -8, 8, 16, -8, 8, -16, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 0, 8, -8, 16, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 8, 8, 8, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 16, 8, -16, -8, -8, -8, 8, 8, 8, -16, -8, 8, }, +{5: 16, -8, 0, -8, 16, -8, 8, -8, -8, 0, -8, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, -8, 16, -8, -8, 8, 8, -8, -8, 0, -8, -8, 8, 0, }, +{9: 16, 0, 0, 8, -16, -8, -8, 8, 0, 0, -8, 0, 8, 8, -8, 0, }, +{a: 16, 0, 0, 8, -16, -8, 8, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -16, 8, -8, -8, 0, 0, 8, 0, -8, 8, 8, 0, }, +{7: 16, -8, -8, -16, 16, 8, 8, 8, -8, -8, -16, -8, 8, 8, 8, -8, }, +{b: 16, 0, 0, 8, -16, 8, -8, -8, 0, 0, -8, 0, -8, 8, 8, 0, }, +{d: 16, 0, 0, -8, -16, -8, 8, -8, 0, 0, 8, 0, 8, -8, 8, 0, }, +{e: 16, 0, 0, -8, -16, -8, -8, 8, 0, 0, 8, 0, 8, 8, -8, 0, }, +{f: 16, 0, 0, -8, -16, 8, 8, 8, 0, 0, 8, 0, -8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , , , x, x, , , x, }, +{5: , , , x, , x, x, , , , , x, , x, , x, }, +{6: , , x, x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, , , , x, x, , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , x, , x, , , , , , , , x, , x, }, +{e: , , x, x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0011,0001,1,}, +{0100,0111,1,}, +{0101,0011,1,}, +{0110,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0001,1,}, +{1100,0111,1,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x03,0x08,0x0b,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +280 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x04,0x03,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 8, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 4, }, +{3: 0, 0, 2, 2, 0, 10, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 2, 2, 0, 0, 8, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 2, 0, 4, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 2, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 4, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 10, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 4, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 2, 6, 2, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 6, }, +}; +Diff: 10, DDT_spectrum: {0:184, 2:48, 4:8, 6:8, 8:3, 10:4, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 6:1, 8:1, 10:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 10, 4, 10, 8, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 8, 10, 8, 0, 10, 8, 10, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 4, 4, 0, 10, 4, 0, 0, 6, 6, 0, 4, 6, 0, 0, 4, }, +{3: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 16, 10, 10, 10, 0, 8, 8, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{6: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{9: 16, 4, 4, 0, 6, 4, 0, 0, 10, 6, 0, 4, 6, 0, 4, 0, }, +{a: 16, 4, 4, 0, 6, 4, 0, 0, 6, 10, 0, 4, 6, 4, 0, 0, }, +{c: 16, 4, 4, 0, 0, 4, 0, 0, 0, 0, 10, 4, 4, 6, 6, 6, }, +{7: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{b: 16, 4, 4, 0, 6, 4, 0, 0, 6, 6, 4, 4, 10, 0, 0, 0, }, +{d: 16, 4, 4, 0, 0, 4, 0, 0, 0, 4, 6, 4, 0, 10, 6, 6, }, +{e: 16, 4, 4, 0, 0, 4, 0, 0, 4, 0, 6, 4, 0, 6, 10, 6, }, +{f: 16, 4, 4, 0, 4, 4, 0, 0, 0, 0, 6, 4, 0, 6, 6, 10, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:72, 4:72, 6:24, 8:21, 10:36, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 4, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 12, 4, 0, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:130, 4:104, 8:12, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:7, 4:5, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -8, -16, 8, -8, 8, 8, -8, -8, -16, 8, -8, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 8, 0, -8, 16, 8, -8, -8, 8, 0, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 8, 8, 8, 0, 0, -8, 0, -8, -8, -8, 0, }, +{3: 16, -8, -8, 8, 16, 8, -8, -16, -8, -8, 8, 8, 8, -8, -16, 8, }, +{5: 16, -8, 8, -8, 16, -8, 8, -8, -8, 8, -8, 0, -8, 8, -8, 0, }, +{6: 16, 0, -8, -8, 16, -8, -8, 8, 0, -8, -8, 8, -8, -8, 8, 8, }, +{9: 16, 0, 0, 8, -16, -8, -8, 8, 0, 0, -8, 0, 8, 8, -8, 0, }, +{a: 16, 0, 0, 8, -16, -8, 8, -8, 0, 0, -8, 0, 8, -8, 8, 0, }, +{c: 16, 0, 0, -8, -16, 8, -8, -8, 0, 0, 8, 0, -8, 8, 8, 0, }, +{7: 16, -8, -8, -16, 16, 8, 8, 8, -8, -8, -16, -8, 8, 8, 8, -8, }, +{b: 16, 0, 0, 8, -16, 8, -8, -8, 0, 0, -8, 0, -8, 8, 8, 0, }, +{d: 16, 0, 0, -8, -16, -8, 8, -8, 0, 0, 8, 0, 8, -8, 8, 0, }, +{e: 16, 0, 0, -8, -16, -8, -8, 8, 0, 0, 8, 0, 8, 8, -8, 0, }, +{f: 16, 0, 0, -8, -16, 8, 8, 8, 0, 0, 8, 0, -8, -8, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , , , x, x, , , x, }, +{5: , x, , x, , x, x, , , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, , , , x, x, , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , x, , x, , x, , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 23 */ +{0011,0010,1,}, +{0100,0111,1,}, +{0101,0001,1,}, +{0110,0011,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1100,0111,1,}, +{1101,0001,1,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_281.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_281.txt new file mode 100644 index 0000000..8be9aa9 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_281.txt @@ -0,0 +1,490 @@ +281 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 2, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 10, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 10, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 2, 0, 0, 0, 10, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 0, 0, 0, 10, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 2, 0, 0, 2, 0, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 8, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 8, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 8, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 8, }, +}; +Diff: 10, DDT_spectrum: {0:186, 2:54, 8:9, 10:6, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 8:1, 10:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 10, 4, 8, 8, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{2: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{8: 16, 4, 4, 4, 8, 4, 4, 4, 6, 4, 6, 0, 6, 4, 6, 0, }, +{3: 16, 10, 8, 8, 4, 10, 10, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{5: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 8, 10, 8, 4, 10, 8, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 4, 4, 4, 6, 4, 4, 4, 8, 6, 4, 0, 4, 6, 0, 6, }, +{a: 16, 4, 4, 4, 4, 4, 4, 4, 6, 8, 6, 0, 6, 0, 6, 4, }, +{c: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 8, 0, 0, 6, 4, 6, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 0, 0, 8, 6, 4, 6, }, +{d: 16, 4, 4, 4, 4, 4, 4, 4, 6, 0, 6, 0, 6, 8, 6, 4, }, +{e: 16, 4, 4, 4, 6, 4, 4, 4, 0, 6, 4, 0, 4, 6, 8, 6, }, +{f: 16, 4, 4, 4, 0, 4, 4, 4, 6, 4, 6, 0, 6, 4, 6, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:24, 4:112, 6:32, 8:29, 10:28, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:138, 4:100, 8:4, 12:12, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 12:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -8, -8, 8, -8, 8, 8, -16, -8, -8, 8, -16, }, +{2: 16, 8, -8, 8, 16, -8, 8, -16, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 8, 8, -16, 16, 8, -8, -8, 8, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, 8, 8, 8, -16, 8, 0, 8, -8, -8, -8, 8, -8, 0, -8, -8, }, +{3: 16, -16, -8, 8, 16, 8, -8, -8, -16, -8, 8, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 16, -16, 8, -8, -8, 8, -8, 8, -16, 8, -8, 8, }, +{6: 16, 8, -16, -8, 16, -8, -8, 8, 8, -16, -8, 8, -8, -8, 8, 8, }, +{9: 16, -8, 8, 8, -16, -8, 0, 8, 8, -8, -8, -8, 8, 0, -8, 8, }, +{a: 16, 8, -8, 8, -16, -8, 0, -8, -8, 8, -8, -8, 8, 0, 8, 8, }, +{c: 16, 8, 8, -8, -16, 8, 0, -8, -8, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, -8, -8, 8, -16, 8, 0, -8, 8, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, -8, 8, -8, -16, -8, 0, -8, 8, -8, 8, 8, 8, 0, 8, -8, }, +{e: 16, 8, -8, -8, -16, -8, 0, 8, -8, 8, 8, 8, 8, 0, -8, -8, }, +{f: 16, -8, -8, -8, -16, 8, 0, 8, 8, 8, 8, -8, -8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , , , x, x, , , x, }, +{5: , x, x, , , , x, , , , , x, , x, , x, }, +{6: , x, , , , , , x, , , , x, , , x, x, }, +{9: , x, x, x, , , , , x, , , , x, x, , x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, x, , , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 27 */ +{0001,0011,1,}, +{0010,0110,1,}, +{0011,0101,1,}, +{0100,0100,1,}, +{0110,0010,1,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0011,1,}, +{1010,0110,1,}, +{1011,0101,1,}, +{1100,0100,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 31, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +281 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 3:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 2, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 10, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 0, }, +{3: 0, 0, 2, 0, 0, 10, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 8, 2, 0, 0, 0, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 8, 2, 0, 2, 0, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 8, 0, 0, 2, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 8, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 8, 2, 0, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 8, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 8, }, +}; +Diff: 10, DDT_spectrum: {0:186, 2:54, 8:9, 10:6, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:9, 2:3, 8:1, 10:3, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 8, 4, 10, 10, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{2: 16, 10, 10, 8, 4, 8, 10, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 10, 10, 10, 4, 8, 8, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{8: 16, 4, 4, 4, 8, 4, 4, 4, 6, 4, 6, 0, 6, 4, 6, 0, }, +{3: 16, 8, 10, 8, 4, 10, 8, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{5: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 4, 4, 4, 6, 4, 4, 4, 8, 6, 4, 0, 4, 6, 0, 6, }, +{a: 16, 4, 4, 4, 4, 4, 4, 4, 6, 8, 6, 0, 6, 0, 6, 4, }, +{c: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 8, 0, 0, 6, 4, 6, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 4, 4, 6, 4, 4, 4, 4, 6, 0, 0, 8, 6, 4, 6, }, +{d: 16, 4, 4, 4, 4, 4, 4, 4, 6, 0, 6, 0, 6, 8, 6, 4, }, +{e: 16, 4, 4, 4, 6, 4, 4, 4, 0, 6, 4, 0, 4, 6, 8, 6, }, +{f: 16, 4, 4, 4, 0, 4, 4, 4, 6, 4, 6, 0, 6, 4, 6, 8, }, +}; +BCT_uniformity: 10, BCT_spectrum: {0:24, 4:112, 6:32, 8:29, 10:28, 16:31, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 12, 0, 4, 0, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:138, 4:100, 8:4, 12:12, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 12:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 16, -8, -8, 8, -16, 8, 8, -8, -8, -8, 8, -8, }, +{2: 16, 8, -8, 8, 16, -16, 8, -8, 8, -8, 8, -8, -16, 8, -8, -8, }, +{4: 16, 8, 8, -8, 16, 8, -8, -8, 8, 8, -8, -16, 8, -8, -8, -16, }, +{8: 16, 8, 8, 8, -16, 8, 0, 8, -8, -8, -8, 8, -8, 0, -8, -8, }, +{3: 16, -8, -16, 8, 16, 8, -8, -8, -8, -16, 8, 8, 8, -8, -8, 8, }, +{5: 16, -8, 8, -8, 16, -8, 8, -16, -8, 8, -8, 8, -8, 8, -16, 8, }, +{6: 16, 8, -8, -16, 16, -8, -8, 8, 8, -8, -16, 8, -8, -8, 8, 8, }, +{9: 16, -8, 8, 8, -16, -8, 0, 8, 8, -8, -8, -8, 8, 0, -8, 8, }, +{a: 16, 8, -8, 8, -16, -8, 0, -8, -8, 8, -8, -8, 8, 0, 8, 8, }, +{c: 16, 8, 8, -8, -16, 8, 0, -8, -8, -8, 8, -8, -8, 0, 8, 8, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, -8, -8, 8, -16, 8, 0, -8, 8, 8, -8, 8, -8, 0, 8, -8, }, +{d: 16, -8, 8, -8, -16, -8, 0, -8, 8, -8, 8, 8, 8, 0, 8, -8, }, +{e: 16, 8, -8, -8, -16, -8, 0, 8, -8, 8, 8, 8, 8, 0, -8, -8, }, +{f: 16, -8, -8, -8, -16, 8, 0, 8, 8, 8, 8, -8, -8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , x, x, , , , , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , , , x, x, , x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, x, x, , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 27 */ +{0001,0001,1,}, +{0010,0011,1,}, +{0011,0010,1,}, +{0100,0110,1,}, +{0110,0101,1,}, +{0111,0100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1010,0011,1,}, +{1011,0010,1,}, +{1100,0110,1,}, +{1110,0101,1,}, +{1111,0100,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 31, 7, +v=3 15, 0, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x08,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x08,0x0f,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x04,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x04,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_282.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_282.txt new file mode 100644 index 0000000..6e5eccb --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_282.txt @@ -0,0 +1,506 @@ +282 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, }, +{3: 0, 6, 0, 2, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 6, 2, 0, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 2, 2, }, +{7: 0, 2, 0, 2, 0, 2, 4, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, }, +}; +Diff: 12, DDT_spectrum: {0:185, 2:36, 4:21, 6:12, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 2, 8, 10, 0, 2, 8, 8, 0, 0, 8, 0, 0, 0, }, +{2: 16, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 16, 8, 8, 8, 8, }, +{4: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 8, 8, 0, 10, 8, 0, 0, 10, 8, 0, 0, 8, 0, 2, 2, }, +{3: 16, 10, 8, 2, 8, 10, 0, 2, 8, 8, 0, 0, 8, 0, 0, 0, }, +{5: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 8, 8, 0, 8, 8, 0, 0, 10, 10, 0, 0, 8, 2, 2, 0, }, +{a: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 2, 0, 10, 2, 0, 0, }, +{c: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 4, 6, 6, }, +{7: 16, 2, 8, 2, 0, 2, 8, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 8, 0, 10, 8, 0, 0, 8, 8, 2, 0, 10, 0, 0, 2, }, +{d: 16, 0, 8, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 6, 4, }, +{e: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 4, 4, }, +{f: 16, 0, 8, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 4, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:28, 4:8, 6:8, 8:60, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 4, 4, 0, 0, 0, 8, 4, 4, 4, 4, 8, 0, 0, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 4, 4, 0, 8, 0, 8, 4, 4, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 0, 0, 8, 4, }, +{f: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 8, 0, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:154, 4:62, 8:36, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, 0, -16, 0, -8, 0, 8, 0, 0, -16, 0, 0, }, +{2: 16, 8, -8, 8, 16, -16, 16, -16, 8, -8, 8, -8, -16, 16, -16, -8, }, +{4: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, 8, 8, -16, 0, 0, 16, 0, -8, -8, 0, 0, 0, -16, 0, }, +{3: 16, -8, 0, 8, 16, 0, -16, 0, -8, 0, 8, 0, 0, -16, 0, 0, }, +{5: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{6: 16, 8, -8, -8, 16, 0, 0, 0, 8, -8, -8, -8, 0, 0, 0, -8, }, +{9: 16, 0, 0, 8, -16, -16, 0, 0, 0, 0, -8, -8, 16, 0, 0, 8, }, +{a: 16, 0, -8, 8, -16, 0, 0, -16, 0, 8, -8, 0, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -16, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -8, 16, 0, 0, 0, -8, 0, -8, 0, 0, 0, 0, 0, }, +{b: 16, 0, 0, 8, -16, 16, 0, 0, 0, 0, -8, 8, -16, 0, 0, -8, }, +{d: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 8, }, +{e: 16, 0, -8, -8, -16, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , , , x, x, , , x, }, +{5: , , x, , , x, x, , , x, , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, x, , , x, x, , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, , , , x, , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , , , , x, , , , x, , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 35 */ +{0011,0010,1,}, +{0011,1001,1,}, +{0011,1011,0,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1011,0010,1,}, +{1011,1001,0,}, +{1011,1011,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 17, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x05,0x08,0x0d,}}, +{{0x05,0x06,}, {0x05,0x08,0x0d,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0e,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +282 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 6, 0, 0, 2, }, +{3: 0, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 6, 0, 2, 0, 0, 2, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, 4, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 4, 4, 2, }, +}; +Diff: 12, DDT_spectrum: {0:185, 2:36, 4:21, 6:12, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 2:1, 4:1, 6:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 0, 8, 10, 2, 0, 8, 8, 0, 2, 8, 0, 0, 0, }, +{2: 16, 8, 16, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, }, +{4: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 16, 8, 8, 0, 10, 8, 0, 0, 8, 8, 2, 0, 10, 0, 0, 2, }, +{3: 16, 10, 8, 0, 8, 10, 2, 0, 8, 8, 0, 2, 8, 0, 0, 0, }, +{5: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 2, 8, 8, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 16, 8, 8, 0, 10, 8, 0, 0, 10, 8, 2, 0, 8, 2, 0, 0, }, +{a: 16, 8, 8, 0, 8, 8, 0, 0, 10, 10, 0, 0, 8, 2, 2, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 6, 6, }, +{7: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 0, 0, 10, 0, 2, 2, }, +{d: 16, 0, 8, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 6, 4, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 0, 8, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 4, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:104, 2:28, 4:8, 6:8, 8:60, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{b: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:154, 4:62, 8:36, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 16, 0, -8, 0, -16, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 16, -16, 8, 16, -16, 8, -8, 16, -16, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{8: 16, 0, 0, 8, -16, 16, 0, 0, 0, 0, -8, 8, -16, 0, 0, -8, }, +{3: 16, -16, 0, 8, 16, 0, -8, 0, -16, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 16, 0, 8, -8, 0, 0, -8, -8, 0, 8, -8, -8, }, +{6: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{9: 16, 0, 16, 8, -16, 0, 0, 8, 0, -16, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -16, -16, 0, 0, 0, 0, -8, -8, 16, 0, 0, 8, }, +{c: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{b: 16, 0, -16, 8, -16, 0, 0, -8, 0, 16, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 8, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , , x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , , x, , , , , x, x, , , x, x, , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 35 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,1001,0,}, +{0010,1011,1,}, +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{0100,0111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,1001,1,}, +{1010,1011,0,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +{1100,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 17, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x03,0x08,0x0b,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_283.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_283.txt new file mode 100644 index 0000000..7f660b4 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_283.txt @@ -0,0 +1,506 @@ +283 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0a,0x08,0x09,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 6, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 2, 2, 2, 0, 0, 4, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 2, 2, 0, 2, 2, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 2, 0, 0, 0, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 6, 2, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 2, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 4, 4, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 2, }, +}; +Diff: 12, DDT_spectrum: {0:185, 2:36, 4:21, 6:12, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:9, 2:2, 4:1, 6:3, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 10, 2, 8, 8, 0, 0, 8, 8, 0, 2, 8, 0, 0, 0, }, +{2: 16, 8, 10, 2, 8, 10, 2, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{4: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 16, 8, 8, 8, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 16, 8, }, +{3: 16, 10, 8, 0, 8, 10, 2, 0, 8, 8, 0, 2, 8, 0, 0, 0, }, +{5: 16, 2, 2, 2, 8, 0, 4, 4, 0, 0, 0, 2, 0, 4, 4, 0, }, +{6: 16, 0, 2, 2, 8, 2, 2, 4, 0, 0, 0, 4, 0, 0, 4, 4, }, +{9: 16, 8, 8, 0, 8, 8, 0, 0, 10, 10, 2, 0, 8, 0, 0, 2, }, +{a: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 2, 0, 10, 2, 0, 0, }, +{c: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 2, 0, 4, 8, 2, 2, 4, 0, 0, 4, 2, 0, 0, 4, 0, }, +{b: 16, 8, 8, 0, 8, 8, 0, 0, 10, 8, 0, 0, 10, 2, 0, 2, }, +{d: 16, 0, 0, 0, 8, 0, 4, 4, 2, 2, 2, 0, 0, 4, 4, 2, }, +{e: 16, 0, 0, 0, 8, 0, 0, 4, 0, 2, 2, 4, 2, 2, 4, 4, }, +{f: 16, 0, 0, 4, 8, 0, 0, 4, 2, 0, 4, 0, 2, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:36, 4:40, 8:48, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 8, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{6: 0, 8, 4, 4, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 0, 4, 4, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{e: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 8, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:154, 4:62, 8:36, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:1, 8:3, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 8, 16, -8, 0, 0, 0, 0, 8, -16, -8, 0, 0, -16, }, +{2: 16, 0, -8, 8, 16, 0, 0, -16, 0, -8, 8, 0, 0, 0, -16, 0, }, +{4: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{8: 16, 16, 8, 8, -16, 8, 8, 16, -16, -8, -8, 16, -8, -8, -16, -16, }, +{3: 16, -16, 0, 8, 16, 0, -8, 0, -16, 0, 8, 0, 0, -8, 0, 0, }, +{5: 16, 0, 0, -8, 16, -8, 0, 0, 0, 0, -8, 0, -8, 0, 0, 0, }, +{6: 16, 0, -8, -8, 16, 0, 0, 0, 0, -8, -8, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 8, -16, -8, 0, 0, 0, 0, -8, -16, 8, 0, 0, 16, }, +{a: 16, 0, -8, 8, -16, 0, 0, -16, 0, 8, -8, 0, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -16, 8, 8, 0, 0, -8, 8, 0, -8, -8, 0, 0, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, -16, 0, 8, -16, 0, -8, 0, 16, 0, -8, 0, 0, 8, 0, 0, }, +{d: 16, 0, 0, -8, -16, -8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, }, +{e: 16, 0, -8, -8, -16, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -8, -16, 0, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , , x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , , , x, x, , , x, }, +{5: , x, x, , , , x, , x, x, , x, , x, , x, }, +{6: , x, , , , , , x, x, , , x, , , x, x, }, +{9: , , x, x, , , , , x, x, , , x, x, , x, }, +{a: , , x, x, , , , , x, x, , , x, , x, x, }, +{c: , , , , , , , , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , , , , , , , x, x, , , , x, , x, }, +{e: , , , , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 35 */ +{0001,0011,1,}, +{0001,1000,0,}, +{0001,1011,1,}, +{0100,0100,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{0111,0001,1,}, +{0111,1000,0,}, +{0111,1001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0011,1,}, +{1001,1000,1,}, +{1001,1011,0,}, +{1100,0100,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +{1111,0001,1,}, +{1111,1000,1,}, +{1111,1001,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 17, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x07,0x08,0x0f,}}, +{{0x03,0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x01,0x08,0x09,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x07,0x08,0x0f,}}, +{{0x05,0x06,}, {0x01,0x08,0x09,}}, +{{0x09,0x06,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x06,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x05,0x0e,}, {0x01,0x08,0x09,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +283 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x09,0x0a,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 6, 0, 0, 0, 6, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 6, 6, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 2, 4, 0, 0, 2, 2, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, }, +{3: 0, 0, 6, 0, 0, 6, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 2, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 6, 2, 0, 2, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 2, 2, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 2, 2, 4, }, +{7: 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 2, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 0, 2, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 2, }, +}; +Diff: 12, DDT_spectrum: {0:185, 2:36, 4:21, 6:12, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:9, 2:2, 4:1, 6:3, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 0, 8, 10, 2, 0, 8, 8, 0, 2, 8, 0, 0, 0, }, +{2: 16, 10, 10, 0, 8, 8, 2, 2, 8, 8, 0, 0, 8, 0, 0, 0, }, +{4: 16, 2, 2, 4, 8, 0, 2, 2, 0, 0, 4, 4, 0, 0, 0, 4, }, +{8: 16, 8, 8, 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 8, 8, }, +{3: 16, 8, 10, 0, 8, 10, 0, 2, 8, 8, 0, 2, 8, 0, 0, 0, }, +{5: 16, 0, 2, 4, 8, 2, 4, 2, 0, 0, 4, 2, 0, 4, 0, 0, }, +{6: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 16, 8, 8, 0, 8, 8, 0, 0, 10, 8, 0, 0, 10, 2, 0, 2, }, +{a: 16, 8, 8, 0, 8, 8, 0, 0, 10, 10, 0, 0, 8, 2, 2, 0, }, +{c: 16, 0, 0, 4, 8, 0, 0, 0, 2, 2, 4, 4, 0, 2, 2, 4, }, +{7: 16, 2, 0, 4, 8, 2, 2, 4, 0, 0, 4, 2, 0, 0, 4, 0, }, +{b: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 0, 0, 10, 0, 2, 2, }, +{d: 16, 0, 0, 4, 8, 0, 4, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{e: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 0, 0, 4, 8, 0, 0, 4, 2, 0, 4, 0, 2, 2, 4, 2, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 2:36, 4:40, 8:48, 10:12, 16:36, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{5: 0, 8, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{a: 0, 0, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 8, 4, 4, 4, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 0, 0, 4, 0, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:154, 4:62, 8:36, 12:2, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:1, 8:3, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 16, 0, -8, 0, -16, 0, 8, 0, 0, -8, 0, 0, }, +{2: 16, 0, 0, 8, 16, -16, 0, 0, 0, 0, 8, -8, -16, 0, 0, -8, }, +{4: 16, 0, 0, -8, 16, 0, 0, 0, 0, 0, -8, -8, 0, 0, 0, -8, }, +{8: 16, 16, 16, 8, -16, 16, 8, 8, -16, -16, -8, 8, -16, -8, -8, -8, }, +{3: 16, 0, -16, 8, 16, 0, 0, -8, 0, -16, 8, 0, 0, 0, -8, 0, }, +{5: 16, 0, 0, -8, 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{6: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{9: 16, -16, 0, 8, -16, 0, -8, 0, 16, 0, -8, 0, 0, 8, 0, 0, }, +{a: 16, 0, 0, 8, -16, -16, 0, 0, 0, 0, -8, -8, 16, 0, 0, 8, }, +{c: 16, 0, 0, -8, -16, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 8, }, +{7: 16, 0, 0, -8, 16, 0, -8, 0, 0, 0, -8, 0, 0, -8, 0, 0, }, +{b: 16, 0, -16, 8, -16, 0, 0, -8, 0, 16, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -16, 0, 8, 8, 0, 0, 8, 8, 0, -8, -8, -8, }, +{f: 16, 0, 0, -8, -16, 0, -8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , , , x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , x, , x, , x, , x, }, +{6: , x, x, , , , , x, x, x, , x, , , x, x, }, +{9: , , , x, , , , , x, x, , , x, x, , x, }, +{a: , , , x, , , , , x, x, , , x, , x, x, }, +{c: , , , x, , , , , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , x, , , , , , x, , , , x, , x, }, +{e: , , , , , , , , x, x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 35 */ +{0001,0001,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{0010,0011,1,}, +{0010,1000,0,}, +{0010,1011,1,}, +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{0100,0110,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,1000,1,}, +{1001,1001,0,}, +{1010,0011,1,}, +{1010,1000,1,}, +{1010,1011,0,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +{1100,0110,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 17, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,}, {0x01,0x08,0x09,}}, +{{0x03,0x04,}, {0x02,0x08,0x0a,}}, +{{0x09,0x04,}, {0x01,0x08,0x09,}}, +{{0x0b,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0c,}, {0x01,0x08,0x09,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x07,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x03,0x08,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_284.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_284.txt new file mode 100644 index 0000000..3554f93 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_284.txt @@ -0,0 +1,510 @@ +284 Sbox: +LUT = { +0x06,0x00,0x01,0x02,0x03,0x05,0x04,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 4, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{7: 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +}; +Diff: 12, DDT_spectrum: {0:188, 2:32, 4:27, 8:7, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:12, 4:1, 8:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 8, 0, 16, 16, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 16, 8, 8, 8, 8, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 8, 8, 8, 0, 16, 16, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 6, 6, }, +{7: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 6, 6, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:16, 4:16, 6:16, 8:40, 16:56, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 0, 4, 0, 4, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 0, 4, 8, 4, 0, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:158, 4:60, 8:32, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 8, 16, -8, -16, 8, -8, 0, 8, 0, -8, -16, 8, 0, }, +{2: 16, 8, -16, 8, 16, -8, 16, -8, 8, -16, 8, -16, -8, 16, -8, -16, }, +{4: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -8, 0, 8, 16, 8, -16, -8, -8, 0, 8, 0, 8, -16, -8, 0, }, +{5: 16, -8, 0, -8, 16, -8, 0, -8, -8, 0, -8, 16, -8, 0, -8, 16, }, +{6: 16, 8, -16, -8, 16, -8, 0, 8, 8, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, -8, 0, -8, 16, 8, 0, 8, -8, 0, -8, -16, 8, 0, 8, -16, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , x, , x, , x, , x, , , , x, x, , , x, }, +{5: , , , , , x, x, x, , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , x, , x, , x, , x, , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , x, , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 37 */ +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0100,1,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0100,1,}, +{1111,0010,1,}, +{1111,0101,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x0b,0x0c,}, {0x07,0x08,0x0f,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x07,0x08,0x0f,}}, +{{0x07,0x08,}, {0x07,0x08,0x0f,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x07,0x08,0x0f,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x09,0x0e,}, {0x07,0x08,0x0f,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +284 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x06,0x05,0x00,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{3: 0, 4, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 2, 0, 0, 2, 0, 2, 2, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{7: 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 4, 2, 0, 4, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 2, 2, }, +{e: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 2, 4, 4, }, +}; +Diff: 12, DDT_spectrum: {0:188, 2:32, 4:27, 8:7, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:12, 4:1, 8:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 8, 16, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, }, +{4: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{3: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 8, 16, 0, 8, 16, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 8, 0, 4, 0, 0, 0, 4, 6, 0, 0, 6, 0, 2, 2, }, +{a: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{c: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 6, 6, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 8, 0, 6, 0, 0, 0, 6, 4, 2, 0, 4, 2, 0, 0, }, +{d: 16, 0, 8, 0, 0, 0, 0, 0, 0, 2, 4, 0, 2, 4, 6, 6, }, +{e: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +{f: 16, 0, 8, 0, 2, 0, 0, 0, 2, 0, 6, 0, 0, 6, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:112, 2:16, 4:16, 6:16, 8:40, 16:56, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 12, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 4, 0, 8, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 12, 4, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:158, 4:60, 8:32, 12:4, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:2, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 8, 16, 0, -8, 8, -16, 0, 8, -8, 0, -8, 8, -8, }, +{2: 16, 16, -16, 8, 16, -16, 8, -8, 16, -16, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 0, -8, 16, 16, -8, -8, 0, 0, -8, -8, 16, -8, -8, -8, }, +{8: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{3: 16, -16, 0, 8, 16, 0, -8, -8, -16, 0, 8, 8, 0, -8, -8, 8, }, +{5: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -8, 16, -16, -8, 8, 0, 0, -8, 8, -16, -8, 8, 8, }, +{9: 16, 0, 0, 8, -16, 0, 0, 8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{a: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{c: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{7: 16, 0, -16, -8, 16, 0, 8, 8, 0, -16, -8, -8, 0, 8, 8, -8, }, +{b: 16, 0, 0, 8, -16, 0, 0, -8, 0, 0, -8, 0, 0, 0, 8, 0, }, +{d: 16, 0, 0, -8, -16, 0, 0, -8, 0, 0, 8, 0, 0, 0, 8, 0, }, +{e: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +{f: 16, 0, 0, -8, -16, 0, 0, 8, 0, 0, 8, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , , x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, x, , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, , , , x, x, , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 37 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0101,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +{1100,0101,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x02,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x03,0x08,0x0b,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x03,0x08,0x0b,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x04,}, {0x03,0x08,0x0b,}}, +{{0x0b,0x04,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,0x08,0x0b,}}, +{{0x0d,0x06,}, {0x03,0x08,0x0b,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_285.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_285.txt new file mode 100644 index 0000000..a0496aa --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_285.txt @@ -0,0 +1,490 @@ +285 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x08,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 2, 0, 4, 0, 0, 0, 0, 2, 2, 0, 0, 0, }, +{8: 0, 0, 0, 2, 6, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 2, 2, 0, 6, 4, 2, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 2, 6, 2, 2, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 2, 2, 0, 2, 0, 6, 4, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 2, 2, 2, 6, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 0, 2, 0, 2, 0, 6, 2, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 2, 0, 2, 0, 2, 6, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 12, DDT_spectrum: {0:192, 2:24, 4:27, 6:8, 8:3, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:10, 2:2, 6:2, 8:1, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{2: 16, 8, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, }, +{4: 16, 4, 8, 6, 2, 4, 8, 4, 0, 0, 0, 10, 2, 0, 0, 0, }, +{8: 16, 4, 8, 2, 6, 4, 0, 0, 8, 4, 0, 2, 10, 0, 0, 0, }, +{3: 16, 8, 8, 4, 4, 16, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{5: 16, 4, 8, 10, 2, 4, 6, 8, 2, 0, 0, 4, 0, 0, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 10, 6, 2, 2, 0, 8, 0, 0, 0, 0, }, +{9: 16, 4, 8, 2, 10, 4, 2, 0, 6, 8, 0, 0, 4, 0, 0, 0, }, +{a: 16, 4, 8, 0, 4, 4, 2, 2, 10, 6, 0, 0, 8, 0, 0, 0, }, +{c: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{7: 16, 4, 8, 8, 0, 4, 4, 10, 0, 2, 0, 6, 2, 0, 0, 0, }, +{b: 16, 4, 8, 0, 8, 4, 0, 2, 4, 10, 0, 2, 6, 0, 0, 0, }, +{d: 16, 8, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 8, 8, 0, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:16, 4:40, 6:8, 8:52, 10:8, 16:42, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:138, 4:90, 8:20, 12:6, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -16, 8, -8, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 16, -8, -8, 16, -16, -16, }, +{4: 16, 0, 8, -8, 8, 8, 0, -8, 0, 8, -16, 0, 0, 0, -8, -8, }, +{8: 16, 0, 8, 8, -8, 8, 0, 8, 0, -8, -16, 0, 0, 0, -8, -8, }, +{3: 16, -16, -8, 8, 8, 8, -8, 0, -8, 0, 16, 0, 0, -16, -8, 8, }, +{5: 16, 0, 8, -8, 8, -8, 0, 0, 0, 0, -16, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, -8, 8, -8, 0, 8, 0, -8, -16, 0, 0, 0, 8, 8, }, +{9: 16, 0, 8, 8, -8, -8, 0, 0, 0, 0, -16, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 8, -8, -8, 0, -8, 0, 8, -16, 0, 0, 0, 8, 8, }, +{c: 16, 0, 8, -16, -16, 8, 0, -8, 0, -8, 16, -8, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 8, 8, 0, 0, 0, 0, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, 0, 0, 0, -16, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, -8, 0, -8, 0, 16, 0, 0, 0, 8, -8, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, -8, 0, 16, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, x, x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, x, , , x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 27 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,1100,1,}, +{1000,1100,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 9, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x06,0x0a,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +285 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x08,0x05,0x06,0x07,0x04,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, }, +{4: 0, 0, 0, 6, 2, 0, 2, 0, 2, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 2, 6, 0, 2, 0, 2, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 4, 0, 0, 6, 2, 2, 2, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 6, 0, 2, 0, 2, 2, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 2, 2, 6, 2, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 2, 4, 6, 0, 2, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 2, 2, 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, }, +{b: 0, 0, 0, 2, 2, 0, 0, 0, 0, 4, 0, 2, 6, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, }, +{e: 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, }, +}; +Diff: 12, DDT_spectrum: {0:192, 2:24, 4:27, 6:8, 8:3, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:10, 2:2, 6:2, 8:1, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 4, 4, 8, 4, 4, 4, 4, 8, 4, 4, 8, 0, 0, }, +{2: 16, 8, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, }, +{4: 16, 4, 8, 6, 2, 4, 10, 4, 2, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 4, 8, 2, 6, 4, 2, 0, 10, 4, 0, 0, 8, 0, 0, 0, }, +{3: 16, 8, 8, 4, 4, 16, 4, 4, 4, 4, 8, 4, 4, 0, 0, 8, }, +{5: 16, 4, 8, 8, 0, 4, 6, 10, 2, 2, 0, 4, 0, 0, 0, 0, }, +{6: 16, 4, 8, 4, 0, 4, 8, 6, 0, 2, 0, 10, 2, 0, 0, 0, }, +{9: 16, 4, 8, 0, 8, 4, 2, 2, 6, 10, 0, 0, 4, 0, 0, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 2, 8, 6, 0, 2, 10, 0, 0, 0, }, +{c: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{7: 16, 4, 8, 10, 2, 4, 4, 8, 0, 0, 0, 6, 2, 0, 0, 0, }, +{b: 16, 4, 8, 2, 10, 4, 0, 0, 4, 8, 0, 2, 6, 0, 0, 0, }, +{d: 16, 8, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 8, 8, 0, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 0, 8, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 0, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:90, 2:16, 4:40, 6:8, 8:52, 10:8, 16:42, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 12, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 0, 0, 0, 4, 12, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{6: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 8, 0, 0, 4, 4, }, +{9: 0, 8, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 8, 0, 0, }, +{a: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 0, 8, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 4, 4, 4, 4, 0, 4, 8, 0, 8, 0, 0, 4, 4, }, +{b: 0, 0, 4, 4, 4, 4, 4, 8, 4, 0, 0, 0, 8, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:138, 4:90, 8:20, 12:6, 16:2, }; +Lin1: 12, LAT1_spectrum: {0:10, 4:2, 8:1, 12:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 8, -8, -8, 0, -8, 0, 16, 0, 0, -16, 8, -8, }, +{2: 16, 16, -16, 8, 8, -16, 8, -8, 8, -8, 16, -8, -8, 16, -16, -16, }, +{4: 16, 0, 8, -8, 8, 8, 0, 0, 0, 0, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 8, -8, 8, 0, 0, 0, 0, -16, 8, -8, 0, -8, -8, }, +{3: 16, -16, -8, 8, 8, 8, -8, 0, -8, 0, 16, 0, 0, -16, -8, 8, }, +{5: 16, 0, 8, -8, 8, -8, 0, -8, 0, 8, -16, 0, 0, 0, -8, 8, }, +{6: 16, 0, -8, -8, 8, -8, 0, 0, 0, 0, -16, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 8, -8, -8, 0, 8, 0, -8, -16, 0, 0, 0, -8, 8, }, +{a: 16, 0, -8, 8, -8, -8, 0, 0, 0, 0, -16, -8, 8, 0, 8, 8, }, +{c: 16, 0, 8, -16, -16, 8, 0, -8, 0, -8, 16, -8, -8, 0, 8, 8, }, +{7: 16, 0, -8, -8, 8, 8, 0, 8, 0, -8, -16, 0, 0, 0, 8, -8, }, +{b: 16, 0, -8, 8, -8, 8, 0, -8, 0, 8, -16, 0, 0, 0, 8, -8, }, +{d: 16, 0, 8, -8, -8, -8, -8, 0, -8, 0, 16, 0, 0, 0, 8, -8, }, +{e: 16, 0, -8, -8, -8, -8, 8, 0, 8, 0, 16, 0, 0, 0, -8, -8, }, +{f: 16, 0, -8, -8, -8, 8, -8, 0, -8, 0, 16, 0, 0, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, , x, , , x, x, x, , x, }, +{2: , , x, x, x, x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, x, x, , , , , , x, x, , , x, }, +{5: , , x, x, x, , x, , , , , x, , x, , x, }, +{6: , , , x, x, x, , x, , , , x, , , x, x, }, +{9: , , x, x, x, , , , x, , , , x, x, , x, }, +{a: , , , x, x, x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , x, x, , , , , , , x, , , , x, }, +{b: , , , x, x, , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 27 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,1100,1,}, +{1000,1100,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 9, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x0c,}}, +{{0x01,0x04,0x08,}, {0x0c,}}, +{{0x03,0x04,0x08,}, {0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x0c,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x0c,}}, +{{0x01,0x0a,0x04,}, {0x0c,}}, +{{0x09,0x0a,0x04,}, {0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x07,0x0b,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x0c,}}, +{{0x0b,0x04,}, {0x0c,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x0c,}}, +{{0x07,0x08,}, {0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x0c,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x0c,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x09,0x0e,}, {0x06,0x0a,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_286.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_286.txt new file mode 100644 index 0000000..8eff45b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_286.txt @@ -0,0 +1,494 @@ +286 Sbox: +LUT = { +0x04,0x00,0x01,0x02,0x03,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 0, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 2, 0, 10, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 2, 0, 2, 0, 2, 8, 2, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 6, }, +}; +Diff: 12, DDT_spectrum: {0:189, 2:38, 4:13, 6:8, 8:4, 10:2, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 2:1, 6:1, 8:1, 10:1, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 10, 4, 10, 8, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{2: 16, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 16, 8, 8, 8, 8, }, +{4: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 4, 8, 0, 6, 4, 0, 0, 8, 4, 2, 0, 10, 0, 0, 2, }, +{3: 16, 10, 8, 10, 4, 10, 8, 10, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 4, 8, 0, 8, 4, 0, 0, 6, 10, 0, 0, 4, 2, 2, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 10, 6, 0, 0, 8, 2, 2, 0, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 8, 4, 10, }, +{7: 16, 10, 8, 10, 0, 10, 8, 10, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 8, 0, 0, 6, 10, 4, }, +{e: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 10, 6, 8, }, +{f: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 10, 0, 2, 4, 8, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:80, 2:16, 4:40, 6:8, 8:48, 10:24, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 4, 4, 12, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 4, 4, 4, 0, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 12, 0, }, +{f: 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:142, 4:88, 8:16, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:1, 12:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 8, 16, -8, -16, 8, -8, 8, 8, -8, -8, -16, 8, -8, }, +{2: 16, 8, -8, 8, 16, -16, 16, -16, 8, -8, 8, -8, -16, 16, -16, -8, }, +{4: 16, 0, 8, -16, 16, 8, 0, -8, 0, 8, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 8, -16, 8, 0, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, -8, -8, 8, 16, 8, -16, -8, -8, -8, 8, 8, 8, -16, -8, 8, }, +{5: 16, -8, 8, -8, 16, -8, 0, -8, -8, 8, -8, 8, -8, 0, -8, 8, }, +{6: 16, 8, -16, -8, 16, -8, 0, 8, 8, -16, -8, 0, -8, 0, 8, 0, }, +{9: 16, 0, 8, 8, -16, -8, 0, 8, 0, -8, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -16, -8, 0, -8, 0, 8, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, -8, -8, -8, 16, 8, 0, 8, -8, -8, -8, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -16, 8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 8, 0, }, +{e: 16, 0, -8, -8, -16, -8, 0, 8, 0, 8, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, -8, -16, 8, 0, 8, 0, 8, 8, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , x, x, x, , x, , , , , , x, x, , , x, }, +{5: , , x, , , x, x, , , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , , x, , , , x, x, , x, }, +{a: , x, x, x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, x, x, , x, , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 29 */ +{0010,0110,1,}, +{0011,0010,1,}, +{0100,0100,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1100,0100,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 11, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x08,0x0a,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x08,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x08,}}, +{{0x07,0x08,}, {0x08,}}, +{{0x01,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x06,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x06,}, {0x02,0x08,0x0a,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x08,}}, +{{0x09,0x0e,}, {0x08,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +286 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x04,0x00,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:2, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 10, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 2, 0, 8, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 2, 0, 2, 0, 0, 2, }, +{3: 0, 2, 0, 0, 0, 10, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 2, 8, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 6, 2, 0, 0, 0, 2, 2, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 0, 4, 2, 2, 0, }, +{c: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 2, 4, 0, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 6, 0, 0, 2, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 0, 0, 6, 2, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 6, 4, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 4, 6, }, +}; +Diff: 12, DDT_spectrum: {0:189, 2:38, 4:13, 6:8, 8:4, 10:2, 12:1, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 2:1, 6:1, 8:1, 10:1, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 10, 8, 8, 4, 10, 10, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{2: 16, 8, 16, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, }, +{4: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{8: 16, 4, 8, 0, 6, 4, 0, 0, 8, 4, 2, 0, 10, 0, 0, 2, }, +{3: 16, 10, 8, 8, 4, 10, 10, 8, 4, 4, 4, 10, 4, 4, 4, 4, }, +{5: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 10, 8, 8, 0, 10, 10, 8, 0, 0, 0, 10, 0, 0, 0, 0, }, +{9: 16, 4, 8, 0, 8, 4, 0, 0, 6, 10, 0, 0, 4, 2, 2, 0, }, +{a: 16, 4, 8, 0, 4, 4, 0, 0, 10, 6, 0, 0, 8, 2, 2, 0, }, +{c: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 6, 0, 2, 8, 4, 10, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 4, 8, 0, 10, 4, 0, 0, 4, 8, 2, 0, 6, 0, 0, 2, }, +{d: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 8, 0, 0, 6, 10, 4, }, +{e: 16, 4, 8, 0, 0, 4, 0, 0, 2, 2, 4, 0, 0, 10, 6, 8, }, +{f: 16, 4, 8, 0, 2, 4, 0, 0, 0, 0, 10, 0, 2, 4, 8, 6, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:80, 2:16, 4:40, 6:8, 8:48, 10:24, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 4, }, +{7: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:142, 4:88, 8:16, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:1, 12:2, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 16, -8, -8, 8, -16, 8, 8, -8, -8, -8, 8, -8, }, +{2: 16, 16, -16, 8, 16, -16, 8, -8, 16, -16, 8, -8, -16, 8, -8, -8, }, +{4: 16, 0, 8, -8, 16, 8, -8, -8, 0, 8, -8, -8, 8, -8, -8, -8, }, +{8: 16, 0, 8, 8, -16, 8, 0, 8, 0, -8, -8, 0, -8, 0, -8, 0, }, +{3: 16, -16, -8, 8, 16, 8, -8, -8, -16, -8, 8, 8, 8, -8, -8, 8, }, +{5: 16, 0, 8, -8, 16, -8, 8, -16, 0, 8, -8, 0, -8, 8, -16, 0, }, +{6: 16, 0, -8, -8, 16, -8, -8, 8, 0, -8, -8, 8, -8, -8, 8, 8, }, +{9: 16, 0, 8, 8, -16, -8, 0, 8, 0, -8, -8, 0, 8, 0, -8, 0, }, +{a: 16, 0, -8, 8, -16, -8, 0, -8, 0, 8, -8, 0, 8, 0, 8, 0, }, +{c: 16, 0, 8, -8, -16, 8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, }, +{7: 16, 0, -8, -16, 16, 8, 0, 8, 0, -8, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 8, -16, 8, 0, -8, 0, 8, -8, 0, -8, 0, 8, 0, }, +{d: 16, 0, 8, -8, -16, -8, 0, -8, 0, -8, 8, 0, 8, 0, 8, 0, }, +{e: 16, 0, -8, -8, -16, -8, 0, 8, 0, 8, 8, 0, 8, 0, -8, 0, }, +{f: 16, 0, -8, -8, -16, 8, 0, 8, 0, 8, 8, 0, -8, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , , x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , , , x, , x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , , , x, x, , x, }, +{a: , , , x, , x, , , , x, , , x, , x, x, }, +{c: , x, x, x, , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , x, , , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , , , x, , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 29 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0111,1,}, +{0110,0101,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0111,1,}, +{1110,0101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 27, 11, +v=3 15, 3, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x08,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x06,0x08,}, {0x08,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x08,}}, +{{0x0b,0x04,}, {0x08,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x08,}}, +{{0x0d,0x06,}, {0x08,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_287.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_287.txt new file mode 100644 index 0000000..bfcfc4b --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_287.txt @@ -0,0 +1,526 @@ +287 Sbox: +LUT = { +0x01,0x00,0x04,0x03,0x02,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, }, +{3: 0, 0, 2, 6, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 6, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 0, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 6, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 0, 0, }, +{e: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, }, +}; +Diff: 8, DDT_spectrum: {0:198, 2:24, 4:6, 6:24, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 6:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 0, 0, 0, 0, 0, 16, 0, 8, 8, 16, 8, 8, 0, 0, }, +{2: 16, 0, 10, 2, 0, 2, 10, 0, 8, 0, 8, 8, 8, 0, 8, 0, }, +{4: 16, 0, 2, 10, 0, 10, 2, 0, 8, 8, 0, 8, 0, 8, 8, 0, }, +{8: 16, 0, 0, 0, 10, 8, 8, 8, 2, 0, 0, 0, 8, 8, 10, 2, }, +{3: 16, 0, 2, 10, 8, 10, 2, 0, 0, 0, 8, 8, 8, 0, 0, 8, }, +{5: 16, 0, 10, 2, 8, 2, 10, 0, 0, 8, 0, 8, 0, 8, 0, 8, }, +{6: 16, 16, 0, 0, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 8, 8, }, +{9: 16, 0, 8, 8, 2, 0, 0, 8, 10, 0, 0, 0, 8, 8, 2, 10, }, +{a: 16, 8, 0, 8, 0, 0, 8, 0, 0, 10, 2, 0, 10, 2, 8, 8, }, +{c: 16, 8, 8, 0, 0, 8, 0, 0, 0, 2, 10, 0, 2, 10, 8, 8, }, +{7: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 2, 0, 10, 2, 0, 0, }, +{d: 16, 8, 0, 8, 8, 0, 8, 0, 8, 2, 10, 0, 2, 10, 0, 0, }, +{e: 16, 0, 8, 8, 10, 0, 0, 8, 2, 8, 8, 0, 0, 0, 10, 2, }, +{f: 16, 0, 0, 0, 2, 8, 8, 8, 10, 8, 8, 0, 0, 0, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:24, 8:72, 10:24, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{a: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:132, 4:96, 8:24, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, -8, -8, 16, -8, 0, 0, -8, -8, -8, 16, -8, }, +{2: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{4: 16, 0, 0, 0, 16, 8, -8, -16, 0, 0, 0, 0, 8, -8, -16, 0, }, +{8: 16, 8, 0, 0, -16, 0, 0, 16, -8, 0, 0, 8, 0, 0, -16, -8, }, +{3: 16, 0, 0, 0, 16, 8, -8, -16, 0, 0, 0, 0, 8, -8, -16, 0, }, +{5: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{6: 16, 0, -8, -8, 16, -8, -8, 16, 0, -8, -8, 0, -8, -8, 16, 0, }, +{9: 16, -8, 0, 0, -16, 0, 0, 16, 8, 0, 0, -8, 0, 0, -16, 8, }, +{a: 16, 0, -8, 8, -16, 0, 0, -16, 0, 8, -8, 0, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -16, 0, 0, -16, 0, -8, 8, 0, 0, 0, 16, 0, }, +{7: 16, -8, -8, -8, 16, 0, 0, 16, -8, -8, -8, -8, 0, 0, 16, -8, }, +{b: 16, 0, -8, 8, -16, 0, 0, -16, 0, 8, -8, 0, 0, 0, 16, 0, }, +{d: 16, 0, 8, -8, -16, 0, 0, -16, 0, -8, 8, 0, 0, 0, 16, 0, }, +{e: 16, 8, 0, 0, -16, 0, 0, 16, -8, 0, 0, 8, 0, 0, -16, -8, }, +{f: 16, -8, 0, 0, -16, 0, 0, 16, 8, 0, 0, -8, 0, 0, -16, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 45 */ +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 7, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +287 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x03,0x02,0x05,0x06,0x07,0x0f,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x08, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 6, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, }, +{3: 0, 0, 2, 6, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 6, 2, 0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 6, 2, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 0, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 0, 6, 2, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 0, 2, 6, 0, 0, }, +{e: 0, 0, 0, 0, 6, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 2, }, +{f: 0, 0, 0, 0, 2, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, }, +}; +Diff: 8, DDT_spectrum: {0:198, 2:24, 4:6, 6:24, 8:3, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:10, 2:2, 6:3, 8:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 0, 0, 0, 0, 0, 16, 0, 8, 8, 16, 8, 8, 0, 0, }, +{2: 16, 0, 10, 2, 0, 2, 10, 0, 8, 0, 8, 8, 8, 0, 8, 0, }, +{4: 16, 0, 2, 10, 0, 10, 2, 0, 8, 8, 0, 8, 0, 8, 8, 0, }, +{8: 16, 0, 0, 0, 10, 8, 8, 8, 2, 0, 0, 0, 8, 8, 10, 2, }, +{3: 16, 0, 2, 10, 8, 10, 2, 0, 0, 0, 8, 8, 8, 0, 0, 8, }, +{5: 16, 0, 10, 2, 8, 2, 10, 0, 0, 8, 0, 8, 0, 8, 0, 8, }, +{6: 16, 16, 0, 0, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 8, 8, }, +{9: 16, 0, 8, 8, 2, 0, 0, 8, 10, 0, 0, 0, 8, 8, 2, 10, }, +{a: 16, 8, 0, 8, 0, 0, 8, 0, 0, 10, 2, 0, 10, 2, 8, 8, }, +{c: 16, 8, 8, 0, 0, 8, 0, 0, 0, 2, 10, 0, 2, 10, 8, 8, }, +{7: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 8, 8, 0, 8, 8, 0, 0, 8, 10, 2, 0, 10, 2, 0, 0, }, +{d: 16, 8, 0, 8, 8, 0, 8, 0, 8, 2, 10, 0, 2, 10, 0, 0, }, +{e: 16, 0, 8, 8, 10, 0, 0, 8, 2, 8, 8, 0, 0, 0, 10, 2, }, +{f: 16, 0, 0, 0, 2, 8, 8, 8, 10, 8, 8, 0, 0, 0, 2, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 2:24, 8:72, 10:24, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{4: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +{a: 0, 4, 0, 8, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{7: 0, 8, 4, 4, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 0, 0, }, +{b: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 4, 4, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:132, 4:96, 8:24, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:8, 4:4, 8:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 0, 16, -8, -8, 16, -8, 0, 0, -8, -8, -8, 16, -8, }, +{2: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{4: 16, 0, 0, 0, 16, 8, -8, -16, 0, 0, 0, 0, 8, -8, -16, 0, }, +{8: 16, 8, 0, 0, -16, 0, 0, 16, -8, 0, 0, 8, 0, 0, -16, -8, }, +{3: 16, 0, 0, 0, 16, 8, -8, -16, 0, 0, 0, 0, 8, -8, -16, 0, }, +{5: 16, 0, 0, 0, 16, -8, 8, -16, 0, 0, 0, 0, -8, 8, -16, 0, }, +{6: 16, 0, -8, -8, 16, -8, -8, 16, 0, -8, -8, 0, -8, -8, 16, 0, }, +{9: 16, -8, 0, 0, -16, 0, 0, 16, 8, 0, 0, -8, 0, 0, -16, 8, }, +{a: 16, 0, -8, 8, -16, 0, 0, -16, 0, 8, -8, 0, 0, 0, 16, 0, }, +{c: 16, 0, 8, -8, -16, 0, 0, -16, 0, -8, 8, 0, 0, 0, 16, 0, }, +{7: 16, -8, -8, -8, 16, 0, 0, 16, -8, -8, -8, -8, 0, 0, 16, -8, }, +{b: 16, 0, -8, 8, -16, 0, 0, -16, 0, 8, -8, 0, 0, 0, 16, 0, }, +{d: 16, 0, 8, -8, -16, 0, 0, -16, 0, -8, 8, 0, 0, 0, 16, 0, }, +{e: 16, 8, 0, 0, -16, 0, 0, 16, -8, 0, 0, 8, 0, 0, -16, -8, }, +{f: 16, -8, 0, 0, -16, 0, 0, 16, 8, 0, 0, -8, 0, 0, -16, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, x, x, , x, x, x, x, x, x, x, , x, x, x, }, +{5: , x, x, x, , x, x, x, x, x, x, x, x, , x, x, }, +{6: , x, x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{9: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , x, , , , x, x, x, x, x, x, x, , x, x, x, }, +{d: , x, , , , x, x, x, x, x, x, x, x, , x, x, }, +{e: , , x, x, , x, x, x, x, x, x, x, x, x, , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 45 */ +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 7, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x06,0x08,0x0e,}}, +{{0x09,0x06,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x06,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_288.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_288.txt new file mode 100644 index 0000000..f73a8b2 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_288.txt @@ -0,0 +1,550 @@ +288 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x05,0x04,0x06,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 2:4, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:207, 4:36, 8:12, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 4:1, 8:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 0, 8, 16, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{2: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{4: 16, 0, 8, 16, 4, 8, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 16, 16, 0, 16, 16, 0, 16, 0, 16, 0, 16, 0, 0, 16, 0, 0, }, +{3: 16, 16, 16, 0, 8, 16, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{5: 16, 0, 8, 0, 4, 8, 16, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 0, 8, 16, 4, 8, 0, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{9: 16, 16, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{a: 16, 16, 0, 16, 0, 0, 16, 0, 0, 16, 0, 0, 16, 0, 16, 16, }, +{c: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 0, 8, 0, 4, 8, 16, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{b: 16, 16, 0, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{d: 16, 0, 0, 0, 4, 0, 16, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 0, 0, 4, 0, 16, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 4:64, 8:32, 16:68, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{6: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{9: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{a: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 8, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{d: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{e: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 8, 4, }, +}; +Lin: 16, LAT_spectrum: {0:156, 4:64, 8:32, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 16, 16, -8, -8, 0, -8, 0, 16, -8, -8, -8, 0, -8, }, +{2: 16, 0, -16, 16, 16, 0, 0, -16, 0, -16, 16, 0, 0, 0, -16, 0, }, +{4: 16, 8, 0, -16, 16, 8, -8, 0, 8, 0, -16, -8, 8, -8, 0, -8, }, +{8: 16, 0, 16, 16, -16, 0, 0, 16, 0, -16, -16, 0, 0, 0, -16, 0, }, +{3: 16, -8, 0, 16, 16, -8, -8, 0, -8, 0, 16, -8, -8, -8, 0, -8, }, +{5: 16, -8, 0, -16, 16, -8, 8, 0, -8, 0, -16, 8, -8, 8, 0, 8, }, +{6: 16, 8, 0, -16, 16, 8, -8, 0, 8, 0, -16, -8, 8, -8, 0, -8, }, +{9: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, -16, 16, -16, 0, 0, -16, 0, 16, -16, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, -8, 0, -16, 16, -8, 8, 0, -8, 0, -16, 8, -8, 8, 0, 8, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , x, x, x, , x, x, x, }, +{8: , x, , , x, , x, , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , x, x, , , , x, , , x, , x, , x, , x, }, +{6: , , , , , , x, x, , , , x, , , x, x, }, +{9: , x, , , , , , , x, x, , , x, x, , x, }, +{a: , x, , , , , x, , , x, , , x, , x, x, }, +{c: , x, , , , , x, , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , x, , , , , , , , x, , , , x, , x, }, +{e: , , , , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0010,0010,1,}, +{0010,1000,0,}, +{0010,1010,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1010,1000,1,}, +{1010,1010,0,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 19, +v=3 15, 15, 3, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,}, {0x04,0x08,0x0c,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +288 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x04,0x06,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 2:4, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 8, DDT_spectrum: {0:207, 4:36, 8:12, 16:1, }; +Diff1: 8, DDT1_spectrum: {0:11, 4:1, 8:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{2: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 16, 0, 16, 16, 16, 0, 0, 16, 0, 16, 16, 0, 0, 0, 16, 0, }, +{8: 16, 8, 0, 4, 16, 8, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{3: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 0, 16, 0, 16, 0, 16, 0, 0, 16, 0, 16, 0, 16, 0, 16, }, +{6: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 8, 0, 4, 16, 8, 4, 4, 8, 0, 4, 4, 8, 4, 4, 4, }, +{a: 16, 8, 0, 4, 0, 8, 4, 4, 8, 16, 4, 4, 8, 4, 4, 4, }, +{c: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 0, 4, 0, 8, 4, 4, 8, 16, 4, 4, 8, 4, 4, 4, }, +{d: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 16, 0, 0, 4, 0, 0, 4, 4, 0, 16, 4, 4, 0, 4, 4, 4, }, +{f: 16, 0, 0, 4, 0, 0, 4, 4, 0, 16, 4, 4, 0, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:92, 4:64, 8:32, 16:68, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{b: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:156, 4:64, 8:32, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 0, -8, 16, 16, -8, 0, -8, 0, -8, 16, -8, -8, 0, -8, -8, }, +{4: 16, 16, 0, -16, 16, 0, -16, 0, 16, 0, -16, 0, 0, -16, 0, 0, }, +{8: 16, 0, 8, 16, -16, 8, 0, 8, 0, -8, -16, 8, -8, 0, -8, -8, }, +{3: 16, 0, -8, 16, 16, -8, 0, -8, 0, -8, 16, -8, -8, 0, -8, -8, }, +{5: 16, -16, 0, -16, 16, 0, 16, 0, -16, 0, -16, 0, 0, 16, 0, 0, }, +{6: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{9: 16, 0, 8, 16, -16, 8, 0, 8, 0, -8, -16, 8, -8, 0, -8, -8, }, +{a: 16, 0, -8, 16, -16, -8, 0, -8, 0, 8, -16, -8, 8, 0, 8, 8, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{b: 16, 0, -8, 16, -16, -8, 0, -8, 0, 8, -16, -8, 8, 0, 8, 8, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, x, , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , , x, x, , , x, x, , x, x, x, , x, x, x, }, +{8: , x, x, , x, , x, , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , x, , , , x, , , x, , x, , x, , x, }, +{6: , , x, , , , x, x, , , , x, , , x, x, }, +{9: , , , , , , , , x, x, , , x, x, , x, }, +{a: , x, x, , , , x, , , x, , , x, , x, x, }, +{c: , , x, , , , x, , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , , , x, , , , x, , x, }, +{e: , , x, , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0001,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0100,1,}, +{0101,0101,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0100,0,}, +{1001,0101,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0100,1,}, +{1101,0101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 19, +v=3 15, 15, 3, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x02,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_289.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_289.txt new file mode 100644 index 0000000..e6db2bf --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_289.txt @@ -0,0 +1,526 @@ +289 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x07,0x04,0x06,0x05,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 10, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 10, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 10, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:198, 2:12, 4:38, 8:3, 10:4, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 4:3, 8:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{8: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 16, 0, 0, }, +{3: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{6: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 16, 4, 4, 0, 0, 0, }, +{a: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 16, }, +{c: 16, 0, 0, 4, 0, 0, 4, 4, 16, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{b: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 16, 0, }, +{d: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 16, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 16, 4, 4, 4, }, +{f: 16, 0, 0, 4, 0, 0, 4, 4, 0, 16, 4, 4, 0, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:72, 4:96, 8:24, 10:16, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{5: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{d: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{e: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:132, 4:96, 8:24, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 16, 16, -8, -8, 0, -8, 0, 16, -8, -8, -8, 0, -8, }, +{2: 16, 0, -8, 16, 16, -8, 0, -8, 0, -8, 16, -8, -8, 0, -8, -8, }, +{4: 16, 8, 8, -16, 16, 8, -8, -8, 8, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -8, -8, 16, 16, 0, -8, -8, -8, -8, 16, 0, 0, -8, -8, 0, }, +{5: 16, -8, 8, -16, 16, -8, 8, -8, -8, 8, -16, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, -16, 16, -8, -8, 8, 8, -8, -16, 8, -8, -8, 8, 8, }, +{9: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, -8, -8, -16, 16, 8, 8, 8, -8, -8, -16, -8, 8, 8, 8, -8, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , x, , , , x, x, x, , , , x, , x, , x, }, +{6: , , x, , , x, x, x, , , , x, , , x, x, }, +{9: , x, x, , , x, , x, x, , , x, x, x, , x, }, +{a: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{c: , x, x, , , x, x, x, , , x, x, , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , x, , , , x, , x, , , , x, , x, , x, }, +{e: , , x, , , x, x, x, , , , x, , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 45 */ +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 7, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x02,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +289 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x07,0x06,0x04,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 10, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 10, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 10, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 10, DDT_spectrum: {0:198, 2:12, 4:38, 8:3, 10:4, 16:1, }; +Diff1: 10, DDT1_spectrum: {0:10, 4:3, 8:2, 10:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{8: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 16, 0, 0, }, +{3: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{6: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 16, 4, 4, 0, 0, 0, }, +{a: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 16, }, +{c: 16, 0, 0, 4, 0, 0, 4, 4, 16, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{b: 16, 0, 0, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 16, 0, }, +{d: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{e: 16, 0, 0, 4, 0, 0, 4, 4, 0, 0, 4, 4, 16, 4, 4, 4, }, +{f: 16, 0, 0, 4, 0, 0, 4, 4, 0, 16, 4, 4, 0, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:72, 4:96, 8:24, 10:16, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{5: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 4, 8, 0, 0, 4, 4, 0, 4, 8, 0, 4, 4, 4, 0, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{d: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{e: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:132, 4:96, 8:24, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 8:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 0, 16, 16, -8, -8, 0, -8, 0, 16, -8, -8, -8, 0, -8, }, +{2: 16, 0, -8, 16, 16, -8, 0, -8, 0, -8, 16, -8, -8, 0, -8, -8, }, +{4: 16, 8, 8, -16, 16, 8, -8, -8, 8, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -8, -8, 16, 16, 0, -8, -8, -8, -8, 16, 0, 0, -8, -8, 0, }, +{5: 16, -8, 8, -16, 16, -8, 8, -8, -8, 8, -16, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, -16, 16, -8, -8, 8, 8, -8, -16, 8, -8, -8, 8, 8, }, +{9: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, -8, -8, -16, 16, 8, 8, 8, -8, -8, -16, -8, 8, 8, 8, -8, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , x, , , , x, x, x, , , , x, , x, , x, }, +{6: , , x, , , , x, x, , , , x, , , x, x, }, +{9: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{a: , x, x, , , , x, , , x, , , x, , x, x, }, +{c: , x, x, , , x, x, x, , , x, x, , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , x, , , , x, x, x, , , , x, , x, , x, }, +{e: , , x, , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 45 */ +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 7, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x02,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_290.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_290.txt new file mode 100644 index 0000000..92497ac --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_290.txt @@ -0,0 +1,542 @@ +290 Sbox: +LUT = { +0x01,0x00,0x04,0x03,0x02,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 10, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 10, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 2, 2, 0, 10, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 8, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 8, }, +}; +Diff: 12, DDT_spectrum: {0:208, 2:12, 4:20, 8:9, 10:4, 12:2, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:10, 2:2, 8:1, 10:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{2: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 16, 8, 4, 4, 16, 4, 4, 8, 8, 4, 4, 0, 4, 4, 8, 0, }, +{3: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{9: 16, 8, 4, 4, 8, 4, 4, 8, 16, 4, 4, 0, 4, 4, 0, 8, }, +{a: 16, 8, 4, 4, 4, 4, 4, 8, 4, 16, 8, 0, 8, 0, 4, 4, }, +{c: 16, 8, 4, 4, 4, 4, 4, 8, 4, 8, 16, 0, 0, 8, 4, 4, }, +{7: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 8, 4, 4, 4, 4, 4, 8, 4, 8, 0, 0, 16, 8, 4, 4, }, +{d: 16, 8, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 8, 16, 4, 4, }, +{e: 16, 8, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 16, 8, }, +{f: 16, 8, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 8, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:24, 4:96, 8:72, 10:16, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:148, 4:88, 8:8, 12:8, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 12:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 16, -8, -8, 16, -16, 8, 8, -16, -8, -8, 16, -16, }, +{2: 16, 8, -8, 8, 16, -8, 8, -16, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 8, 8, -8, 16, 8, -8, -16, 8, 8, -8, -8, 8, -8, -16, -8, }, +{8: 16, 8, 8, 8, -16, 0, 0, 16, -8, -8, -8, 8, 0, 0, -16, -8, }, +{3: 16, -8, -8, 8, 16, 8, -8, -16, -8, -8, 8, 8, 8, -8, -16, 8, }, +{5: 16, -8, 8, -8, 16, -8, 8, -16, -8, 8, -8, 8, -8, 8, -16, 8, }, +{6: 16, 8, -16, -16, 16, -8, -8, 16, 8, -16, -16, 8, -8, -8, 16, 8, }, +{9: 16, -8, 8, 8, -16, 0, 0, 16, 8, -8, -8, -8, 0, 0, -16, 8, }, +{a: 16, 8, -8, 8, -16, 0, 0, -16, -8, 8, -8, -8, 0, 0, 16, 8, }, +{c: 16, 8, 8, -8, -16, 0, 0, -16, -8, -8, 8, -8, 0, 0, 16, 8, }, +{7: 16, -8, -8, -8, 16, 0, 0, 16, -8, -8, -8, -8, 0, 0, 16, -8, }, +{b: 16, -8, -8, 8, -16, 0, 0, -16, 8, 8, -8, 8, 0, 0, 16, -8, }, +{d: 16, -8, 8, -8, -16, 0, 0, -16, 8, -8, 8, 8, 0, 0, 16, -8, }, +{e: 16, 8, -8, -8, -16, 0, 0, 16, -8, 8, 8, 8, 0, 0, -16, -8, }, +{f: 16, -8, -8, -8, -16, 0, 0, 16, 8, 8, 8, -8, 0, 0, -16, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , x, , , , , , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , , , x, x, , x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, x, x, , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 53 */ +{0001,0001,1,}, +{0010,0110,1,}, +{0100,0110,1,}, +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1010,0110,1,}, +{1100,0110,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +290 Inverse Sbox: +LUT = { +0x01,0x00,0x04,0x03,0x02,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 10, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 2, 10, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{3: 0, 0, 2, 2, 0, 10, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 2, 2, 0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 8, 0, 0, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 8, }, +}; +Diff: 12, DDT_spectrum: {0:208, 2:12, 4:20, 8:9, 10:4, 12:2, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:10, 2:2, 8:1, 10:2, 12:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{2: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{4: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{8: 16, 8, 4, 4, 16, 4, 4, 8, 8, 4, 4, 0, 4, 4, 8, 0, }, +{3: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{5: 16, 8, 10, 10, 4, 10, 10, 8, 4, 4, 4, 8, 4, 4, 4, 4, }, +{6: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{9: 16, 8, 4, 4, 8, 4, 4, 8, 16, 4, 4, 0, 4, 4, 0, 8, }, +{a: 16, 8, 4, 4, 4, 4, 4, 8, 4, 16, 8, 0, 8, 0, 4, 4, }, +{c: 16, 8, 4, 4, 4, 4, 4, 8, 4, 8, 16, 0, 0, 8, 4, 4, }, +{7: 16, 16, 8, 8, 0, 8, 8, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 8, 4, 4, 4, 4, 4, 8, 4, 8, 0, 0, 16, 8, 4, 4, }, +{d: 16, 8, 4, 4, 4, 4, 4, 8, 4, 0, 8, 0, 8, 16, 4, 4, }, +{e: 16, 8, 4, 4, 8, 4, 4, 8, 0, 4, 4, 0, 4, 4, 16, 8, }, +{f: 16, 8, 4, 4, 0, 4, 4, 8, 8, 4, 4, 0, 4, 4, 8, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:24, 4:96, 8:72, 10:16, 16:48, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 0, 12, 4, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 0, 0, 4, 12, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{5: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 4, 4, 0, 4, 4, 0, 0, 12, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 4, 4, 0, 4, 4, 0, 0, 4, 12, 0, 4, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 4, 4, 0, 8, 0, 0, 4, 4, 4, 4, 8, 0, 0, 4, }, +{d: 0, 4, 4, 4, 0, 0, 8, 0, 4, 4, 4, 4, 0, 8, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:148, 4:88, 8:8, 12:8, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:10, 4:2, 12:3, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 8, 16, -8, -8, 16, -16, 8, 8, -16, -8, -8, 16, -16, }, +{2: 16, 8, -8, 8, 16, -8, 8, -16, 8, -8, 8, -8, -8, 8, -16, -8, }, +{4: 16, 8, 8, -8, 16, 8, -8, -16, 8, 8, -8, -8, 8, -8, -16, -8, }, +{8: 16, 8, 8, 8, -16, 0, 0, 16, -8, -8, -8, 8, 0, 0, -16, -8, }, +{3: 16, -8, -8, 8, 16, 8, -8, -16, -8, -8, 8, 8, 8, -8, -16, 8, }, +{5: 16, -8, 8, -8, 16, -8, 8, -16, -8, 8, -8, 8, -8, 8, -16, 8, }, +{6: 16, 8, -16, -16, 16, -8, -8, 16, 8, -16, -16, 8, -8, -8, 16, 8, }, +{9: 16, -8, 8, 8, -16, 0, 0, 16, 8, -8, -8, -8, 0, 0, -16, 8, }, +{a: 16, 8, -8, 8, -16, 0, 0, -16, -8, 8, -8, -8, 0, 0, 16, 8, }, +{c: 16, 8, 8, -8, -16, 0, 0, -16, -8, -8, 8, -8, 0, 0, 16, 8, }, +{7: 16, -8, -8, -8, 16, 0, 0, 16, -8, -8, -8, -8, 0, 0, 16, -8, }, +{b: 16, -8, -8, 8, -16, 0, 0, -16, 8, 8, -8, 8, 0, 0, 16, -8, }, +{d: 16, -8, 8, -8, -16, 0, 0, -16, 8, -8, 8, 8, 0, 0, 16, -8, }, +{e: 16, 8, -8, -8, -16, 0, 0, 16, -8, 8, 8, 8, 0, 0, -16, -8, }, +{f: 16, -8, -8, -8, -16, 0, 0, 16, 8, 8, 8, -8, 0, 0, -16, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, x, , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , , , x, x, , , x, }, +{5: , , x, x, , , x, , , , , x, , x, , x, }, +{6: , x, , , , , , x, , , , x, , , x, x, }, +{9: , , x, x, , , , , x, , , , x, x, , x, }, +{a: , x, x, x, , , , , , x, , , x, , x, x, }, +{c: , x, x, x, , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , x, x, , , , , , , , , x, , , x, }, +{d: , , x, x, , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 53 */ +{0001,0001,1,}, +{0010,0110,1,}, +{0100,0110,1,}, +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1010,0110,1,}, +{1100,0110,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 15, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x03,0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x06,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x04,0x08,}, {0x06,0x08,0x0e,}}, +{{0x02,0x08,}, {0x06,0x08,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x06,0x08,0x0e,}}, +{{0x02,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x04,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x04,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x0b,0x0c,}, {0x06,0x08,0x0e,}}, +{{0x01,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x06,0x08,0x0e,}}, +{{0x05,0x08,}, {0x06,0x08,0x0e,}}, +{{0x07,0x08,}, {0x06,0x08,0x0e,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x02,}, {0x06,0x08,0x0e,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0a,}, {0x06,0x08,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x09,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x0d,0x0e,}, {0x06,0x08,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_291.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_291.txt new file mode 100644 index 0000000..59e7262 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_291.txt @@ -0,0 +1,558 @@ +291 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x05,0x04,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 2:4, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 12, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 6, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 2, 2, }, +{7: 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 6, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 6, }, +}; +Diff: 12, DDT_spectrum: {0:206, 2:16, 4:9, 6:16, 8:5, 12:3, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 4:1, 6:1, 8:1, 12:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{2: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{4: 16, 8, 8, 16, 8, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 8, }, +{8: 16, 8, 0, 8, 10, 0, 8, 0, 10, 2, 8, 0, 2, 8, 0, 0, }, +{3: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 8, 8, 8, 8, 16, 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, }, +{6: 16, 8, 8, 16, 0, 16, 8, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 8, 0, 8, 10, 0, 8, 0, 10, 2, 8, 0, 2, 8, 0, 0, }, +{a: 16, 8, 0, 8, 2, 0, 8, 0, 2, 10, 0, 0, 10, 0, 8, 8, }, +{c: 16, 8, 0, 8, 8, 0, 8, 0, 8, 0, 10, 0, 0, 10, 2, 2, }, +{7: 16, 8, 8, 8, 0, 16, 16, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 0, 8, 2, 0, 8, 0, 2, 10, 0, 0, 10, 0, 8, 8, }, +{d: 16, 8, 0, 8, 8, 0, 8, 0, 8, 0, 10, 0, 0, 10, 2, 2, }, +{e: 16, 8, 0, 8, 0, 0, 8, 0, 0, 8, 2, 0, 8, 2, 10, 10, }, +{f: 16, 8, 0, 8, 0, 0, 8, 0, 0, 8, 2, 0, 8, 2, 10, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:80, 2:16, 8:88, 10:16, 16:56, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{6: 0, 4, 4, 0, 0, 0, 4, 12, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{d: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +}; +Lin: 16, LAT_spectrum: {0:164, 4:60, 8:24, 12:4, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:1, 12:1, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 16, 16, -16, -8, 8, -8, 8, 16, -16, -16, -8, 8, -16, }, +{2: 16, 0, -16, 16, 16, 0, 0, -16, 0, -16, 16, 0, 0, 0, -16, 0, }, +{4: 16, 8, 8, -16, 16, 16, -8, -8, 8, 8, -16, -16, 16, -8, -8, -16, }, +{8: 16, 0, 8, 16, -16, 0, 0, 8, 0, -8, -16, 0, 0, 0, -8, 0, }, +{3: 16, -8, -8, 16, 16, 0, -8, -8, -8, -8, 16, 0, 0, -8, -8, 0, }, +{5: 16, -8, 8, -16, 16, -16, 8, -8, -8, 8, -16, 16, -16, 8, -8, 16, }, +{6: 16, 8, -8, -16, 16, 0, -8, 8, 8, -8, -16, 0, 0, -8, 8, 0, }, +{9: 16, 0, 8, 16, -16, 0, 0, 8, 0, -8, -16, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 16, -16, 0, 0, -8, 0, 8, -16, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -16, -16, 0, 0, -8, 0, -8, 16, 0, 0, 0, 8, 0, }, +{7: 16, -8, -8, -16, 16, 0, 8, 8, -8, -8, -16, 0, 0, 8, 8, 0, }, +{b: 16, 0, -8, 16, -16, 0, 0, -8, 0, 8, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -16, -16, 0, 0, -8, 0, -8, 16, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -16, -16, 0, 0, 8, 0, 8, 16, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -16, -16, 0, 0, 8, 0, 8, 16, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, , x, , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , x, x, , , , x, , , , , x, , x, , x, }, +{6: , , , , , , x, x, , , , x, , , x, x, }, +{9: , x, x, , , , , , x, , , , x, x, , x, }, +{a: , x, , , , , x, , , x, , , x, , x, x, }, +{c: , x, x, , , , x, , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , , , , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 61 */ +{0010,0010,1,}, +{0011,0001,1,}, +{0011,0100,0,}, +{0011,0101,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0110,0010,1,}, +{0111,0001,1,}, +{0111,0100,1,}, +{0111,0101,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1010,0010,1,}, +{1011,0001,1,}, +{1011,0100,0,}, +{1011,0101,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1110,0010,1,}, +{1111,0001,1,}, +{1111,0100,1,}, +{1111,0101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 23, +v=3 15, 15, 3, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +291 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x04,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 2:4, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 4, 8, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 6, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 6, 0, 0, 0, 6, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 6, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 2, 2, }, +{7: 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 6, 0, 0, 6, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 6, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 6, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 6, 6, }, +}; +Diff: 12, DDT_spectrum: {0:206, 2:16, 4:9, 6:16, 8:5, 12:3, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 4:1, 6:1, 8:1, 12:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{2: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{4: 16, 8, 16, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, }, +{8: 16, 8, 0, 8, 10, 0, 8, 0, 10, 2, 8, 0, 2, 8, 0, 0, }, +{3: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 16, 8, 8, 8, 8, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 8, 0, 8, 10, 0, 8, 0, 10, 2, 8, 0, 2, 8, 0, 0, }, +{a: 16, 8, 0, 8, 2, 0, 8, 0, 2, 10, 0, 0, 10, 0, 8, 8, }, +{c: 16, 8, 0, 8, 8, 0, 8, 0, 8, 0, 10, 0, 0, 10, 2, 2, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 0, 8, 2, 0, 8, 0, 2, 10, 0, 0, 10, 0, 8, 8, }, +{d: 16, 8, 0, 8, 8, 0, 8, 0, 8, 0, 10, 0, 0, 10, 2, 2, }, +{e: 16, 8, 0, 8, 0, 0, 8, 0, 0, 8, 2, 0, 8, 2, 10, 10, }, +{f: 16, 8, 0, 8, 0, 0, 8, 0, 0, 8, 2, 0, 8, 2, 10, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:80, 2:16, 8:88, 10:16, 16:56, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{5: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 4, 0, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{b: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:164, 4:60, 8:24, 12:4, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 8:1, 12:1, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 16, 16, -8, -16, 8, -16, 8, 16, -8, -8, -16, 8, -8, }, +{2: 16, 0, -8, 16, 16, -8, 0, -8, 0, -8, 16, -8, -8, 0, -8, -8, }, +{4: 16, 16, 8, -16, 16, 8, -16, -8, 16, 8, -16, -8, 8, -16, -8, -8, }, +{8: 16, 0, 8, 16, -16, 0, 0, 8, 0, -8, -16, 0, 0, 0, -8, 0, }, +{3: 16, 0, -16, 16, 16, 0, 0, -16, 0, -16, 16, 0, 0, 0, -16, 0, }, +{5: 16, -16, 8, -16, 16, -8, 16, -8, -16, 8, -16, 8, -8, 16, -8, 8, }, +{6: 16, 0, -8, -16, 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 16, -16, 0, 0, 8, 0, -8, -16, 0, 0, 0, -8, 0, }, +{a: 16, 0, -8, 16, -16, 0, 0, -8, 0, 8, -16, 0, 0, 0, 8, 0, }, +{c: 16, 0, 8, -16, -16, 0, 0, -8, 0, -8, 16, 0, 0, 0, 8, 0, }, +{7: 16, 0, -8, -16, 16, 8, 0, 8, 0, -8, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 16, -16, 0, 0, -8, 0, 8, -16, 0, 0, 0, 8, 0, }, +{d: 16, 0, 8, -16, -16, 0, 0, -8, 0, -8, 16, 0, 0, 0, 8, 0, }, +{e: 16, 0, -8, -16, -16, 0, 0, 8, 0, 8, 16, 0, 0, 0, -8, 0, }, +{f: 16, 0, -8, -16, -16, 0, 0, 8, 0, 8, 16, 0, 0, 0, -8, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , , x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, , x, , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , x, , , , x, , , , , x, , x, , x, }, +{6: , , x, , , , x, x, , , , x, , , x, x, }, +{9: , , x, , , , , , x, , , , x, x, , x, }, +{a: , x, x, , , , x, , , x, , , x, , x, x, }, +{c: , , x, , , , x, , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , , x, , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 61 */ +{0001,0001,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0010,0011,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0100,1,}, +{0101,0101,0,}, +{0110,0011,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0100,0,}, +{1001,0101,1,}, +{1010,0011,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0100,1,}, +{1101,0101,0,}, +{1110,0011,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 23, +v=3 15, 15, 3, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0a,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x02,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_292.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_292.txt new file mode 100644 index 0000000..8015504 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_292.txt @@ -0,0 +1,550 @@ +292 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 10, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 10, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 10, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 10, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 10, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 10, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 10, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 10, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 10, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 10, }, +}; +Diff: 12, DDT_spectrum: {0:201, 2:36, 4:3, 10:12, 12:3, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 4:1, 10:2, 12:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{2: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{4: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{8: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{3: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{5: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{6: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{a: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{c: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{7: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{b: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{d: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{e: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{f: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {4:96, 8:72, 10:48, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 4, 12, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 4, 0, 0, 0, 4, 12, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 0, 4, 4, 0, 0, 0, 4, 12, 4, 4, 0, 0, 0, 4, 4, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 4, 4, 0, 0, 0, 4, 4, 4, 12, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 12, 0, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:156, 4:84, 12:12, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 12:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -8, 8, 16, 16, -16, -8, 8, -8, 8, 16, -16, -16, -8, 8, -16, }, +{2: 16, 8, -16, 16, 16, -8, 8, -16, 8, -16, 16, -8, -8, 8, -16, -8, }, +{4: 16, 8, 8, -16, 16, 8, -8, -8, 8, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, 8, 8, 16, -16, 8, 8, 8, -8, -8, -16, 8, -8, -8, -8, -8, }, +{3: 16, -16, -8, 16, 16, 8, -16, -8, -16, -8, 16, 8, 8, -16, -8, 8, }, +{5: 16, -8, 8, -16, 16, -8, 8, -8, -8, 8, -16, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, -16, 16, -8, -8, 8, 8, -8, -16, 8, -8, -8, 8, 8, }, +{9: 16, -8, 8, 16, -16, -8, -8, 8, 8, -8, -16, -8, 8, 8, -8, 8, }, +{a: 16, 8, -8, 16, -16, -8, 8, -8, -8, 8, -16, -8, 8, -8, 8, 8, }, +{c: 16, 8, 8, -16, -16, 8, -8, -8, -8, -8, 16, -8, -8, 8, 8, 8, }, +{7: 16, -8, -8, -16, 16, 8, 8, 8, -8, -8, -16, -8, 8, 8, 8, -8, }, +{b: 16, -8, -8, 16, -16, 8, -8, -8, 8, 8, -16, 8, -8, 8, 8, -8, }, +{d: 16, -8, 8, -16, -16, -8, 8, -8, 8, -8, 16, 8, 8, -8, 8, -8, }, +{e: 16, 8, -8, -16, -16, -8, -8, 8, -8, 8, 16, 8, 8, 8, -8, -8, }, +{f: 16, -8, -8, -16, -16, 8, 8, 8, 8, 8, 16, -8, -8, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, , , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , x, x, , , , x, , , , , x, , x, , x, }, +{6: , x, , , , , , x, , , , x, , , x, x, }, +{9: , x, x, , , , , , x, , , , x, x, , x, }, +{a: , x, , , , , , , , x, , , x, , x, x, }, +{c: , x, x, , , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , x, x, , , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0001,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1011,0001,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 19, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +292 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 4, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 10, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 10, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 2, 0, 0, 10, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{6: 0, 0, 0, 2, 0, 0, 2, 10, 0, 0, 0, 2, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 2, 0, 0, 0, 10, 2, 0, 0, 2, 0, 0, 0, }, +{a: 0, 0, 0, 0, 2, 0, 0, 0, 2, 10, 0, 0, 2, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 2, 2, 2, }, +{7: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 10, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 10, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 10, 2, 2, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 10, 2, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 10, }, +}; +Diff: 12, DDT_spectrum: {0:201, 2:36, 4:3, 10:12, 12:3, 16:1, }; +Diff1: 12, DDT1_spectrum: {0:11, 4:1, 10:2, 12:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{2: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{4: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{8: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{3: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{5: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{6: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{9: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{a: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{c: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{7: 16, 8, 8, 10, 4, 8, 10, 10, 4, 4, 4, 10, 4, 4, 4, 4, }, +{b: 16, 8, 8, 4, 10, 8, 4, 4, 10, 10, 4, 4, 10, 4, 4, 4, }, +{d: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{e: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +{f: 16, 8, 8, 4, 4, 8, 4, 4, 4, 4, 10, 4, 4, 10, 10, 10, }, +}; +BCT_uniformity: 16, BCT_spectrum: {4:96, 8:72, 10:48, 16:40, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 4, 0, 0, 0, 12, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 4, 4, 0, 0, 0, 4, 4, 12, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 12, 4, 0, 4, }, +{d: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 12, 4, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:156, 4:84, 12:12, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 4:1, 12:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 16, 16, -8, -16, 8, -16, 8, 16, -8, -8, -16, 8, -8, }, +{2: 16, 8, -8, 16, 16, -16, 8, -8, 8, -8, 16, -16, -16, 8, -8, -16, }, +{4: 16, 8, 8, -16, 16, 8, -8, -8, 8, 8, -16, -8, 8, -8, -8, -8, }, +{8: 16, 8, 8, 16, -16, 8, 8, 8, -8, -8, -16, 8, -8, -8, -8, -8, }, +{3: 16, -8, -16, 16, 16, 8, -8, -16, -8, -16, 16, 8, 8, -8, -16, 8, }, +{5: 16, -8, 8, -16, 16, -8, 8, -8, -8, 8, -16, 8, -8, 8, -8, 8, }, +{6: 16, 8, -8, -16, 16, -8, -8, 8, 8, -8, -16, 8, -8, -8, 8, 8, }, +{9: 16, -8, 8, 16, -16, -8, -8, 8, 8, -8, -16, -8, 8, 8, -8, 8, }, +{a: 16, 8, -8, 16, -16, -8, 8, -8, -8, 8, -16, -8, 8, -8, 8, 8, }, +{c: 16, 8, 8, -16, -16, 8, -8, -8, -8, -8, 16, -8, -8, 8, 8, 8, }, +{7: 16, -8, -8, -16, 16, 8, 8, 8, -8, -8, -16, -8, 8, 8, 8, -8, }, +{b: 16, -8, -8, 16, -16, 8, -8, -8, 8, 8, -16, 8, -8, 8, 8, -8, }, +{d: 16, -8, 8, -16, -16, -8, 8, -8, 8, -8, 16, 8, 8, -8, 8, -8, }, +{e: 16, 8, -8, -16, -16, -8, -8, 8, -8, 8, 16, 8, 8, 8, -8, -8, }, +{f: 16, -8, -8, -16, -16, 8, 8, 8, 8, 8, 16, -8, -8, -8, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, , , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , x, , , , x, , , , , x, , x, , x, }, +{6: , x, x, , , , , x, , , , x, , , x, x, }, +{9: , , x, , , , , , x, , , , x, x, , x, }, +{a: , x, x, , , , , , , x, , , x, , x, x, }, +{c: , x, x, , , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , x, x, , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0001,1,}, +{0010,0011,1,}, +{0011,0010,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0110,0011,1,}, +{0111,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1010,0011,1,}, +{1011,0010,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1110,0011,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 19, +v=3 15, 15, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_293.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_293.txt new file mode 100644 index 0000000..49ced03 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_293.txt @@ -0,0 +1,478 @@ +293 Sbox: +LUT = { +0x08,0x00,0x0a,0x02,0x03,0x05,0x01,0x07,0x04,0x09,0x06,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y1 = + + x1 + x2 + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + +ANF of components: +y0 + + + = + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + + x1 + x2 + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, }, +{3: 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, }, +{5: 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 4, 0, 0, 0, 0, }, +{9: 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 0, }, +{c: 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 4, }, +{b: 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, }, +}; +Diff: 16, DDT_spectrum: {0:198, 4:56, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:10, 4:5, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 16, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{8: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 4, 16, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{5: 16, 4, 16, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{9: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 4, 16, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{b: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{d: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{e: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 4:112, 16:60, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 8, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +{c: 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:163, 4:56, 8:28, 12:8, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 8:5, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 0, -8, 0, 8, 0, -8, 0, 8, -8, -16, 8, -8, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 8, 0, 0, 8, 0, -8, 0, 8, -16, 8, -8, 0, -8, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 8, 0, -8, 0, -8, -8, 0, -8, 8, }, +{3: 16, 0, -8, 0, 0, 8, 0, -8, 0, 8, 0, -8, 8, -16, -8, 8, }, +{5: 16, -16, 8, 0, 0, -8, 0, -8, 0, -8, 0, 8, 8, 0, -8, 8, }, +{6: 16, 0, -8, 0, 0, -8, 0, 8, 0, -8, -16, -8, 8, 0, 8, 8, }, +{9: 16, 0, 8, 0, 0, -8, -16, 8, 0, 8, 0, -8, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -16, -8, 0, -8, 0, 8, 0, 8, 8, 0, 8, -8, }, +{c: 16, 0, 8, -16, 0, 8, 0, -8, 0, -8, 0, -8, 8, 0, 8, -8, }, +{7: 16, -16, -8, 0, 0, 8, 0, 8, 0, 8, 0, -8, -8, 0, 8, -8, }, +{b: 16, 0, -8, 0, 0, 8, -16, -8, 0, -8, 0, 8, -8, 0, 8, 8, }, +{d: 16, 0, 8, 0, 0, -8, 0, -8, -16, 8, 0, -8, -8, 0, 8, 8, }, +{e: 16, 0, -8, -16, 0, -8, 0, 8, 0, 8, 0, 8, -8, 0, -8, 8, }, +{f: 16, 0, -8, 0, 0, 8, 0, 8, -16, -8, 0, 8, 8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , x, , x, , x, x, , , x, }, +{5: , , x, x, x, x, x, x, , x, , x, , x, , x, }, +{6: , , , , , x, , x, , x, , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , , , , , x, , x, , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , x, , x, , x, , , , x, }, +{b: , , , , , x, , x, , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 29 */ +{0001,0010,0,}, +{0001,0101,1,}, +{0001,0111,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0010,0,}, +{0100,1100,1,}, +{0100,1110,1,}, +{0101,0010,0,}, +{0101,1001,1,}, +{0101,1011,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1000,0010,0,}, +{1000,1000,1,}, +{1000,1010,1,}, +{1001,0010,0,}, +{1001,1101,1,}, +{1001,1111,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0010,0,}, +{1100,0100,1,}, +{1100,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 7, +v=3 7, 7, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x01,0x04,0x05,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0b,0x04,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x03,0x0c,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0c,}, {0x01,0x04,0x05,}}, +{{0x0b,0x0c,}, {0x01,0x04,0x05,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x06,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x08,0x09,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x01,0x08,0x09,}}, +{{0x01,0x0e,}, {0x04,0x09,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x04,0x05,}}, +{{0x09,0x0e,}, {0x01,0x04,0x05,}}, +{{0x0d,0x0e,}, {0x04,0x09,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +293 Inverse Sbox: +LUT = { +0x01,0x06,0x03,0x04,0x08,0x05,0x0a,0x07,0x00,0x09,0x02,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + + y3 = + x0 + x1 + x2 + + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, }, +{8: 0, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, }, +{3: 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, }, +{5: 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 4, 0, }, +{6: 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 4, 0, }, +{9: 0, 0, 0, 0, 4, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, }, +{b: 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, 0, }, +{d: 0, 4, 0, 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, }, +}; +Diff: 16, DDT_spectrum: {0:198, 4:56, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:10, 4:5, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 16, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{8: 16, 4, 16, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{3: 16, 4, 16, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{6: 16, 4, 16, 4, 0, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{9: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{a: 16, 4, 16, 4, 4, 4, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 0, 16, 4, 0, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{b: 16, 0, 16, 4, 4, 0, 4, 4, 4, 4, 0, 4, 4, 0, 0, 0, }, +{d: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 4, 16, 0, 4, 4, 4, 0, 0, 4, 4, 4, 0, 0, 4, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 4:112, 16:60, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 8, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{c: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +}; +Lin: 12, LAT_spectrum: {0:163, 4:56, 8:28, 12:8, 16:1, }; +Lin1: 12, LAT1_spectrum: {0:10, 8:5, 12:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 0, -8, 0, 8, 0, -8, 0, -8, 8, 0, 8, -8, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 8, 0, 0, 8, -16, -8, 0, -8, 0, -8, 8, 0, -8, 8, }, +{8: 16, 0, 8, 0, 0, 8, 0, 8, 0, 8, 0, -8, -8, -16, -8, -8, }, +{3: 16, -16, -8, 0, 0, 8, 0, -8, 0, 8, 0, 8, -8, 0, -8, 8, }, +{5: 16, 0, 8, -16, 0, -8, 0, -8, 0, 8, 0, 8, 8, 0, -8, -8, }, +{6: 16, 0, -8, 0, 0, -8, -16, 8, 0, 8, 0, 8, -8, 0, 8, -8, }, +{9: 16, 0, 8, 0, 0, -8, 0, 8, 0, -8, -16, 8, -8, 0, -8, 8, }, +{a: 16, 0, -8, 0, 0, -8, 0, -8, 0, -8, 0, 8, 8, -16, 8, 8, }, +{c: 16, 0, 8, 0, -16, 8, 0, -8, 0, -8, 0, 8, -8, 0, 8, -8, }, +{7: 16, 0, -8, -16, 0, 8, 0, 8, 0, -8, 0, -8, -8, 0, 8, 8, }, +{b: 16, 0, -8, 0, 0, 8, 0, -8, 0, 8, -16, -8, 8, 0, 8, -8, }, +{d: 16, 0, 8, 0, 0, -8, 0, -8, -16, 8, 0, -8, -8, 0, 8, 8, }, +{e: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +{f: 16, 0, -8, 0, 0, 8, 0, 8, -16, -8, 0, 8, 8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, x, x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , x, , x, , x, x, , , x, }, +{5: , , x, , x, , x, x, , x, , x, , x, , x, }, +{6: , , , , , x, , x, , x, , x, , , x, x, }, +{9: , , x, x, x, , , x, x, x, , , x, x, , x, }, +{a: , , , , , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , x, , x, , , , x, }, +{b: , , , , , , , x, , x, , , x, , , x, }, +{d: , , x, , , , , x, , , , , , x, , x, }, +{e: , , , , , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 29 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0010,0,}, +{0100,0101,1,}, +{0100,0111,1,}, +{0101,0010,0,}, +{0101,0100,1,}, +{0101,0110,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1000,0010,0,}, +{1000,1100,1,}, +{1000,1110,1,}, +{1001,0010,0,}, +{1001,1101,1,}, +{1001,1111,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0010,0,}, +{1100,1001,1,}, +{1100,1011,1,}, +{1101,0010,0,}, +{1101,1000,1,}, +{1101,1010,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 7, +v=3 7, 7, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x05,0x08,0x0d,}}, +{{0x01,0x02,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x04,0x09,0x0d,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x02,0x04,}, {0x05,0x09,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x05,0x08,0x0d,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x05,0x08,0x0d,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x05,0x08,0x0d,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,}}, +{{0x09,0x04,}, {0x05,0x09,0x0c,}}, +{{0x0b,0x04,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x04,0x09,0x0d,}}, +{{0x07,0x08,}, {0x04,0x09,0x0d,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,}}, +{{0x09,0x06,}, {0x05,0x09,0x0c,}}, +{{0x0d,0x06,}, {0x05,0x09,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x09,0x0a,}, {0x01,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x04,0x09,0x0d,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_294.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_294.txt new file mode 100644 index 0000000..62541be --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_294.txt @@ -0,0 +1,550 @@ +294 Sbox: +LUT = { +0x04,0x00,0x01,0x03,0x02,0x05,0x06,0x07,0x0c,0x08,0x09,0x0b,0x0a,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + x0x2 + x1x2 + + + ; deg = 2, term_n = 3, related_n = 3 +y1 = + + + x2 + + x0x1 + x0x2 + + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + x0x2 + x1x2 + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + + + x2 + + x0x1 + x0x2 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:1, 2:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, }, +}; +Diff: 16, DDT_spectrum: {0:198, 4:56, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:9, 4:6, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 4, 4, 16, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{2: 16, 0, 4, 4, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{4: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{8: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{3: 16, 4, 0, 0, 16, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{6: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 16, 4, 4, 4, 16, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{a: 16, 0, 4, 4, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{7: 16, 4, 0, 4, 16, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{b: 16, 4, 0, 0, 16, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{d: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{e: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{f: 16, 4, 0, 4, 16, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 4:112, 16:60, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 0, 8, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 8, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, }, +{7: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 8, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:198, 8:56, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 8:5, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -16, }, +{2: 16, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{4: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{8: 16, 16, 16, 16, -16, 16, 16, 16, -16, -16, -16, 16, -16, -16, -16, -16, }, +{3: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{6: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 16, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{b: 16, -16, 0, 0, -16, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{e: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , , , , x, , , , x, x, x, , x, x, x, x, }, +{3: , , x, x, , x, , , , x, x, x, x, , , x, }, +{5: , x, x, , , , x, , x, x, , x, , x, , x, }, +{6: , x, , , , , , x, x, , , x, , , x, x, }, +{9: , , , , , , , , x, x, x, , x, x, , x, }, +{a: , , , , , , , , x, x, x, , x, , x, x, }, +{c: , , , , , , , , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , x, x, , x, , , x, }, +{d: , , , , , , , , x, x, , , , x, , x, }, +{e: , , , , , , , , x, , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0011,1,}, +{0001,1000,0,}, +{0001,1011,1,}, +{0010,0110,1,}, +{0010,1000,0,}, +{0010,1110,1,}, +{0011,0101,1,}, +{0011,1000,0,}, +{0011,1101,1,}, +{0100,0100,1,}, +{0100,1000,0,}, +{0100,1100,1,}, +{0101,0111,1,}, +{0101,1000,0,}, +{0101,1111,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{0111,0001,1,}, +{0111,1000,0,}, +{0111,1001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0011,1,}, +{1001,1000,1,}, +{1001,1011,0,}, +{1010,0110,1,}, +{1010,1000,1,}, +{1010,1110,0,}, +{1011,0101,1,}, +{1011,1000,1,}, +{1011,1101,0,}, +{1100,0100,1,}, +{1100,1000,1,}, +{1100,1100,0,}, +{1101,0111,1,}, +{1101,1000,1,}, +{1101,1111,0,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +{1111,0001,1,}, +{1111,1000,1,}, +{1111,1001,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 7, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x02,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x02,0x04,}, {0x08,}}, +{{0x09,0x02,0x04,}, {0x08,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x08,}}, +{{0x09,0x02,0x0c,}, {0x08,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x02,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x06,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x0e,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +294 Inverse Sbox: +LUT = { +0x01,0x02,0x04,0x03,0x00,0x05,0x06,0x07,0x09,0x0a,0x0c,0x0b,0x08,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + x0x2 + x1x2 + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = + + x1 + + + x0x1 + x0x2 + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + x0x2 + x1x2 + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + ; deg = 2, term_n = 6, related_n = 3 + + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:1, 2:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 4, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 0, 4, 4, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 0, 4, 0, 4, 0, }, +}; +Diff: 16, DDT_spectrum: {0:198, 4:56, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:9, 4:6, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 4, 0, 0, 16, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{4: 16, 4, 4, 4, 16, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{8: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{3: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 16, 0, 4, 4, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{6: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{9: 16, 4, 0, 0, 16, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{a: 16, 4, 4, 0, 16, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{c: 16, 4, 4, 4, 16, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 4, }, +{7: 16, 4, 0, 4, 16, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{b: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{d: 16, 0, 4, 4, 16, 4, 4, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{e: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{f: 16, 4, 0, 4, 16, 4, 0, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:84, 4:112, 16:60, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 8, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 8, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 8, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 8, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:198, 8:56, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:10, 8:5, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 0, 0, 0, 16, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{4: 16, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, -16, }, +{8: 16, 16, 16, 16, -16, 16, 16, 16, -16, -16, -16, 16, -16, -16, -16, -16, }, +{3: 16, 0, -16, 0, 16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, 0, 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{9: 16, -16, 0, 0, -16, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 16, }, +{7: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{b: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, , x, x, x, x, x, x, , x, }, +{2: , x, x, x, , x, , x, x, x, x, x, x, , x, x, }, +{4: , x, x, x, , , x, x, x, x, x, x, , x, x, x, }, +{8: , , , , x, , , , x, x, x, , x, x, x, x, }, +{3: , , , x, , x, , , , , x, x, x, , , x, }, +{5: , , x, x, , , x, , , x, x, x, , x, , x, }, +{6: , x, x, , , , , x, x, x, , x, , , x, x, }, +{9: , , , , , , , , x, x, x, , x, x, , x, }, +{a: , , , , , , , , x, x, x, , x, , x, x, }, +{c: , , , , , , , , x, x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , x, , x, , , x, }, +{d: , , , , , , , , , x, x, , , x, , x, }, +{e: , , , , , , , , x, x, , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0001,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{0010,0011,1,}, +{0010,1000,0,}, +{0010,1011,1,}, +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{0100,0110,1,}, +{0100,1000,0,}, +{0100,1110,1,}, +{0101,0111,1,}, +{0101,1000,0,}, +{0101,1111,1,}, +{0110,0101,1,}, +{0110,1000,0,}, +{0110,1101,1,}, +{0111,0100,1,}, +{0111,1000,0,}, +{0111,1100,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,1000,1,}, +{1001,1001,0,}, +{1010,0011,1,}, +{1010,1000,1,}, +{1010,1011,0,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +{1100,0110,1,}, +{1100,1000,1,}, +{1100,1110,0,}, +{1101,0111,1,}, +{1101,1000,1,}, +{1101,1111,0,}, +{1110,0101,1,}, +{1110,1000,1,}, +{1110,1101,0,}, +{1111,0100,1,}, +{1111,1000,1,}, +{1111,1100,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 7, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x04,0x08,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x06,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x04,}, {0x08,}}, 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{0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_295.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_295.txt new file mode 100644 index 0000000..980ff3f --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_295.txt @@ -0,0 +1,550 @@ +295 Sbox: +LUT = { +0x04,0x00,0x06,0x02,0x03,0x05,0x01,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + + x0x3 + + x2x3; deg = 2, term_n = 3, related_n = 3 +y1 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + + x2 + + + + + x0x3 + + x2x3; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + + x0x2 + + + + x2x3; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3; deg = 2, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + x2x3; deg = 2, term_n = 3, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3; deg = 2, term_n = 8, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:1, 2:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{3: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, }, +}; +Diff: 16, DDT_spectrum: {0:198, 4:56, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:11, 4:4, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 16, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 8, 16, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 8, 16, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 8, 16, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:108, 4:64, 8:24, 16:60, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{4: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{c: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{d: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{e: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +}; +Lin: 16, LAT_spectrum: {0:198, 8:56, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{8: 16, 0, 0, 0, -16, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{3: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{5: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{9: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{c: 16, 0, 16, 0, -16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{7: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{b: 16, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 16, }, +{e: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, -16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , x, , , , x, x, , , x, }, +{5: , , x, , , x, x, , , x, , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, x, , , x, x, , x, }, +{a: , , , , , x, , x, , x, , , x, , x, x, }, +{c: , x, , , , x, , , , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , x, , x, , , , , x, , , x, }, +{d: , , , , , x, , , , x, , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0010,0,}, +{0001,0101,1,}, +{0001,0111,1,}, +{0010,0010,1,}, +{0010,1100,0,}, +{0010,1110,1,}, +{0011,0010,1,}, +{0011,1001,1,}, +{0011,1011,0,}, +{0100,0010,0,}, +{0100,0100,1,}, +{0100,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0110,1000,0,}, +{0110,1010,1,}, +{0111,0010,1,}, +{0111,1101,1,}, +{0111,1111,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0010,0,}, +{1001,0101,1,}, +{1001,0111,1,}, +{1010,0010,1,}, +{1010,1100,1,}, +{1010,1110,0,}, +{1011,0010,1,}, +{1011,1001,0,}, +{1011,1011,1,}, +{1100,0010,0,}, +{1100,0100,1,}, +{1100,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1110,1000,1,}, +{1110,1010,0,}, +{1111,0010,1,}, +{1111,1101,0,}, +{1111,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 7, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x02,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x03,0x0c,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0b,0x0c,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x01,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x03,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x05,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x0a,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x0d,0x0a,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x01,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x0e,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x09,0x0e,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x0e,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +295 Inverse Sbox: +LUT = { +0x01,0x06,0x03,0x04,0x00,0x05,0x02,0x07,0x0a,0x09,0x08,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + + x0x3 + + x2x3; deg = 2, term_n = 3, related_n = 3 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + + x2x3; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + x0 + + + + + + + x0x3 + + x2x3; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + + x3 + + x0x2 + + x0x3 + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3; deg = 2, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + + x2x3; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + x2 + + + + + x0x3 + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3; deg = 2, term_n = 8, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:1, 2:14, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 4, }, +{3: 0, 4, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{6: 0, 4, 0, 4, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 4, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 4, 4, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 4, }, +{e: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, }, +}; +Diff: 16, DDT_spectrum: {0:198, 4:56, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:11, 4:4, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 16, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 8, 16, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 8, 16, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 16, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 0, 16, 8, 0, 0, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:108, 4:64, 8:24, 16:60, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 8, 0, 0, 8, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 8, 0, 0, 8, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 8, 0, 0, 0, }, +{c: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{7: 0, 0, 0, 0, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 8, }, +{b: 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 8, 0, }, +}; +Lin: 16, LAT_spectrum: {0:198, 8:56, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 8:4, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{8: 16, 0, 0, 0, -16, 16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, }, +{3: 16, -16, 0, 0, 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{6: 16, 0, 0, 0, 16, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, }, +{9: 16, 0, 16, 0, -16, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 0, -16, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{c: 16, 0, 0, 0, -16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, }, +{7: 16, 0, 0, -16, 16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{b: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 16, }, +{e: 16, 0, 0, 0, -16, 0, 0, 16, 0, 0, 0, 0, 0, 0, -16, 0, }, +{f: 16, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, -16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, x, , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , x, x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , x, , , , x, x, , , x, }, +{5: , , x, , , , x, x, , x, , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , , x, , , , x, x, x, , , x, x, , x, }, +{a: , , , , , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , x, x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , x, , , , , x, , , x, }, +{d: , , , , , , , x, , x, , , , x, , x, }, +{e: , , , , , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 57 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,1001,0,}, +{0010,1011,1,}, +{0011,0010,1,}, +{0011,1000,0,}, +{0011,1010,1,}, +{0100,0010,0,}, +{0100,0101,1,}, +{0100,0111,1,}, +{0101,0010,0,}, +{0101,0100,1,}, +{0101,0110,1,}, +{0110,0010,1,}, +{0110,1100,1,}, +{0110,1110,0,}, +{0111,0010,1,}, +{0111,1101,1,}, +{0111,1111,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,1001,1,}, +{1010,1011,0,}, +{1011,0010,1,}, +{1011,1000,1,}, +{1011,1010,0,}, +{1100,0010,0,}, +{1100,0101,1,}, +{1100,0111,1,}, +{1101,0010,0,}, +{1101,0100,1,}, +{1101,0110,1,}, +{1110,0010,1,}, +{1110,1100,0,}, +{1110,1110,1,}, +{1111,0010,1,}, +{1111,1101,0,}, +{1111,1111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 7, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x03,0x05,0x06,0x08,0x0b,0x0d,0x0e,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0b,0x04,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x0d,0x06,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x06,0x07,0x08,0x09,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_296.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_296.txt new file mode 100644 index 0000000..baf23f5 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_296.txt @@ -0,0 +1,518 @@ +296 Sbox: +LUT = { +0x04,0x00,0x06,0x02,0x03,0x05,0x01,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y1 = + + x1 + x2 + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + + x1 + x2 + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, }, +{3: 0, 0, 0, 4, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 4, 0, 0, 0, 4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, }, +}; +Diff: 16, DDT_spectrum: {0:204, 4:44, 8:6, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:11, 4:2, 8:2, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{5: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 4:64, 8:24, 16:72, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:166, 4:56, 8:24, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 8:3, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 8, 0, 16, -8, -16, 8, 0, 8, 0, -8, -8, -16, 8, -8, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 8, -16, 16, 8, 0, -8, 0, 8, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 8, 0, -8, 0, -8, -8, 0, -8, 8, }, +{3: 16, 0, -8, 0, 16, 8, -16, -8, 0, -8, 0, 8, 8, -16, -8, 8, }, +{5: 16, -16, 8, 0, 16, -8, 0, -8, -16, 8, 0, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, -16, 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 0, -16, -8, 0, 8, 0, -8, 0, 8, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -16, -8, 0, -8, 0, 8, 0, 8, 8, 0, 8, -8, }, +{c: 16, 0, 8, 0, -16, 8, 0, -8, 0, -8, 0, 8, -8, 0, 8, -8, }, +{7: 16, -16, -8, 0, 16, 8, 0, 8, -16, -8, 0, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, -8, -8, 0, 8, 8, }, +{d: 16, 0, 8, 0, -16, -8, 0, -8, 0, -8, 0, -8, 8, 0, 8, 8, }, +{e: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +{f: 16, 0, -8, 0, -16, 8, 0, 8, 0, 8, 0, 8, -8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , x, , , , x, x, , , x, }, +{5: , , x, , , x, x, , , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , x, x, x, , x, , x, x, , , , x, x, , x, }, +{a: , , , , , x, , x, , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , x, , x, , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 41 */ +{0001,0010,0,}, +{0001,0101,1,}, +{0001,0111,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0010,0,}, +{0100,0100,1,}, +{0100,0110,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0010,0,}, +{1001,0101,1,}, +{1001,0111,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0010,0,}, +{1100,0100,1,}, +{1100,0110,1,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 11, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x03,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x09,0x0c,}, {0x01,0x08,0x09,}}, +{{0x0b,0x0c,}, {0x01,0x08,0x09,}}, +{{0x01,0x08,}, {0x05,0x08,0x0d,}}, +{{0x03,0x08,}, {0x05,0x08,0x0d,}}, +{{0x05,0x08,}, {0x01,0x08,0x09,}}, +{{0x07,0x08,}, {0x01,0x08,0x09,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x08,0x09,}}, +{{0x09,0x0a,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x0a,}, {0x01,0x08,0x09,}}, +{{0x01,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x08,0x09,}}, +{{0x09,0x0e,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0e,}, {0x05,0x08,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +296 Inverse Sbox: +LUT = { +0x01,0x06,0x03,0x04,0x00,0x05,0x02,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:1, 2:6, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 4, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, }, +{3: 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 4, 4, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, 0, }, +{c: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 4, 4, 0, 0, }, +{7: 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 4, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 4, 4, }, +{f: 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 4, 4, }, +}; +Diff: 16, DDT_spectrum: {0:204, 4:44, 8:6, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:11, 4:2, 8:2, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 16, 16, 8, 0, 16, 8, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 16, 0, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 4:64, 8:24, 16:72, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +}; +Lin: 16, LAT_spectrum: {0:166, 4:56, 8:24, 12:8, 16:2, }; +Lin1: 16, LAT1_spectrum: {0:11, 8:3, 12:1, 16:1, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 0, 16, -8, 0, 8, -16, 8, 0, -8, -8, 0, 8, -8, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 8, 0, 16, 8, -16, -8, 0, 8, 0, -8, 8, -16, -8, -8, }, +{8: 16, 0, 8, 0, -16, 8, 0, 8, 0, -8, 0, -8, -8, 0, -8, 8, }, +{3: 16, -16, -8, 0, 16, 8, 0, -8, -16, -8, 0, 8, 8, 0, -8, 8, }, +{5: 16, 0, 8, -16, 16, -8, 0, -8, 0, 8, -16, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, 0, 16, -8, -16, 8, 0, -8, 0, 8, -8, -16, 8, 8, }, +{9: 16, 0, 8, 0, -16, -8, 0, 8, 0, -8, 0, 8, 8, 0, -8, -8, }, +{a: 16, 0, -8, 0, -16, -8, 0, -8, 0, 8, 0, 8, 8, 0, 8, -8, }, +{c: 16, 0, 8, 0, -16, 8, 0, -8, 0, -8, 0, 8, -8, 0, 8, -8, }, +{7: 16, 0, -8, -16, 16, 8, 0, 8, 0, -8, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 0, -16, 8, 0, -8, 0, 8, 0, -8, -8, 0, 8, 8, }, +{d: 16, 0, 8, 0, -16, -8, 0, -8, 0, -8, 0, -8, 8, 0, 8, 8, }, +{e: 16, 0, -8, 0, -16, -8, 0, 8, 0, 8, 0, -8, 8, 0, -8, 8, }, +{f: 16, 0, -8, 0, -16, 8, 0, 8, 0, 8, 0, 8, -8, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, , x, x, x, x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, x, x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , x, , , , x, x, , , x, }, +{5: , , x, , , , x, x, , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , x, x, , , , x, x, , , , x, x, , x, }, +{a: , , , , , x, , x, , x, , , x, , x, x, }, +{c: , x, x, x, , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , x, , , , , x, , , x, }, +{d: , , x, , , , , x, , , , , , x, , x, }, +{e: , , , , , x, , x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 41 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0010,0,}, +{0100,0101,1,}, +{0100,0111,1,}, +{0101,0010,0,}, +{0101,0100,1,}, +{0101,0110,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0010,0,}, +{1100,0101,1,}, +{1100,0111,1,}, +{1101,0010,0,}, +{1101,0100,1,}, +{1101,0110,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 11, +v=3 15, 7, 1, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x05,0x08,0x0d,}}, +{{0x01,0x04,0x08,}, {0x08,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x08,}}, +{{0x05,0x06,0x08,}, {0x08,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0a,0x04,}, {0x08,}}, +{{0x09,0x0a,0x04,}, {0x08,}}, +{{0x01,0x02,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x08,}}, +{{0x09,0x0a,0x0c,}, {0x08,}}, +{{0x04,0x08,}, {0x05,0x08,0x0d,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x05,0x08,0x0d,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x05,0x08,0x0d,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x05,0x08,0x0d,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x05,0x08,0x0d,}}, +{{0x0b,0x04,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0c,}, {0x01,0x08,0x09,}}, +{{0x03,0x0c,}, {0x01,0x08,0x09,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x08,0x09,}}, +{{0x03,0x08,}, {0x01,0x08,0x09,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x05,0x08,0x0d,}}, +{{0x0d,0x06,}, {0x05,0x08,0x0d,}}, +{{0x01,0x0a,}, {0x01,0x08,0x09,}}, +{{0x05,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,}, {0x01,0x08,0x09,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x08,0x09,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x08,0x09,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_297.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_297.txt new file mode 100644 index 0000000..7fc27f5 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_297.txt @@ -0,0 +1,598 @@ +297 Sbox: +LUT = { +0x02,0x00,0x01,0x03,0x06,0x04,0x05,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + + x1 + + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 3, related_n = 3 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y2 = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + + x1 + + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = 1 + x0 + + + x3 + + + + + x1x3 + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 4, related_n = 4 + + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + + x1 + + x3 + + + + x0x3 + x1x3 + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + + + + + + + x1x3 + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + + + + x1x3 + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:3, 2:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 16, DDT_spectrum: {0:210, 4:32, 8:12, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:11, 4:1, 8:3, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{4: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{8: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 4:64, 16:96, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{2: 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{9: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{a: 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{e: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:204, 8:48, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 8:3, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 16, 16, -16, 0, 0, 0, 0, 16, -16, -16, 0, 0, -16, }, +{2: 16, 0, -16, 16, 16, 0, 0, -16, 0, -16, 16, 0, 0, 0, -16, 0, }, +{4: 16, 16, 16, -16, 16, 16, -16, -16, 16, 16, -16, -16, 16, -16, -16, -16, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 0, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, 0, 16, }, +{6: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{9: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, -16, 0, -16, 16, 0, 16, 0, -16, 0, -16, 0, 0, 16, 0, 0, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , , , x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, , x, x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, x, , , , x, , x, , x, }, +{6: , , , , , , x, x, , , , x, , , x, x, }, +{9: , x, x, , , , x, x, x, , , , x, x, , x, }, +{a: , x, , , , , x, , , x, , , x, , x, x, }, +{c: , , , , , , x, x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , x, x, , , , , , x, , x, }, +{e: , , , , , , x, , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 81 */ +{0001,0011,1,}, +{0001,0100,0,}, +{0001,0111,1,}, +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0011,0001,1,}, +{0011,0100,0,}, +{0011,0101,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0011,1,}, +{0101,0100,1,}, +{0101,0111,0,}, +{0110,0010,1,}, +{0110,0100,1,}, +{0110,0110,0,}, +{0111,0001,1,}, +{0111,0100,1,}, +{0111,0101,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0011,1,}, +{1001,0100,0,}, +{1001,0111,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1011,0001,1,}, +{1011,0100,0,}, +{1011,0101,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0011,1,}, +{1101,0100,1,}, +{1101,0111,0,}, +{1110,0010,1,}, +{1110,0100,1,}, +{1110,0110,0,}, +{1111,0001,1,}, +{1111,0100,1,}, +{1111,0101,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x04,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0a,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x01,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +297 Inverse Sbox: +LUT = { +0x01,0x02,0x00,0x03,0x05,0x06,0x04,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + + + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 3, related_n = 3 +y2 = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + + + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:3, 2:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 16, DDT_spectrum: {0:210, 4:32, 8:12, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:11, 4:1, 8:3, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{4: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{8: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{3: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{a: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{c: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{d: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{e: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +{f: 16, 0, 0, 16, 4, 0, 0, 0, 4, 4, 4, 0, 4, 4, 4, 4, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 4:64, 16:96, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +{9: 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +{b: 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +{f: 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:204, 8:48, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:11, 8:3, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 0, 0, 16, 16, -16, 0, 0, 0, 0, 16, -16, -16, 0, 0, -16, }, +{4: 16, 16, 16, -16, 16, 16, -16, -16, 16, 16, -16, -16, 16, -16, -16, -16, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, 0, -16, 16, 16, 0, 0, -16, 0, -16, 16, 0, 0, 0, -16, 0, }, +{5: 16, -16, 0, -16, 16, 0, 16, 0, -16, 0, -16, 0, 0, 16, 0, 0, }, +{6: 16, 0, 0, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, 0, 16, }, +{9: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{2: , x, x, , , x, x, x, , x, , x, x, , x, x, }, +{4: , , , x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, , x, x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, x, , , , x, , x, , x, }, +{6: , , , , , , x, x, , , , x, , , x, x, }, +{9: , , x, , , , , x, x, , , , x, x, , x, }, +{a: , x, x, , , , x, x, , x, , , x, , x, x, }, +{c: , , , , , , x, x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , , , , x, x, , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 81 */ +{0001,0001,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0010,0011,1,}, +{0010,0100,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0100,1,}, +{0101,0101,0,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0111,0,}, +{0111,0010,1,}, +{0111,0100,1,}, +{0111,0110,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0100,0,}, +{1001,0101,1,}, +{1010,0011,1,}, +{1010,0100,0,}, +{1010,0111,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0100,1,}, +{1101,0101,0,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0111,0,}, +{1111,0010,1,}, +{1111,0100,1,}, +{1111,0110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x02,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_298.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_298.txt new file mode 100644 index 0000000..d3661d4 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_298.txt @@ -0,0 +1,598 @@ +298 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x06,0x05,0x04,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y2 = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3; deg = 2, term_n = 3, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:3, 2:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 16, DDT_spectrum: {0:210, 4:32, 8:12, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:12, 4:1, 8:2, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{a: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{d: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:128, 8:32, 16:96, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +{b: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +}; +Lin: 16, LAT_spectrum: {0:204, 8:48, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 0, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, 0, 16, }, +{6: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{9: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, 0, 0, -16, 16, 16, 0, 0, 0, 0, -16, -16, 16, 0, 0, -16, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , x, x, x, , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , x, , , x, , x, x, , , , x, x, , x, }, +{a: , , , , , x, , , , x, , , x, , x, x, }, +{c: , x, , , , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , x, , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 81 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0100,0,}, +{0010,0110,1,}, +{0011,0010,1,}, +{0011,0101,1,}, +{0011,0111,0,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0110,0100,1,}, +{0110,0110,0,}, +{0111,0010,1,}, +{0111,0101,0,}, +{0111,0111,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,0100,0,}, +{1010,0110,1,}, +{1011,0010,1,}, +{1011,0101,1,}, +{1011,0111,0,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1110,0100,1,}, +{1110,0110,0,}, +{1111,0010,1,}, +{1111,0101,0,}, +{1111,0111,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x07,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x09,0x0e,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +298 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x06,0x05,0x04,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3; deg = 2, term_n = 5, related_n = 4 +y2 = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + x2x3; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:3, 2:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{3: 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{7: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 4, 4, 0, 0, 4, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +}; +Diff: 16, DDT_spectrum: {0:210, 4:32, 8:12, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:12, 4:1, 8:2, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{3: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{a: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{c: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 0, 16, 0, 8, 0, 0, 0, 8, 8, 0, 0, 8, 0, 0, 0, }, +{d: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{e: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{f: 16, 0, 16, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:128, 8:32, 16:96, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 8, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +{b: 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 8, 8, }, +{f: 0, 0, 8, 0, 0, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:204, 8:48, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:2, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 0, -16, 16, 16, 0, 0, 0, 0, -16, -16, 16, 0, 0, -16, }, +{8: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{3: 16, -16, 0, 16, 16, 0, -16, 0, -16, 0, 16, 0, 0, -16, 0, 0, }, +{5: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{6: 16, 0, 0, -16, 16, -16, 0, 0, 0, 0, -16, 16, -16, 0, 0, 16, }, +{9: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{a: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{c: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{b: 16, 0, 0, 16, -16, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, }, +{d: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{e: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{f: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, x, x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , x, x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, x, , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , x, , , , , x, x, , , , x, x, , x, }, +{a: , , , , , x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , x, , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , x, , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 81 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0010,0101,0,}, +{0010,0111,1,}, +{0011,0010,1,}, +{0011,0100,0,}, +{0011,0110,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0110,0101,1,}, +{0110,0111,0,}, +{0111,0010,1,}, +{0111,0100,1,}, +{0111,0110,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1010,0101,0,}, +{1010,0111,1,}, +{1011,0010,1,}, +{1011,0100,0,}, +{1011,0110,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1110,0101,1,}, +{1110,0111,0,}, +{1111,0010,1,}, +{1111,0100,1,}, +{1111,0110,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 7, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x04,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0d,0x06,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_299.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_299.txt new file mode 100644 index 0000000..a762aa0 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_299.txt @@ -0,0 +1,566 @@ +299 Sbox: +LUT = { +0x03,0x00,0x01,0x02,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 2:4, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 4, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 8, }, +}; +Diff: 16, DDT_spectrum: {0:214, 4:26, 8:12, 12:2, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:12, 8:2, 12:1, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 8, 16, 0, 8, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 0, }, +{3: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{5: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 8, 16, 0, 16, 8, 0, 0, 8, 16, 0, 0, 8, 0, 0, 0, }, +{a: 16, 8, 16, 0, 8, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 0, }, +{c: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 16, 0, 16, 8, 0, 0, 8, 16, 0, 0, 8, 0, 0, 0, }, +{d: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 8, 16, 8, }, +{e: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{f: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 8, 16, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 8:72, 16:88, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:172, 4:56, 8:16, 12:8, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:1, 12:1, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 16, 16, -8, -16, 8, -16, 8, 16, -8, -8, -16, 8, -8, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 8, -16, 16, 8, 0, -8, 0, 8, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 16, -16, 8, 0, 8, 0, -8, -16, 8, -8, 0, -8, -8, }, +{3: 16, -16, -8, 16, 16, 8, -16, -8, -16, -8, 16, 8, 8, -16, -8, 8, }, +{5: 16, 0, 8, -16, 16, -8, 0, -8, 0, 8, -16, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, -16, 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 16, -16, -8, 0, 8, 0, -8, -16, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 16, -16, -8, 0, -8, 0, 8, -16, -8, 8, 0, 8, 8, }, +{c: 16, 0, 8, -16, -16, 8, 0, -8, 0, -8, 16, -8, -8, 0, 8, 8, }, +{7: 16, 0, -8, -16, 16, 8, 0, 8, 0, -8, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 16, -16, 8, 0, -8, 0, 8, -16, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, -16, -16, -8, 0, -8, 0, -8, 16, 8, 8, 0, 8, -8, }, +{e: 16, 0, -8, -16, -16, -8, 0, 8, 0, 8, 16, 8, 8, 0, -8, -8, }, +{f: 16, 0, -8, -16, -16, 8, 0, 8, 0, 8, 16, -8, -8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , x, , , x, x, , , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , x, , , x, , , x, , , , x, x, , x, }, +{a: , , , , , x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , x, , , x, , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 65 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 19, +v=3 15, 15, 3, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +299 Inverse Sbox: +LUT = { +0x01,0x02,0x03,0x00,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:3, 2:4, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 4, 0, 4, }, +{7: 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8, 4, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 8, }, +}; +Diff: 16, DDT_spectrum: {0:214, 4:26, 8:12, 12:2, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:12, 8:2, 12:1, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 8, 16, 0, 8, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 0, }, +{3: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{5: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{6: 16, 8, 16, 8, 0, 8, 16, 8, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 8, 16, 0, 16, 8, 0, 0, 8, 16, 0, 0, 8, 0, 0, 0, }, +{a: 16, 8, 16, 0, 8, 8, 0, 0, 16, 8, 0, 0, 16, 0, 0, 0, }, +{c: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{7: 16, 8, 16, 16, 0, 8, 8, 16, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 16, 8, 16, 0, 16, 8, 0, 0, 8, 16, 0, 0, 8, 0, 0, 0, }, +{d: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 8, 16, 8, }, +{e: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 8, 0, 0, 16, 8, 16, }, +{f: 16, 8, 16, 0, 0, 8, 0, 0, 0, 0, 16, 0, 0, 8, 16, 8, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 8:72, 16:88, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 4, 0, 0, 4, 0, 12, 0, 4, 0, 4, 4, 0, 4, 4, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 4, 0, 0, 4, 0, 4, 0, 12, 0, 4, 4, 0, 4, 4, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 12, 4, 0, 4, 4, }, +{b: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 12, 0, 4, 4, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 12, 4, }, +{f: 0, 0, 4, 0, 0, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 12, }, +}; +Lin: 16, LAT_spectrum: {0:172, 4:56, 8:16, 12:8, 16:4, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:1, 12:1, 16:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 8, 16, 16, -8, -16, 8, -16, 8, 16, -8, -8, -16, 8, -8, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 8, -16, 16, 8, 0, -8, 0, 8, -16, -8, 8, 0, -8, -8, }, +{8: 16, 0, 8, 16, -16, 8, 0, 8, 0, -8, -16, 8, -8, 0, -8, -8, }, +{3: 16, -16, -8, 16, 16, 8, -16, -8, -16, -8, 16, 8, 8, -16, -8, 8, }, +{5: 16, 0, 8, -16, 16, -8, 0, -8, 0, 8, -16, 8, -8, 0, -8, 8, }, +{6: 16, 0, -8, -16, 16, -8, 0, 8, 0, -8, -16, 8, -8, 0, 8, 8, }, +{9: 16, 0, 8, 16, -16, -8, 0, 8, 0, -8, -16, -8, 8, 0, -8, 8, }, +{a: 16, 0, -8, 16, -16, -8, 0, -8, 0, 8, -16, -8, 8, 0, 8, 8, }, +{c: 16, 0, 8, -16, -16, 8, 0, -8, 0, -8, 16, -8, -8, 0, 8, 8, }, +{7: 16, 0, -8, -16, 16, 8, 0, 8, 0, -8, -16, -8, 8, 0, 8, -8, }, +{b: 16, 0, -8, 16, -16, 8, 0, -8, 0, 8, -16, 8, -8, 0, 8, -8, }, +{d: 16, 0, 8, -16, -16, -8, 0, -8, 0, -8, 16, 8, 8, 0, 8, -8, }, +{e: 16, 0, -8, -16, -16, -8, 0, 8, 0, 8, 16, 8, 8, 0, -8, -8, }, +{f: 16, 0, -8, -16, -16, 8, 0, 8, 0, 8, 16, -8, -8, 0, -8, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, , , x, x, , x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, x, x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, x, , x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , x, , , , x, , , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , x, , , , , , x, , , , x, x, , x, }, +{a: , , , , , x, , , , x, , , x, , x, x, }, +{c: , x, x, , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , x, , , , , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 65 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0010,1,}, +{0011,0010,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0010,1,}, +{0111,0010,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0010,1,}, +{1011,0010,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0010,1,}, +{1111,0010,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 19, +v=3 15, 15, 3, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x02,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x04,0x08,0x0c,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x04,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x04,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x0c,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x0b,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x01,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x03,0x08,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x06,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x09,0x06,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x06,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0a,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0d,0x0a,}, {0x04,0x08,0x0c,}}, +{{0x01,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x05,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x09,0x0e,}, {0x04,0x08,0x0c,}}, +{{0x0d,0x0e,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_300.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_300.txt new file mode 100644 index 0000000..7568f82 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_300.txt @@ -0,0 +1,662 @@ +300 Sbox: +LUT = { +0x01,0x00,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + x1 + + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + x1 + + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 4, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 12, }, +}; +Diff: 16, DDT_spectrum: {0:226, 4:14, 12:14, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:12, 12:3, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{2: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{4: 16, 16, 8, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{8: 16, 16, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, }, +{3: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{5: 16, 16, 8, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{6: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{9: 16, 16, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, }, +{a: 16, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, 8, }, +{c: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, }, +{7: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{b: 16, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, 8, }, +{d: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, }, +{e: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, }, +{f: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {8:168, 16:88, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 0, 0, 0, 4, 12, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 12, 4, 0, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:184, 4:56, 12:8, 16:8, }; +Lin1: 16, LAT1_spectrum: {0:12, 12:1, 16:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 16, 16, 16, -16, -16, 16, -16, 16, 16, -16, -16, -16, 16, -16, }, +{2: 16, 8, -16, 16, 16, -8, 8, -16, 8, -16, 16, -8, -8, 8, -16, -8, }, +{4: 16, 8, 16, -16, 16, 8, -8, -16, 8, 16, -16, -8, 8, -8, -16, -8, }, +{8: 16, 8, 16, 16, -16, 8, 8, 16, -8, -16, -16, 8, -8, -8, -16, -8, }, +{3: 16, -8, -16, 16, 16, 8, -8, -16, -8, -16, 16, 8, 8, -8, -16, 8, }, +{5: 16, -8, 16, -16, 16, -8, 8, -16, -8, 16, -16, 8, -8, 8, -16, 8, }, +{6: 16, 8, -16, -16, 16, -8, -8, 16, 8, -16, -16, 8, -8, -8, 16, 8, }, +{9: 16, -8, 16, 16, -16, -8, -8, 16, 8, -16, -16, -8, 8, 8, -16, 8, }, +{a: 16, 8, -16, 16, -16, -8, 8, -16, -8, 16, -16, -8, 8, -8, 16, 8, }, +{c: 16, 8, 16, -16, -16, 8, -8, -16, -8, -16, 16, -8, -8, 8, 16, 8, }, +{7: 16, -8, -16, -16, 16, 8, 8, 16, -8, -16, -16, -8, 8, 8, 16, -8, }, +{b: 16, -8, -16, 16, -16, 8, -8, -16, 8, 16, -16, 8, -8, 8, 16, -8, }, +{d: 16, -8, 16, -16, -16, -8, 8, -16, 8, -16, 16, 8, 8, -8, 16, -8, }, +{e: 16, 8, -16, -16, -16, -8, -8, 16, -8, 16, 16, 8, 8, 8, -16, -8, }, +{f: 16, -8, -16, -16, -16, 8, 8, 16, 8, 16, 16, -8, -8, -8, -16, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, , , , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, , , x, , , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, , , , , x, , x, , x, }, +{6: , x, , , , , , x, , , , x, , , x, x, }, +{9: , , , , , , , , x, , , , x, x, , x, }, +{a: , x, , , , , , , , x, , , x, , x, x, }, +{c: , x, , , , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 113 */ +{0001,0001,1,}, +{0010,0001,0,}, +{0010,0010,1,}, +{0010,0011,1,}, +{0010,0100,0,}, +{0010,0101,0,}, +{0010,0110,1,}, +{0010,0111,1,}, +{0010,1000,0,}, +{0010,1001,0,}, +{0010,1010,1,}, +{0010,1011,1,}, +{0010,1100,0,}, +{0010,1101,0,}, +{0010,1110,1,}, +{0010,1111,1,}, +{0011,0001,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1010,0001,0,}, +{1010,0010,1,}, +{1010,0011,1,}, +{1010,0100,0,}, +{1010,0101,0,}, +{1010,0110,1,}, +{1010,0111,1,}, +{1010,1000,1,}, +{1010,1001,1,}, +{1010,1010,0,}, +{1010,1011,0,}, +{1010,1100,1,}, +{1010,1101,1,}, +{1010,1110,0,}, +{1010,1111,0,}, +{1011,0001,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 15, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +300 Inverse Sbox: +LUT = { +0x01,0x00,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + x1 + + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y2 = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + x1 + + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + = + + x1 + x2 + + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + + + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + + x1 + + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +Max degree: 3, Min degree: 1, Spectrum of degree: { 1:7, 3:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 12, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 12, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 4, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 4, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 4, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 4, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 12, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 4, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 12, }, +}; +Diff: 16, DDT_spectrum: {0:226, 4:14, 12:14, 16:2, }; +Diff1: 16, DDT1_spectrum: {0:12, 12:3, 16:1, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{2: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{4: 16, 16, 8, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{8: 16, 16, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, }, +{3: 16, 16, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{5: 16, 16, 8, 16, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, }, +{6: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{9: 16, 16, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, 8, 8, 8, }, +{a: 16, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, 8, }, +{c: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, }, +{7: 16, 16, 8, 8, 8, 8, 8, 16, 8, 8, 8, 16, 8, 8, 8, 8, }, +{b: 16, 16, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, 8, }, +{d: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 16, 8, 8, 16, 8, 8, }, +{e: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, }, +{f: 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {8:168, 16:88, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 12, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 4, 0, 0, 0, 12, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{5: 0, 4, 0, 0, 0, 4, 12, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 4, 0, 0, 0, 4, 4, 0, 12, 0, 0, 4, 4, 4, 0, 4, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 12, 4, 4, 0, 4, }, +{b: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 12, 4, 0, 4, }, +{d: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 12, 0, 4, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 4, 0, 0, 0, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 12, }, +}; +Lin: 16, LAT_spectrum: {0:184, 4:56, 12:8, 16:8, }; +Lin1: 16, LAT1_spectrum: {0:12, 12:1, 16:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 16, 16, 16, -16, -16, 16, -16, 16, 16, -16, -16, -16, 16, -16, }, +{2: 16, 8, -16, 16, 16, -8, 8, -16, 8, -16, 16, -8, -8, 8, -16, -8, }, +{4: 16, 8, 16, -16, 16, 8, -8, -16, 8, 16, -16, -8, 8, -8, -16, -8, }, +{8: 16, 8, 16, 16, -16, 8, 8, 16, -8, -16, -16, 8, -8, -8, -16, -8, }, +{3: 16, -8, -16, 16, 16, 8, -8, -16, -8, -16, 16, 8, 8, -8, -16, 8, }, +{5: 16, -8, 16, -16, 16, -8, 8, -16, -8, 16, -16, 8, -8, 8, -16, 8, }, +{6: 16, 8, -16, -16, 16, -8, -8, 16, 8, -16, -16, 8, -8, -8, 16, 8, }, +{9: 16, -8, 16, 16, -16, -8, -8, 16, 8, -16, -16, -8, 8, 8, -16, 8, }, +{a: 16, 8, -16, 16, -16, -8, 8, -16, -8, 16, -16, -8, 8, -8, 16, 8, }, +{c: 16, 8, 16, -16, -16, 8, -8, -16, -8, -16, 16, -8, -8, 8, 16, 8, }, +{7: 16, -8, -16, -16, 16, 8, 8, 16, -8, -16, -16, -8, 8, 8, 16, -8, }, +{b: 16, -8, -16, 16, -16, 8, -8, -16, 8, 16, -16, 8, -8, 8, 16, -8, }, +{d: 16, -8, 16, -16, -16, -8, 8, -16, 8, -16, 16, 8, 8, -8, 16, -8, }, +{e: 16, 8, -16, -16, -16, -8, -8, 16, -8, 16, 16, 8, 8, 8, -16, -8, }, +{f: 16, -8, -16, -16, -16, 8, 8, 16, 8, 16, 16, -8, -8, -8, -16, 8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, , , , x, x, , x, , , x, x, x, , x, }, +{2: , x, x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, , , x, x, , , x, x, , x, x, x, }, +{8: , x, , , x, , , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, , , , , x, , x, , x, }, +{6: , x, , , , , , x, , , , x, , , x, x, }, +{9: , , , , , , , , x, , , , x, x, , x, }, +{a: , x, , , , , , , , x, , , x, , x, x, }, +{c: , x, , , , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , , , , , , , x, , x, }, +{e: , x, , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 113 */ +{0001,0001,1,}, +{0010,0001,0,}, +{0010,0010,1,}, +{0010,0011,1,}, +{0010,0100,0,}, +{0010,0101,0,}, +{0010,0110,1,}, +{0010,0111,1,}, +{0010,1000,0,}, +{0010,1001,0,}, +{0010,1010,1,}, +{0010,1011,1,}, +{0010,1100,0,}, +{0010,1101,0,}, +{0010,1110,1,}, +{0010,1111,1,}, +{0011,0001,1,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{0111,0001,1,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1010,0001,0,}, +{1010,0010,1,}, +{1010,0011,1,}, +{1010,0100,0,}, +{1010,0101,0,}, +{1010,0110,1,}, +{1010,0111,1,}, +{1010,1000,1,}, +{1010,1001,1,}, +{1010,1010,0,}, +{1010,1011,0,}, +{1010,1100,1,}, +{1010,1101,1,}, +{1010,1110,0,}, +{1010,1111,0,}, +{1011,0001,1,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +{1111,0001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 15, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x02,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_301.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_301.txt new file mode 100644 index 0000000..3f2ca53 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_301.txt @@ -0,0 +1,694 @@ +301 Sbox: +LUT = { +0x01,0x00,0x03,0x02,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y2 = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + x2 + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + + x1 + + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:7, 2:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +}; +Diff: 16, DDT_spectrum: {0:228, 8:24, 16:4, }; +Diff1: 16, DDT1_spectrum: {0:12, 8:2, 16:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{3: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{a: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{c: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{d: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +{e: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +{f: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 16:160, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +{b: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:216, 8:32, 16:8, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:1, 16:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 16, 16, 16, -16, -16, 16, -16, 16, 16, -16, -16, -16, 16, -16, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{8: 16, 0, 16, 16, -16, 0, 0, 16, 0, -16, -16, 0, 0, 0, -16, 0, }, +{3: 16, -16, -16, 16, 16, 16, -16, -16, -16, -16, 16, 16, 16, -16, -16, 16, }, +{5: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{6: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{9: 16, 0, 16, 16, -16, 0, 0, 16, 0, -16, -16, 0, 0, 0, -16, 0, }, +{a: 16, 0, -16, 16, -16, 0, 0, -16, 0, 16, -16, 0, 0, 0, 16, 0, }, +{c: 16, 0, 16, -16, -16, 0, 0, -16, 0, -16, 16, 0, 0, 0, 16, 0, }, +{7: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{b: 16, 0, -16, 16, -16, 0, 0, -16, 0, 16, -16, 0, 0, 0, 16, 0, }, +{d: 16, 0, 16, -16, -16, 0, 0, -16, 0, -16, 16, 0, 0, 0, 16, 0, }, +{e: 16, 0, -16, -16, -16, 0, 0, 16, 0, 16, 16, 0, 0, 0, -16, 0, }, +{f: 16, 0, -16, -16, -16, 0, 0, 16, 0, 16, 16, 0, 0, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, , , , x, x, , x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, , , x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, , , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , , , , , , , x, , , , x, x, , x, }, +{a: , , , , , x, , , , x, , , x, , x, x, }, +{c: , x, , , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 129 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0001,0,}, +{0010,0010,1,}, +{0010,0011,1,}, +{0010,0100,0,}, +{0010,0101,0,}, +{0010,0110,1,}, +{0010,0111,1,}, +{0010,1000,0,}, +{0010,1001,0,}, +{0010,1010,1,}, +{0010,1011,1,}, +{0010,1100,0,}, +{0010,1101,0,}, +{0010,1110,1,}, +{0010,1111,1,}, +{0011,0001,1,}, +{0011,0010,1,}, +{0011,0011,0,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{0111,0001,1,}, +{0111,0010,1,}, +{0111,0011,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0001,0,}, +{1010,0010,1,}, +{1010,0011,1,}, +{1010,0100,0,}, +{1010,0101,0,}, +{1010,0110,1,}, +{1010,0111,1,}, +{1010,1000,1,}, +{1010,1001,1,}, +{1010,1010,0,}, +{1010,1011,0,}, +{1010,1100,1,}, +{1010,1101,1,}, +{1010,1110,0,}, +{1010,1111,0,}, +{1011,0001,1,}, +{1011,0010,1,}, +{1011,0011,0,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +{1111,0001,1,}, +{1111,0010,1,}, +{1111,0011,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 15, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +301 Inverse Sbox: +LUT = { +0x01,0x00,0x03,0x02,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 +y1 = + + x1 + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y2 = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 3 + + y1 + + = + + x1 + + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = 1 + x0 + + + x3 + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + = + + x1 + x2 + + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + + + + x2x3; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + + + + + ; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 3 + + y1 + + y3 = + + x1 + + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3; deg = 2, term_n = 5, related_n = 4 + + + y2 + y3 = + + + x2 + x3 + + + + + + ; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = 1 + x0 + + + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + + + ; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + + + x2x3; deg = 2, term_n = 4, related_n = 4 +Max degree: 2, Min degree: 1, Spectrum of degree: { 1:7, 2:8, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, }, +}; +Diff: 16, DDT_spectrum: {0:228, 8:24, 16:4, }; +Diff1: 16, DDT1_spectrum: {0:12, 8:2, 16:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{8: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{3: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{5: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{6: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{9: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{a: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{c: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +{7: 16, 16, 16, 16, 0, 16, 16, 16, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 16, 16, 16, 0, 16, 16, 0, 0, 16, 16, 0, 0, 16, 0, 0, 0, }, +{d: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +{e: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +{f: 16, 16, 16, 0, 0, 16, 0, 0, 0, 0, 16, 0, 0, 16, 16, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:96, 16:160, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +{5: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +{b: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +{d: 0, 8, 0, 0, 0, 0, 8, 0, 8, 0, 0, 0, 0, 8, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 8, }, +}; +Lin: 16, LAT_spectrum: {0:216, 8:32, 16:8, }; +Lin1: 16, LAT1_spectrum: {0:12, 8:1, 16:3, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 16, 16, 16, -16, -16, 16, -16, 16, 16, -16, -16, -16, 16, -16, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{8: 16, 0, 16, 16, -16, 0, 0, 16, 0, -16, -16, 0, 0, 0, -16, 0, }, +{3: 16, -16, -16, 16, 16, 16, -16, -16, -16, -16, 16, 16, 16, -16, -16, 16, }, +{5: 16, 0, 16, -16, 16, 0, 0, -16, 0, 16, -16, 0, 0, 0, -16, 0, }, +{6: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{9: 16, 0, 16, 16, -16, 0, 0, 16, 0, -16, -16, 0, 0, 0, -16, 0, }, +{a: 16, 0, -16, 16, -16, 0, 0, -16, 0, 16, -16, 0, 0, 0, 16, 0, }, +{c: 16, 0, 16, -16, -16, 0, 0, -16, 0, -16, 16, 0, 0, 0, 16, 0, }, +{7: 16, 0, -16, -16, 16, 0, 0, 16, 0, -16, -16, 0, 0, 0, 16, 0, }, +{b: 16, 0, -16, 16, -16, 0, 0, -16, 0, 16, -16, 0, 0, 0, 16, 0, }, +{d: 16, 0, 16, -16, -16, 0, 0, -16, 0, -16, 16, 0, 0, 0, 16, 0, }, +{e: 16, 0, -16, -16, -16, 0, 0, 16, 0, 16, 16, 0, 0, 0, -16, 0, }, +{f: 16, 0, -16, -16, -16, 0, 0, 16, 0, 16, 16, 0, 0, 0, -16, 0, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 2| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, , , , x, x, , x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , x, , x, , x, x, x, , , x, x, , x, x, x, }, +{8: , x, , , x, x, , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, , , , , x, , x, , x, }, +{6: , , , , , x, , x, , , , x, , , x, x, }, +{9: , , , , , , , , x, , , , x, x, , x, }, +{a: , , , , , x, , , , x, , , x, , x, x, }, +{c: , x, , , , x, , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , , , , , , , x, , x, }, +{e: , , , , , x, , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 129 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0010,0001,0,}, +{0010,0010,1,}, +{0010,0011,1,}, +{0010,0100,0,}, +{0010,0101,0,}, +{0010,0110,1,}, +{0010,0111,1,}, +{0010,1000,0,}, +{0010,1001,0,}, +{0010,1010,1,}, +{0010,1011,1,}, +{0010,1100,0,}, +{0010,1101,0,}, +{0010,1110,1,}, +{0010,1111,1,}, +{0011,0001,1,}, +{0011,0010,1,}, +{0011,0011,0,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, +{0100,1100,1,}, +{0100,1101,1,}, +{0100,1110,1,}, +{0100,1111,1,}, +{0101,0001,1,}, +{0101,0010,0,}, +{0101,0011,1,}, +{0110,0001,0,}, +{0110,0010,1,}, +{0110,0011,1,}, +{0110,0100,1,}, +{0110,0101,1,}, +{0110,0110,0,}, +{0110,0111,0,}, +{0110,1000,0,}, +{0110,1001,0,}, +{0110,1010,1,}, +{0110,1011,1,}, +{0110,1100,1,}, +{0110,1101,1,}, +{0110,1110,0,}, +{0110,1111,0,}, +{0111,0001,1,}, +{0111,0010,1,}, +{0111,0011,0,}, +{1000,0001,0,}, +{1000,0010,0,}, +{1000,0011,0,}, +{1000,0100,0,}, +{1000,0101,0,}, +{1000,0110,0,}, +{1000,0111,0,}, +{1000,1000,1,}, +{1000,1001,1,}, +{1000,1010,1,}, +{1000,1011,1,}, +{1000,1100,1,}, +{1000,1101,1,}, +{1000,1110,1,}, +{1000,1111,1,}, +{1001,0001,1,}, +{1001,0010,0,}, +{1001,0011,1,}, +{1010,0001,0,}, +{1010,0010,1,}, +{1010,0011,1,}, +{1010,0100,0,}, +{1010,0101,0,}, +{1010,0110,1,}, +{1010,0111,1,}, +{1010,1000,1,}, +{1010,1001,1,}, +{1010,1010,0,}, +{1010,1011,0,}, +{1010,1100,1,}, +{1010,1101,1,}, +{1010,1110,0,}, +{1010,1111,0,}, +{1011,0001,1,}, +{1011,0010,1,}, +{1011,0011,0,}, +{1100,0001,0,}, +{1100,0010,0,}, +{1100,0011,0,}, +{1100,0100,1,}, +{1100,0101,1,}, +{1100,0110,1,}, +{1100,0111,1,}, +{1100,1000,1,}, +{1100,1001,1,}, +{1100,1010,1,}, +{1100,1011,1,}, +{1100,1100,0,}, +{1100,1101,0,}, +{1100,1110,0,}, +{1100,1111,0,}, +{1101,0001,1,}, +{1101,0010,0,}, +{1101,0011,1,}, +{1110,0001,0,}, +{1110,0010,1,}, +{1110,0011,1,}, +{1110,0100,1,}, +{1110,0101,1,}, +{1110,0110,0,}, +{1110,0111,0,}, +{1110,1000,1,}, +{1110,1001,1,}, +{1110,1010,0,}, +{1110,1011,0,}, +{1110,1100,0,}, +{1110,1101,0,}, +{1110,1110,1,}, +{1110,1111,1,}, +{1111,0001,1,}, +{1111,0010,1,}, +{1111,0011,0,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 15, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x04,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x02,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0b,0x0c,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x07,0x08,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x06,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x01,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x09,0x0e,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x0d,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_302.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_302.txt new file mode 100644 index 0000000..c0a5ada --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/302classes4bits/properties_302.txt @@ -0,0 +1,886 @@ +302 Sbox: +LUT = { +0x00,0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + + + ; deg = 1, term_n = 1, related_n = 1 +y1 = + + x1 + + ; deg = 1, term_n = 1, related_n = 1 +y2 = + + + x2 + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + x0 + + + ; deg = 1, term_n = 1, related_n = 1 + + y1 + + = + + x1 + + ; deg = 1, term_n = 1, related_n = 1 +y0 + y1 + + = + x0 + x1 + + ; deg = 1, term_n = 2, related_n = 2 + + + y2 + = + + + x2 + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = + x0 + + x2 + ; deg = 1, term_n = 2, related_n = 2 + + y1 + y2 + = + + x1 + x2 + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = + x0 + x1 + x2 + ; deg = 1, term_n = 3, related_n = 3 + + + + y3 = + + + + x3; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + x0 + + + x3; deg = 1, term_n = 2, related_n = 2 + + y1 + + y3 = + + x1 + + x3; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + + y3 = + x0 + x1 + + x3; deg = 1, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + x0 + + x2 + x3; deg = 1, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + x3; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3; deg = 1, term_n = 4, related_n = 4 +Max degree: 1, Min degree: 1, Spectrum of degree: { 1:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, }, +}; +Diff: 16, DDT_spectrum: {0:240, 16:16, }; +Diff1: 16, DDT1_spectrum: {0:12, 16:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{8: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{3: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{5: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{6: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{9: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{a: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{c: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{7: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{b: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{d: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{e: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{f: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {16:256, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, }, +}; +Lin: 16, LAT_spectrum: {0:240, 16:16, }; +Lin1: 16, LAT1_spectrum: {0:12, 16:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 16, 16, 16, -16, -16, 16, -16, 16, 16, -16, -16, -16, 16, -16, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 16, 16, -16, 16, 16, -16, -16, 16, 16, -16, -16, 16, -16, -16, -16, }, +{8: 16, 16, 16, 16, -16, 16, 16, 16, -16, -16, -16, 16, -16, -16, -16, -16, }, +{3: 16, -16, -16, 16, 16, 16, -16, -16, -16, -16, 16, 16, 16, -16, -16, 16, }, +{5: 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, 16, -16, 16, -16, 16, }, +{6: 16, 16, -16, -16, 16, -16, -16, 16, 16, -16, -16, 16, -16, -16, 16, 16, }, +{9: 16, -16, 16, 16, -16, -16, -16, 16, 16, -16, -16, -16, 16, 16, -16, 16, }, +{a: 16, 16, -16, 16, -16, -16, 16, -16, -16, 16, -16, -16, 16, -16, 16, 16, }, +{c: 16, 16, 16, -16, -16, 16, -16, -16, -16, -16, 16, -16, -16, 16, 16, 16, }, +{7: 16, -16, -16, -16, 16, 16, 16, 16, -16, -16, -16, -16, 16, 16, 16, -16, }, +{b: 16, -16, -16, 16, -16, 16, -16, -16, 16, 16, -16, 16, -16, 16, 16, -16, }, +{d: 16, -16, 16, -16, -16, -16, 16, -16, 16, -16, 16, 16, 16, -16, 16, -16, }, +{e: 16, 16, -16, -16, -16, -16, -16, 16, -16, 16, 16, 16, 16, 16, -16, -16, }, +{f: 16, -16, -16, -16, -16, 16, 16, 16, 16, 16, 16, -16, -16, -16, -16, 16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 1| 2| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, , , , x, x, , x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: , , , x, , , x, x, , , x, x, , x, x, x, }, +{8: , , , , x, , , , x, x, x, , x, x, x, x, }, +{3: , , , , , x, , , , , , x, x, , , x, }, +{5: , , , , , , x, , , , , x, , x, , x, }, +{6: , , , , , , , x, , , , x, , , x, x, }, +{9: , , , , , , , , x, , , , x, x, , x, }, +{a: , , , , , , , , , x, , , x, , x, x, }, +{c: , , , , , , , , , , x, , , x, x, x, }, +{7: , , , , , , , , , , , x, , , , x, }, +{b: , , , , , , , , , , , , x, , , x, }, +{d: , , , , , , , , , , , , , x, , x, }, +{e: , , , , , , , , , , , , , , x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 225 */ +{0001,0001,1,}, +{0001,0010,0,}, +{0001,0011,1,}, +{0001,0100,0,}, +{0001,0101,1,}, +{0001,0110,0,}, +{0001,0111,1,}, +{0001,1000,0,}, +{0001,1001,1,}, +{0001,1010,0,}, +{0001,1011,1,}, +{0001,1100,0,}, +{0001,1101,1,}, +{0001,1110,0,}, +{0001,1111,1,}, +{0010,0001,0,}, +{0010,0010,1,}, +{0010,0011,1,}, +{0010,0100,0,}, +{0010,0101,0,}, +{0010,0110,1,}, +{0010,0111,1,}, +{0010,1000,0,}, +{0010,1001,0,}, +{0010,1010,1,}, +{0010,1011,1,}, +{0010,1100,0,}, +{0010,1101,0,}, +{0010,1110,1,}, +{0010,1111,1,}, +{0011,0001,1,}, +{0011,0010,1,}, +{0011,0011,0,}, +{0011,0100,0,}, +{0011,0101,1,}, +{0011,0110,1,}, +{0011,0111,0,}, +{0011,1000,0,}, +{0011,1001,1,}, +{0011,1010,1,}, +{0011,1011,0,}, +{0011,1100,0,}, +{0011,1101,1,}, +{0011,1110,1,}, +{0011,1111,0,}, +{0100,0001,0,}, +{0100,0010,0,}, +{0100,0011,0,}, +{0100,0100,1,}, +{0100,0101,1,}, +{0100,0110,1,}, +{0100,0111,1,}, +{0100,1000,0,}, +{0100,1001,0,}, +{0100,1010,0,}, +{0100,1011,0,}, 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w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 35, 35, +v=3 15, 15, 15, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x04,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x02,0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,0x04,}, 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{0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +302 Inverse Sbox: +LUT = { +0x00,0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f, +}; + +ANF of coordinates: +y0 = + x0 + + + ; deg = 1, term_n = 1, related_n = 1 +y1 = + + x1 + + ; deg = 1, term_n = 1, related_n = 1 +y2 = + + + x2 + ; deg = 1, term_n = 1, related_n = 1 +y3 = + + + + x3; deg = 1, term_n = 1, related_n = 1 + +ANF of components: +y0 + + + = + x0 + + + ; deg = 1, term_n = 1, related_n = 1 + + y1 + + = + + x1 + + ; deg = 1, term_n = 1, related_n = 1 +y0 + y1 + + = + x0 + x1 + + ; deg = 1, term_n = 2, related_n = 2 + + + y2 + = + + + x2 + ; deg = 1, term_n = 1, related_n = 1 +y0 + + y2 + = + x0 + + x2 + ; deg = 1, term_n = 2, related_n = 2 + + y1 + y2 + = + + x1 + x2 + ; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + y2 + = + x0 + x1 + x2 + ; deg = 1, term_n = 3, related_n = 3 + + + + y3 = + + + + x3; deg = 1, term_n = 1, related_n = 1 +y0 + + + y3 = + x0 + + + x3; deg = 1, term_n = 2, related_n = 2 + + y1 + + y3 = + + x1 + + x3; deg = 1, term_n = 2, related_n = 2 +y0 + y1 + + y3 = + x0 + x1 + + x3; deg = 1, term_n = 3, related_n = 3 + + + y2 + y3 = + + + x2 + x3; deg = 1, term_n = 2, related_n = 2 +y0 + + y2 + y3 = + x0 + + x2 + x3; deg = 1, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + x3; deg = 1, term_n = 3, related_n = 3 +y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3; deg = 1, term_n = 4, related_n = 4 +Max degree: 1, Min degree: 1, Spectrum of degree: { 1:15, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, }, +}; +Diff: 16, DDT_spectrum: {0:240, 16:16, }; +Diff1: 16, DDT1_spectrum: {0:12, 16:4, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{2: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{4: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{8: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{3: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{5: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{6: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{9: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{a: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{c: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{7: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{b: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{d: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{e: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{f: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +}; +BCT_uniformity: 16, BCT_spectrum: {16:256, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{4: 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{8: 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{3: 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{6: 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, }, +{9: 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, }, +{a: 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{c: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{7: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, }, +{b: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, }, +{d: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, }, +{e: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, }, +{f: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, }, +}; +Lin: 16, LAT_spectrum: {0:240, 16:16, }; +Lin1: 16, LAT1_spectrum: {0:12, 16:4, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, -16, 16, 16, 16, -16, -16, 16, -16, 16, 16, -16, -16, -16, 16, -16, }, +{2: 16, 16, -16, 16, 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, -16, }, +{4: 16, 16, 16, -16, 16, 16, -16, -16, 16, 16, -16, -16, 16, -16, -16, -16, }, +{8: 16, 16, 16, 16, -16, 16, 16, 16, -16, -16, -16, 16, -16, -16, -16, -16, }, +{3: 16, -16, -16, 16, 16, 16, -16, -16, -16, -16, 16, 16, 16, -16, -16, 16, }, +{5: 16, -16, 16, -16, 16, -16, 16, -16, -16, 16, -16, 16, -16, 16, -16, 16, }, +{6: 16, 16, -16, -16, 16, -16, -16, 16, 16, -16, -16, 16, -16, -16, 16, 16, }, +{9: 16, -16, 16, 16, -16, -16, -16, 16, 16, -16, -16, -16, 16, 16, -16, 16, }, +{a: 16, 16, -16, 16, -16, -16, 16, -16, -16, 16, -16, -16, 16, -16, 16, 16, }, +{c: 16, 16, 16, -16, -16, 16, -16, -16, -16, -16, 16, -16, -16, 16, 16, 16, }, +{7: 16, -16, -16, -16, 16, 16, 16, 16, -16, -16, -16, -16, 16, 16, 16, -16, }, +{b: 16, -16, -16, 16, -16, 16, -16, -16, 16, 16, -16, 16, -16, 16, 16, -16, }, +{d: 16, -16, 16, -16, -16, -16, 16, -16, 16, -16, 16, 16, 16, -16, 16, -16, }, +{e: 16, 16, -16, -16, -16, -16, -16, 16, -16, 16, 16, 16, 16, 16, -16, -16, }, +{f: 16, -16, -16, -16, -16, 16, 16, 16, 16, 16, 16, -16, -16, -16, -16, 16, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 1| 2| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, , , , x, x, , x, , , x, x, x, , x, }, +{2: , , x, , , x, , x, , x, , x, x, , x, x, }, +{4: 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+300,010002030405060708090a0b0c0d0e0f,ff00_f0f0_cccc_aaa9,True,True,16,2,16,4,16,8,16,4,3,1,8,7,[3|3|3|4],113,"(3, 3)","(3, 3)",-,0,-,010002030405060708090a0b0c0d0e0f,ff00_f0f0_cccc_aaa9,3,1,8,7,[3|3|3|4],113,"(3, 3)","(3, 3)",- +301,010003020405060708090a0b0c0d0e0f,ff00_f0f0_cccc_aaa5,True,True,16,4,16,4,16,8,16,4,2,1,8,7,[2|3|3|4],129,"(3, 3)","(3, 3)",-,0,-,010003020405060708090a0b0c0d0e0f,ff00_f0f0_cccc_aaa5,2,1,8,7,[2|3|3|4],129,"(3, 3)","(3, 3)",- +302,000102030405060708090a0b0c0d0e0f,ff00_f0f0_cccc_aaaa,True,True,16,16,16,4,16,16,16,4,1,1,15,15,[1|2|3|4],225,"(3, 3)","(3, 3)",-,0,-,000102030405060708090a0b0c0d0e0f,ff00_f0f0_cccc_aaaa,1,1,15,15,[1|2|3|4],225,"(3, 3)","(3, 3)",- diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S0.txt index 2cad8a5..cc52c63 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S1.txt index f7999a3..9348f90 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Anubis_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_1.txt index 5c93278..fe783f9 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_2.txt index fd3fc31..f589ec1 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y1 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -215,26 +215,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_3.txt index 1474f34..7f2e57d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + x1 + + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = 1 + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_4.txt index bb95148..9511e7f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -208,26 +208,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 -y1 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 - + y1 + + = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_5.txt index 03d2b70..e40564b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -208,26 +208,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_6.txt index 2ea0598..393c39e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + + x1 + + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y1 = 1 + x0 + + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y1 = + x0 + + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + + = 1 + x0 + + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + x1 + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + x0 + + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_7.txt index c0999c9..bd8b72c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_8.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_8.txt index cd42a95..99da577 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_8.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_8.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + x2 + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_9.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_9.txt index e05fafc..29169d5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_9.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_BLAKE_9.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + + + = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -210,26 +210,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 -y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS0.txt index 5e8008a..4bd65ed 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS1.txt index 3957206..6dde198 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS2.txt index 461f164..7862f1b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS3.txt index 611d892..65c510a 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CLEFIA_SS3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_F.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_F.txt index e071568..87d54c6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_F.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_F.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + + + + x0x3 + + ; deg = 2, term_n = 2, related_n = 2 -y1 = + x0 + + + + x0x1 + + + + + ; deg = 2, term_n = 2, related_n = 2 -y2 = + + x1 + + + + + x1x2 + + + ; deg = 2, term_n = 2, related_n = 2 -y3 = + + + x2 + + + + + + + x2x3; deg = 2, term_n = 2, related_n = 2 +y0 = 1 + + + + x3 + + + + x0x3 + + ; deg = 2, term_n = 3, related_n = 2 +y1 = 1 + x0 + + + + x0x1 + + + + + ; deg = 2, term_n = 3, related_n = 2 +y2 = 1 + + x1 + + + + + x1x2 + + + ; deg = 2, term_n = 3, related_n = 2 +y3 = 1 + + + x2 + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 2 ANF of components: -y0 + + + = + + + + x3 + + + + x0x3 + + ; deg = 2, term_n = 2, related_n = 2 - + y1 + + = + x0 + + + + x0x1 + + + + + ; deg = 2, term_n = 2, related_n = 2 +y0 + + + = 1 + + + + x3 + + + + x0x3 + + ; deg = 2, term_n = 3, related_n = 2 + + y1 + + = 1 + x0 + + + + x0x1 + + + + + ; deg = 2, term_n = 3, related_n = 2 y0 + y1 + + = + x0 + + + x3 + x0x1 + + + x0x3 + + ; deg = 2, term_n = 4, related_n = 3 - + + y2 + = + + x1 + + + + + x1x2 + + + ; deg = 2, term_n = 2, related_n = 2 + + + y2 + = 1 + + x1 + + + + + x1x2 + + + ; deg = 2, term_n = 3, related_n = 2 y0 + + y2 + = + + x1 + + x3 + + + x1x2 + x0x3 + + ; deg = 2, term_n = 4, related_n = 4 + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + ; deg = 2, term_n = 6, related_n = 4 - + + + y3 = + + + x2 + + + + + + + x2x3; deg = 2, term_n = 2, related_n = 2 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + ; deg = 2, term_n = 7, related_n = 4 + + + + y3 = 1 + + + x2 + + + + + + + x2x3; deg = 2, term_n = 3, related_n = 2 y0 + + + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3; deg = 2, term_n = 4, related_n = 3 + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + x2x3; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3; deg = 2, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3; deg = 2, term_n = 4, related_n = 3 -y0 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3; deg = 2, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3; deg = 2, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3; deg = 2, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3; deg = 2, term_n = 8, related_n = 4 Max degree: 2, Min degree: 2, Spectrum of degree: { 2:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_G.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_G.txt index 3e9bfe3..99b20cb 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_G.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_CS_cipher_G.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y1 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = 1 + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + + = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = 1 + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_1.txt index 986e1e1..fec6543 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y1 = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y2 + y3 = + + x1 + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_2.txt index 9008710..a1ce0bd 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_3.txt index 6e68c24..f0160a7 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_4.txt index 0f94e43..ae519ae 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S1_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -225,26 +225,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_1.txt index e24c831..ce66319 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -215,26 +215,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_2.txt index b414a30..761ff46 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -225,26 +225,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_3.txt index 87cc925..8e99933 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + + x1 + + x3 + + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + + x3 + + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -225,26 +225,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_4.txt index 8ea0615..83e66d3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S2_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -211,26 +211,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y2 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_1.txt index f4d14a1..2c4280e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + y1 + + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -216,26 +216,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_2.txt index aeeb8f2..10dea4d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y1 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_3.txt index a1e5b29..acab9c3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -225,26 +225,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_4.txt index e890342..04e533f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S3_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + x3 + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -227,26 +227,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y3 = + + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + x1 + x2 + + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_1.txt index 7668ed4..75fac15 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -211,26 +211,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + x2 + x3 + + + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_2.txt index 337e68d..8832e25 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -211,26 +211,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y2 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_3.txt index 686f5d9..fe1f44b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 13, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -211,26 +211,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_4.txt index e667e2c..53fc0ef 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S4_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 13, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -211,26 +211,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + + x2 + + + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + + x2 + + + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_1.txt index edc4374..cda3cac 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -216,26 +216,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_2.txt index 2674f6c..50f1790 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -216,26 +216,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + + + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_3.txt index d66a950..45b71c0 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -209,26 +209,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_4.txt index 4d836f1..98a436a 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S5_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 - + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -216,26 +216,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_1.txt index 9c850f7..37b6219 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_2.txt index 71d019d..acec3a1 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -210,26 +210,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_3.txt index 25d9b52..3fde7ed 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + + + + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 3, related_n = 4 - + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -211,26 +211,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_4.txt index 5a398bc..4cc4a0b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S6_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + x1 + + + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -215,26 +215,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_1.txt index eb7e40a..af24820 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 3, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_2.txt index 8dff660..88e8cc3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y1 = + + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + + x1 + + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -225,26 +225,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + + + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_3.txt index 88cf7a3..67475e8 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -211,26 +211,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 13, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_4.txt index dee1833..0dbc4b3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S7_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + y2 + = + x0 + + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = 1 + + x1 + + + + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -218,26 +218,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_1.txt index 50c8d84..1978cc3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + + + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -224,26 +224,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_2.txt index 5c3fcd3..1fb2fc5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 3, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -218,26 +218,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 -y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_3.txt index 8d0716c..eaa1507 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -216,26 +216,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + x1 + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_4.txt index dba92e7..07a71be 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_DES_S8_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 3, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + y2 + = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Enocoro_S4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Enocoro_S4.txt index 123ef4b..97cf0fb 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Enocoro_S4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Enocoro_S4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S1.txt index 62fe925..33e58bc 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y1 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S2.txt index 59f519d..96c413c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y2 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y2 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y2 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + + = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + y1 + + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S3.txt index dd21825..f3668c1 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Fox_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y1 = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GIFT.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GIFT.txt index 76010b9..7894aca 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GIFT.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GIFT.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + + + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 - + + y2 + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + x0 + + + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_1.txt index 0bdb7a8..099028f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y1 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_2.txt index bf7761d..e82a91f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST2_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 9, related_n = 4 -y2 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 9, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_1.txt index a245f0c..9961aa1 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 - + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + x2 + + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_2.txt index 334ad2d..74228e6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + x0 + + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -209,26 +209,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_3.txt index ec526cd..5a62f24 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -210,26 +210,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_4.txt index ad38881..4db022c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + + + + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -216,26 +216,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_5.txt index e352f70..d906a17 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + + x2 + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -208,26 +208,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_6.txt index 3ec1da1..07a4faa 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -209,26 +209,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 13, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_7.txt index 63cbf42..656d159 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -215,26 +215,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_8.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_8.txt index e915a02..cd5cd00 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_8.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_8.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -217,26 +217,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_1.txt index 4d0584a..9eb850e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -208,26 +208,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 ANF of components: -y0 + + + = + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + + y3 = + + x1 + + + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_2.txt index 8219be7..2d22281 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 + + + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -225,26 +225,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + y2 + = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_3.txt index b7e9a16..990b9d0 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 13, related_n = 4 - + + y2 + = + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 - + + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_4.txt index c6132bb..9a4bfc3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_5.txt index 0ac3ed3..c3bceb4 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -215,26 +215,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + + + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 - + + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_6.txt index fb5de09..6a1a1f7 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 ANF of components: -y0 + + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + y1 + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_7.txt index 37175bd..157c4bc 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -209,26 +209,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_8.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_8.txt index 4ae4da1..9d28c92 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_8.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_GOST_IETF_8.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y1 = 1 + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + = 1 + + + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -209,26 +209,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S0.txt index 0205be2..31ac6a9 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S1.txt index 35467ba..1b69f76 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S2.txt index cca3092..030ed2f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S3.txt index 526311e..99ccb2d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Golden_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S1.txt index f08ac65..0f477c6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y3 = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S2.txt index 581437a..619c43e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + + y2 + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S3.txt index 8f5093f..53ec29e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S4.txt index 2f11368..ed8c08a 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Hummingbird_2_S4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y3 = + x0 + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + x0 + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y1 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S0.txt index 409584e..c283b5e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S1.txt index ae5f7db..ff54713 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Iceberg_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S0.txt index 25ea034..fe13d9f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S1.txt index 0916753..94c1f25 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_JH_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KLEIN.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KLEIN.txt index 701e1d6..f7b89a5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KLEIN.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KLEIN.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KNOT.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KNOT.txt new file mode 100644 index 0000000..f9aad8d --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_KNOT.txt @@ -0,0 +1,438 @@ +KNOT Sbox: +LUT = { +0x04,0x00,0x0a,0x07,0x0b,0x0e,0x01,0x0d,0x09,0x0f,0x06,0x08,0x05,0x02,0x0c,0x03, +}; + +ANF of coordinates: +y0 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + +ANF of components: +y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + y3 = + + + + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{2: 0, 2, 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, 2, }, +{4: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 4, 2, 2, 2, }, +{8: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 4, 4, }, +{3: 0, 2, 0, 0, 0, 2, 0, 4, 2, 2, 0, 0, 0, 0, 2, 2, }, +{5: 0, 0, 0, 2, 0, 0, 2, 2, 0, 4, 0, 2, 4, 0, 0, 0, }, +{6: 0, 2, 0, 0, 0, 2, 4, 0, 2, 2, 2, 0, 0, 2, 0, 0, }, +{9: 0, 4, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, }, +{a: 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, }, +{c: 0, 4, 4, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{7: 0, 2, 0, 4, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, }, +{b: 0, 0, 2, 0, 4, 2, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, }, +{d: 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 2, 4, 0, 0, 0, }, +{e: 0, 0, 2, 0, 4, 2, 2, 2, 0, 0, 0, 0, 0, 2, 0, 2, }, +{f: 0, 0, 2, 2, 4, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 0, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 2, DDT1_spectrum: {0:14, 2:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, }, +{2: 16, 2, 0, 0, 4, 2, 0, 0, 2, 2, 0, 4, 0, 0, 2, 6, }, +{4: 16, 4, 4, 0, 0, 0, 0, 0, 4, 4, 2, 0, 8, 2, 2, 2, }, +{8: 16, 0, 0, 4, 16, 0, 4, 4, 0, 0, 4, 4, 0, 4, 4, 4, }, +{3: 16, 2, 0, 0, 4, 2, 0, 4, 2, 2, 0, 0, 0, 0, 6, 2, }, +{5: 16, 4, 4, 2, 0, 0, 2, 2, 4, 4, 0, 2, 8, 0, 0, 0, }, +{6: 16, 2, 0, 0, 4, 2, 4, 0, 2, 2, 2, 0, 0, 6, 0, 0, }, +{9: 16, 8, 8, 0, 0, 0, 0, 0, 8, 8, 0, 0, 16, 0, 0, 0, }, +{a: 16, 0, 2, 2, 4, 2, 0, 0, 0, 0, 0, 6, 0, 2, 0, 6, }, +{c: 16, 4, 4, 2, 0, 0, 2, 2, 4, 4, 0, 2, 8, 0, 0, 0, }, +{7: 16, 2, 0, 4, 4, 2, 0, 0, 2, 2, 6, 0, 0, 2, 0, 0, }, +{b: 16, 0, 2, 0, 4, 2, 2, 6, 0, 0, 2, 0, 0, 0, 6, 0, }, +{d: 16, 4, 4, 2, 0, 0, 2, 2, 4, 4, 0, 2, 8, 0, 0, 0, }, +{e: 16, 0, 2, 0, 4, 2, 6, 2, 0, 0, 0, 0, 0, 6, 0, 2, }, +{f: 16, 0, 2, 6, 4, 2, 0, 0, 0, 0, 6, 2, 0, 0, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:60, 4:36, 6:12, 8:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 0, 4, 0, 0, 4, 8, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{2: 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 0, 8, 8, 0, }, +{4: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 8, 4, 4, 4, 0, 4, }, +{8: 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 0, 8, 8, }, +{3: 0, 8, 4, 0, 0, 4, 0, 4, 0, 4, 8, 4, 4, 0, 4, 4, }, +{5: 0, 4, 4, 0, 0, 8, 4, 4, 4, 4, 0, 0, 8, 4, 4, 0, }, +{6: 0, 4, 8, 0, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 0, 4, 8, 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 4, }, +{a: 0, 8, 0, 0, 0, 8, 8, 0, 0, 0, 0, 8, 0, 0, 0, 0, }, +{c: 0, 4, 0, 0, 8, 4, 4, 8, 4, 0, 0, 4, 4, 4, 0, 4, }, +{7: 0, 4, 4, 0, 0, 0, 4, 4, 4, 4, 0, 8, 0, 4, 4, 8, }, +{b: 0, 0, 4, 8, 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 4, }, +{d: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +{e: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{f: 0, 4, 4, 8, 8, 0, 4, 4, 4, 4, 0, 0, 0, 4, 4, 0, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 4, LAT1_spectrum: {0:14, 4:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{2: 16, -8, -8, 0, 0, 0, 0, 8, -8, 0, 0, -8, 8, 0, 0, 0, }, +{4: 16, 0, -8, 0, -16, 0, 0, -8, 0, 8, 0, 0, 0, 0, 8, 0, }, +{8: 16, 0, 0, -16, -16, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, }, +{3: 16, 0, -8, 0, 0, -8, -8, 8, 0, 0, 0, 0, 0, -8, 0, 8, }, +{5: 16, 0, -8, 0, 0, 0, 0, -8, 0, 8, -16, 0, 0, 0, 8, 0, }, +{6: 16, -8, 8, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 0, 0, 8, }, +{9: 16, -8, 0, 16, 0, -8, -8, 0, 8, 0, 0, -8, -8, 8, 0, -8, }, +{a: 16, 0, 0, 0, 0, 8, 8, 0, 0, -8, 0, 0, 0, -8, -8, -8, }, +{c: 16, 0, 0, 0, 16, -8, 0, 0, 0, 0, 0, -8, -8, 0, 0, -8, }, +{7: 16, 0, 8, 0, 0, 0, -8, -8, 0, 0, 0, -8, 8, -8, 0, 0, }, +{b: 16, 8, 0, 0, 0, 0, 0, 0, -8, -8, 0, 8, -8, 0, -8, 0, }, +{d: 16, -8, 0, 0, 0, 0, -8, 0, 8, 0, -16, 0, 0, 8, 0, 0, }, +{e: 16, 0, 0, 0, 0, 0, 8, 0, 0, -8, 0, 8, -8, -8, -8, 0, }, +{f: 16, 8, 0, 0, 0, 8, 0, 0, -8, -8, 0, 0, 0, 0, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , , x, x, x, x, , x, x, x, x, x, x, x, }, +{5: , x, , , , x, , x, x, x, x, x, x, x, x, x, }, +{6: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, x, , , x, x, x, x, x, x, x, x, x, x, x, }, +{a: , x, x, , , x, x, x, x, x, x, , x, x, x, x, }, +{c: , x, x, , , x, x, x, x, x, x, x, x, x, , x, }, +{7: , , , , , , , , , x, , x, x, x, x, x, }, +{b: , x, , , , , , x, , , x, , x, x, x, x, }, +{d: , , , , , , , , x, x, , x, , x, , x, }, +{e: , , x, , , x, x, x, , , x, , x, , , x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0100,0001,1,}, +{0100,1000,1,}, +{0100,1001,0,}, +{1000,0100,1,}, +{1000,1000,1,}, +{1000,1100,0,}, +{1100,0101,1,}, +{1100,1000,0,}, +{1100,1101,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x04,0x08,}, {0x08,}}, +{{0x01,0x02,0x08,}, {0x04,}}, +{{0x05,0x02,0x08,}, {0x0c,}}, +{{0x01,0x06,0x08,}, {0x04,}}, +{{0x05,0x06,0x08,}, {0x0c,}}, +{{0x04,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x08,}, {0x04,0x08,0x0c,}}, +{{0x06,0x08,}, {0x04,0x08,0x0c,}}, +{{0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x0a,0x04,}, {0x05,0x08,0x0d,}}, +{{0x02,0x0c,}, {0x08,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x03,0x04,}, {0x05,0x08,0x0d,}}, +{{0x09,0x04,}, {0x01,0x04,0x05,0x08,0x09,0x0c,0x0d,}}, +{{0x0b,0x04,}, {0x01,0x08,0x09,}}, +{{0x01,0x0c,}, {0x04,0x08,0x0c,}}, +{{0x03,0x0c,}, {0x08,}}, +{{0x09,0x0c,}, {0x03,0x04,0x07,0x08,0x0b,0x0c,0x0f,}}, +{{0x0b,0x0c,}, {0x08,}}, +{{0x01,0x08,}, {0x04,0x08,0x0c,}}, +{{0x03,0x08,}, {0x04,0x08,0x0c,}}, +{{0x05,0x08,}, {0x04,0x08,0x0c,}}, +{{0x07,0x08,}, {0x04,0x08,0x0c,}}, +{{0x01,0x02,}, {0x02,0x04,0x06,}}, +{{0x05,0x02,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x02,}, {0x04,}}, +{{0x0d,0x02,}, {0x0c,}}, +{{0x01,0x06,}, {0x02,0x04,0x06,}}, +{{0x05,0x06,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x06,}, {0x04,}}, +{{0x0d,0x06,}, {0x0c,}}, +{{0x01,0x0a,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x0a,}, {0x03,0x0c,0x0f,}}, +{{0x09,0x0a,}, {0x04,}}, +{{0x0d,0x0a,}, {0x0c,}}, +{{0x01,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x0e,}, {0x07,0x0b,0x0c,}}, +{{0x09,0x0e,}, {0x04,}}, +{{0x0d,0x0e,}, {0x0c,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + +KNOT Inverse Sbox: +LUT = { +0x01,0x06,0x0d,0x0f,0x00,0x0c,0x0a,0x03,0x0b,0x08,0x02,0x04,0x0e,0x07,0x05,0x09, +}; + +ANF of coordinates: +y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 + +ANF of components: +y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + y3 = + x0 + x1 + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; + +DDT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, 4, 2, 0, 0, 0, 0, }, +{2: 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 4, 0, 2, 0, 2, 2, }, +{4: 0, 2, 0, 0, 0, 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 2, }, +{8: 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 4, 4, }, +{3: 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, }, +{5: 0, 2, 0, 0, 0, 0, 2, 4, 0, 0, 2, 0, 2, 2, 2, 0, }, +{6: 0, 2, 0, 0, 0, 4, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, }, +{9: 0, 0, 2, 0, 0, 2, 0, 2, 4, 0, 0, 2, 0, 4, 0, 0, }, +{a: 0, 0, 2, 4, 0, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, }, +{c: 0, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, }, +{7: 0, 2, 4, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, }, +{b: 0, 0, 0, 4, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4, 0, 0, }, +{d: 0, 2, 0, 2, 4, 0, 0, 2, 0, 2, 0, 2, 0, 0, 2, 0, }, +{e: 0, 2, 2, 2, 4, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, }, +{f: 0, 2, 2, 2, 4, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, }, +}; +Diff: 4, DDT_spectrum: {0:159, 2:72, 4:24, 16:1, }; +Diff1: 2, DDT1_spectrum: {0:14, 2:2, }; + +BCT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 2, 4, 0, 2, 4, 2, 8, 0, 4, 2, 0, 4, 0, 0, }, +{2: 16, 0, 0, 4, 0, 0, 4, 0, 8, 2, 4, 0, 2, 4, 2, 2, }, +{4: 16, 2, 0, 0, 4, 0, 2, 0, 0, 2, 2, 4, 0, 2, 0, 6, }, +{8: 16, 0, 4, 0, 16, 4, 0, 4, 0, 4, 0, 4, 4, 0, 4, 4, }, +{3: 16, 0, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, }, +{5: 16, 2, 0, 0, 4, 0, 2, 4, 0, 0, 2, 0, 2, 2, 6, 0, }, +{6: 16, 2, 0, 0, 4, 4, 2, 0, 0, 0, 2, 0, 6, 2, 2, 0, }, +{9: 16, 0, 2, 4, 0, 2, 4, 2, 8, 0, 4, 2, 0, 4, 0, 0, }, +{a: 16, 0, 2, 4, 0, 2, 4, 2, 8, 0, 4, 2, 0, 4, 0, 0, }, +{c: 16, 2, 0, 2, 4, 0, 0, 2, 0, 0, 0, 6, 2, 0, 0, 6, }, +{7: 16, 2, 4, 0, 4, 0, 2, 0, 0, 6, 2, 0, 0, 2, 0, 2, }, +{b: 16, 0, 0, 8, 0, 0, 8, 0, 16, 0, 8, 0, 0, 8, 0, 0, }, +{d: 16, 2, 0, 2, 4, 0, 0, 6, 0, 2, 0, 2, 0, 0, 6, 0, }, +{e: 16, 2, 2, 2, 4, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 2, }, +{f: 16, 2, 6, 2, 4, 2, 0, 0, 0, 6, 0, 0, 0, 0, 2, 0, }, +}; +BCT_uniformity: 16, BCT_spectrum: {0:107, 2:60, 4:36, 6:12, 8:8, 16:33, }; + +LAT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{1: 0, 0, 0, 4, 0, 8, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{2: 0, 4, 0, 0, 0, 4, 4, 8, 4, 0, 0, 4, 4, 4, 8, 4, }, +{4: 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 8, 0, 8, }, +{8: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 8, 8, 8, }, +{3: 0, 4, 0, 4, 0, 4, 8, 4, 4, 8, 4, 0, 4, 0, 4, 0, }, +{5: 0, 8, 0, 4, 0, 0, 4, 4, 0, 8, 4, 4, 0, 4, 4, 4, }, +{6: 0, 4, 0, 8, 0, 4, 4, 0, 4, 0, 8, 4, 4, 4, 0, 4, }, +{9: 0, 0, 8, 4, 0, 0, 4, 4, 0, 0, 4, 4, 8, 4, 4, 4, }, +{a: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{c: 0, 8, 0, 8, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, }, +{7: 0, 4, 0, 4, 0, 4, 0, 4, 4, 8, 4, 8, 4, 0, 4, 0, }, +{b: 0, 4, 0, 4, 8, 4, 8, 4, 4, 0, 4, 0, 4, 0, 4, 0, }, +{d: 0, 0, 8, 4, 0, 0, 4, 4, 8, 0, 4, 4, 0, 4, 4, 4, }, +{e: 0, 4, 8, 0, 8, 4, 4, 0, 4, 0, 0, 4, 4, 4, 0, 4, }, +{f: 0, 4, 0, 4, 8, 4, 0, 4, 4, 0, 4, 8, 4, 0, 4, 0, }, +}; +Lin: 8, LAT_spectrum: {0:123, 4:96, 8:36, 16:1, }; +Lin1: 4, LAT1_spectrum: {0:14, 4:2, }; + +ACT = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, }, +{1: 16, 0, 0, 0, 0, 0, -8, 0, 0, -16, 0, -8, 0, 8, 0, 8, }, +{2: 16, 0, 0, 0, -16, 0, -8, 0, 0, 0, 0, -8, 0, 8, 0, 8, }, +{4: 16, -8, 0, -8, 0, 0, 8, 0, -8, 0, 0, -8, 0, 0, 8, 0, }, +{8: 16, 0, -16, 0, -16, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, }, +{3: 16, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, +{5: 16, 0, 0, -8, 0, -8, -8, 0, 0, 0, 0, 8, -8, 0, 8, 0, }, +{6: 16, -8, 0, 0, 0, 0, -8, -8, -8, 0, 8, 8, 0, 0, 0, 0, }, +{9: 16, -8, 0, 0, 0, -8, 0, 0, 8, -16, 0, 0, 8, 0, 0, 0, }, +{a: 16, 0, 0, -8, 16, 0, 0, -8, 0, 0, -8, 0, 0, 0, -8, 0, }, +{c: 16, 0, 0, 0, 0, 8, 0, 8, 0, 0, -8, 0, -8, -8, 0, -8, }, +{7: 16, 0, 0, 0, 0, -8, 8, -8, 0, 0, 8, -8, -8, 0, 0, 0, }, +{b: 16, -8, 16, -8, 0, -8, 0, -8, 8, 0, -8, 0, 8, 0, -8, 0, }, +{d: 16, 8, 0, 0, 0, 0, 0, 8, -8, 0, -8, 0, 0, -8, 0, -8, }, +{e: 16, 0, 0, 8, 0, 8, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, }, +{f: 16, 8, 0, 8, 0, 0, 0, 0, -8, 0, 0, 0, 0, -8, -8, -8, }, +}; + +d_k table of the S-box: + k| 1| 2| 3| 4| + dk| 3| 3| 3| 4| + +VST = +{ + 0| 1| 2| 4| 8| 3| 5| 6| 9| a| c| 7| b| d| e| f| +{0: x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{1: , x, x, x, x, x, x, x, x, x, x, x, x, , x, x, }, +{2: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{4: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{8: , x, x, x, x, x, x, x, x, x, x, x, x, x, x, x, }, +{3: , x, , x, , x, , , x, x, x, x, x, , x, x, }, +{5: , x, x, , x, , x, x, x, , x, x, x, , x, x, }, +{6: , , x, x, , x, x, x, x, x, x, x, x, x, x, x, }, +{9: , x, , x, , x, x, x, x, x, , x, x, , x, x, }, +{a: , x, , x, , x, x, x, x, x, x, x, x, x, x, x, }, +{c: , x, , x, , x, x, x, x, x, x, x, x, x, x, x, }, +{7: , , , , , , , , , , x, x, x, , x, x, }, +{b: , , , , , , , , x, , , x, , , x, x, }, +{d: , x, , , , , x, x, x, , , x, x, , x, x, }, +{e: , , , x, , x, , x, , x, , , x, x, x, x, }, +{f: , , , , , , , , , , , , , , , x, }, +}; + +LS = { /* size 9 */ +{0010,0011,1,}, +{0010,1000,1,}, +{0010,1011,0,}, +{1000,0010,1,}, +{1000,1000,1,}, +{1000,1010,0,}, +{1010,0001,1,}, +{1010,1000,0,}, +{1010,1001,1,}, +}; + +(v, w)-linearity: number N_(v, w) of subspaces V of dimension v for which there exists a w-dimensional W such that the S-box is (v, w)-linear with respect to (V, W) + w=1, w=2, w=3, +v=1 15, 15, 15, +v=2 35, 23, 3, +v=3 7, 1, 0, +(V_basis, W_spaned) pairs +{{0x02,0x04,0x08,}, {0x08,}}, +{{0x01,0x04,0x08,}, {0x0a,}}, +{{0x03,0x04,0x08,}, {0x02,}}, +{{0x01,0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x02,0x08,}, {0x08,}}, +{{0x01,0x06,0x08,}, {0x0a,}}, +{{0x05,0x06,0x08,}, {0x02,}}, +{{0x04,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x08,}, {0x02,0x08,0x0a,}}, +{{0x06,0x08,}, {0x02,0x08,0x0a,}}, +{{0x02,0x04,}, {0x01,0x08,0x09,}}, +{{0x0a,0x04,}, {0x08,}}, +{{0x02,0x0c,}, {0x03,0x08,0x0b,}}, +{{0x0a,0x0c,}, {0x08,}}, +{{0x01,0x04,}, {0x04,0x0a,0x0e,}}, +{{0x03,0x04,}, {0x02,0x05,0x07,}}, +{{0x09,0x04,}, {0x0a,}}, +{{0x0b,0x04,}, {0x02,}}, +{{0x01,0x0c,}, {0x06,0x0a,0x0c,}}, +{{0x03,0x0c,}, {0x02,0x0d,0x0f,}}, +{{0x09,0x0c,}, {0x0a,}}, +{{0x0b,0x0c,}, {0x02,}}, +{{0x01,0x08,}, {0x02,0x08,0x0a,}}, +{{0x03,0x08,}, {0x02,0x08,0x0a,}}, +{{0x05,0x08,}, {0x02,0x08,0x0a,}}, +{{0x07,0x08,}, {0x02,0x08,0x0a,}}, +{{0x01,0x02,}, {0x02,0x05,0x07,0x08,0x0a,0x0d,0x0f,}}, +{{0x05,0x02,}, {0x03,0x08,0x0b,}}, +{{0x09,0x02,}, {0x01,0x02,0x03,0x08,0x09,0x0a,0x0b,}}, +{{0x0d,0x02,}, {0x01,0x08,0x09,}}, +{{0x01,0x06,}, {0x06,0x0a,0x0c,}}, +{{0x05,0x06,}, {0x02,0x05,0x07,}}, +{{0x09,0x06,}, {0x0a,}}, +{{0x0d,0x06,}, {0x02,}}, +{{0x01,0x0a,}, {0x02,0x04,0x06,0x08,0x0a,0x0c,0x0e,}}, +{{0x05,0x0a,}, {0x08,}}, +{{0x09,0x0a,}, {0x02,0x08,0x0a,}}, +{{0x0d,0x0a,}, {0x08,}}, +{{0x01,0x0e,}, {0x04,0x0a,0x0e,}}, +{{0x05,0x0e,}, {0x02,}}, +{{0x09,0x0e,}, {0x0a,}}, +{{0x0d,0x0e,}, {0x02,0x0d,0x0f,}}, +{{0x08,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x04,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0c,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x02,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x06,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0a,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0e,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x01,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x03,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x05,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x07,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x09,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0b,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0d,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, +{{0x0f,}, {0x01,0x02,0x03,0x04,0x05,0x06,0x07,0x08,0x09,0x0a,0x0b,0x0c,0x0d,0x0e,0x0f,}}, + diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_P.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_P.txt index ce76690..5490282 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_P.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_P.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_Q.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_Q.txt index 49e6cf0..ba9bd93 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_Q.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Khazad_Q.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu0.txt index 9cb63b0..2707e31 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu1.txt index 702035e..db29ebb 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_nu1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = + + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; @@ -243,26 +243,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 -y1 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y2 = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 -y3 = 1 + + x1 + x2 + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + + + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y2 = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + + x1 + x2 + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + = + x0 + x1 + + + + + + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + + = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 + + + y2 + = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + x2 + + + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + y1 + + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 - + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:7, 3:8, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_phi.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_phi.txt index eea103b..86b614b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_phi.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_phi.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + + x0x1x2x3; deg = 4, term_n = 10, related_n = 4 -y1 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 9, related_n = 4 -y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + + x0x1x2x3; deg = 4, term_n = 11, related_n = 4 +y1 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 9, related_n = 4 +y2 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + + x0x1x2x3; deg = 4, term_n = 10, related_n = 4 - + y1 + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + + x0x1x2x3; deg = 4, term_n = 11, related_n = 4 + + y1 + + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 9, related_n = 4 + + + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3 + x0x1x2x3; deg = 4, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + + x0x1x2x3; deg = 4, term_n = 11, related_n = 4 - + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + + x0x1x2x3; deg = 4, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + + x0x1x2x3; deg = 4, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3 + x0x1x2x3; deg = 4, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + + + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + x1x2x3 + x0x1x2x3; deg = 4, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + + x0x1x2x3; deg = 4, term_n = 7, related_n = 4 Max degree: 4, Min degree: 3, Spectrum of degree: { 3:7, 4:8, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_sigma.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_sigma.txt index 4a235ee..c4fbdf6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_sigma.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Kuznyechik_sigma.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -208,26 +208,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LAC.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LAC.txt index 9d5cd30..b8041a5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LAC.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LAC.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = 1 + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = 1 + + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_0.txt index af7f43f..0c32da5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = 1 + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = 1 + + x1 + + + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_1.txt index 4ddd386..9f97f08 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 - + + y2 + = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 + + + y2 + = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = + x0 + x1 + + + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_2.txt index d157e78..b4e6cc4 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 -y3 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + + + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 + + + y2 + = 1 + x0 + + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = + + x1 + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_3.txt index 1bc2760..2a4b462 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 -y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + x0 + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 + + + y2 + = 1 + + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = + + + x2 + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_4.txt index 93a643a..01d1173 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + + y3 = + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = 1 + + + + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_5.txt index b93ddb0..aaca247 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 -y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 + + + y2 + = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_6.txt index 2f7fa3e..3ad5939 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 + + + y2 + = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = + x0 + + + + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_7.txt index 6cbcc62..d88c060 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = 1 + x0 + + + + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_8.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_8.txt index 8bf335e..cbcfbd3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_8.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_8.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 2, related_n = 3 -y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y3 = + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 2, related_n = 3 + + + y2 + = 1 + + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_9.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_9.txt index a540628..36c282e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_9.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_LBlock_9.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + + x2 + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 = 1 + x0 + + x2 + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 ANF of components: -y0 + + + = + x0 + + x2 + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + + y3 = 1 + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S0.txt index 0cf3f91..51120ad 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -210,26 +210,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S1.txt index 09a2825..d080eab 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Lucifer_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa.txt index 8423028..580c7c2 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 -y1 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y1 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 - + y1 + + = + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa_v1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa_v1.txt index f26afcf..5612862 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa_v1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Luffa_v1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 - + + y2 + = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 3 +y2 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 3 y0 + y1 + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MANTIS.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MANTIS.txt index 11480f3..73bb335 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MANTIS.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MANTIS.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 -y2 = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + + = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + + y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + + y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 -y2 = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + + = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + + y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + + y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MIBS.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MIBS.txt index f8dbc54..573c48d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MIBS.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_MIBS.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_1.txt index 165d1ea..54cbcfd 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 = + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 -y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_2.txt index c45da55..2c63fd0 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_3.txt index 3f0e170..ba8815d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y1 = 1 + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + = 1 + + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + y1 + + = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + + + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_4.txt index 62d1fbb..a5bd441 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 - + + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + x0 + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_5.txt index decf621..ea398e0 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 ANF of components: -y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_6.txt index a636ac1..6ac589d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_7.txt index abecbc8..b89e39e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_8.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_8.txt index 2079493..f15e858 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_8.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Magma_8.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb0.txt index 43398b8..cb5776b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 -y2 = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + + = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + + y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + + y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 -y2 = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + + = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + + + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + + y3 = + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + + y3 = 1 + + + + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb1.txt index 7399a10..248d73f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Midori_Sb1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + + + x0x1 + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Minalpher.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Minalpher.txt index d7ca87c..a0652cd 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Minalpher.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Minalpher.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Noekeon.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Noekeon.txt index 6474ab1..6e1da2d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Noekeon.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Noekeon.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 ANF of components: -y0 + + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 ANF of components: -y0 + + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_0.txt index 7aa34af..05e4ab6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_1.txt index ff1e40b..25d8f28 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_04_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + x2 + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + + x1 + + x3 + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_0.txt index 9994e26..91b6e13 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_1.txt index 871ec95..88b724c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_2.txt index 00f954e..7366e7c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_3.txt index b8fbd15..f6cfba9 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_13_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_0.txt index 8a973c9..340f2af 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y2 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + y1 + + = + x0 + + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_1.txt index 56fbd03..5f267e9 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y3 = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_2.txt index 175ef00..24515c5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y3 = + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + + + + + x0x3 + + + + + + ; deg = 2, term_n = 2, related_n = 3 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_3.txt index 90f394d..ed59440 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Num1_DL_22_3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + + + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S0.txt index c402dce..26f8925 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S1.txt index 5622d22..5db97f0 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + x1 + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S10.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S10.txt index d75177c..0d7e846 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S10.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S10.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S11.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S11.txt index 031783d..dc9746c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S11.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S11.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S12.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S12.txt index 38575cf..5704ad2 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S12.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S12.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S13.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S13.txt index c3815a9..53206dc 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S13.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S13.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y1 = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S14.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S14.txt index d9334d2..e3b0569 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S14.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S14.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S15.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S15.txt index 17c8a00..6713aaf 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S15.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S15.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S2.txt index a021cd2..8cecf07 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S3.txt index c2be934..1c9e04d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S4.txt index b262d62..3cfc27d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S5.txt index e4d3f9a..ecc725d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S6.txt index f487600..4d4f16b 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S7.txt index 1b33e2d..5295ce4 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S8.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S8.txt index 70d0bea..36af196 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S8.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S8.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S9.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S9.txt index 0175e94..2088bbc 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S9.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Optimal_S9.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y2 = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 +y2 = + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 +y0 + + + = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = + + + x2 + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRESENT.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRESENT.txt index 9322ca8..0baecad 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRESENT.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRESENT.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + + x1 + + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRINCE.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRINCE.txt index aefa260..e4e7b26 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRINCE.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_PRINCE.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y1 = + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Panda.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Panda.txt index cee801b..e946e35 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Panda.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Panda.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Piccolo.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Piccolo.txt index 802ca81..93a23a5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Piccolo.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Piccolo.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y3 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 -y2 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Pride.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Pride.txt index a3b78ca..fe0e176 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Pride.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Pride.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Prost.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Prost.txt index 3f795f1..423dc15 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Prost.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Prost.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + y2 + = + x0 + + + + + + x1x2 + + + + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + y2 + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma0.txt index b6b1034..ffad4ea 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 3 -y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 3 + + + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 3 -y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 3 + + + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma1.txt index 80bd7f9..5c39c22 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma2.txt index 6feb0ce..6f6811a 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Qarma_sigma2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + x2 + + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_REC_0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_REC_0.txt index 1ca22ed..af8ca2a 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_REC_0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_REC_0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = 1 + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 + = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Rectangle.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Rectangle.txt index 2493cbf..3549df3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Rectangle.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Rectangle.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = 1 + + x1 + + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + y2 + = + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SC2000_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SC2000_4.txt index ce7fb10..cfcdff1 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SC2000_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SC2000_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S0.txt index 9685ed9..e19fe81 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y3 = + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S1.txt index a0a5659..60d3350 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + x1 + + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + + + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + y3 = 1 + + + + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S2.txt index 2b937d7..f828a7f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + + + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S3.txt index b9335ed..17a02e9 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S4.txt index 0befa4f..37d5ec6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + + + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S5.txt index 366cada..fab4db6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y1 = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + + x3 + + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y2 + y3 = 1 + x0 + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S6.txt index c97054f..5b9b8e1 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 -y2 = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 ANF of components: -y0 + + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S7.txt index ea4ad54..55b6d7e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SERPENT_S7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y2 + y3 = + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SKINNY_4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SKINNY_4.txt index 1377e0f..db8ed51 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SKINNY_4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SKINNY_4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y3 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y3 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + y2 + = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 -y2 = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y2 = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + y2 + = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S1.txt index b4235ba..a82ae9a 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + + y2 + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y2 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + y1 + + y3 = 1 + + + x2 + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S2.txt index 4944bc2..32ec612 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + y2 + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + y2 + y3 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 y0 + y1 + y2 + y3 = + + + + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S3.txt index 10a3834..42375ea 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_SMASH_256_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y2 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + + + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S0.txt index d9eca76..16ef16c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + x1 + + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S1.txt index 374e60d..83d876a 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + x0 + x1 + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S10.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S10.txt index 40e940c..2b7ada3 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S10.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S10.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + + + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S11.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S11.txt index 4a3992e..9360db4 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S11.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S11.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + + + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + x0 + + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S12.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S12.txt index 533acd3..ad009d6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S12.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S12.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y0 + + + = + x0 + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + + + + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 3, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S13.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S13.txt index af4ffb3..f339aa5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S13.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S13.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S14.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S14.txt index c0b4e09..431c4d6 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S14.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S14.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 +y0 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + + + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + + + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S15.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S15.txt index f78eba7..e839ab8 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S15.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S15.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S16.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S16.txt index 2bbaa8e..ba10fb7 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S16.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S16.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S17.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S17.txt index a834801..8e386db 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S17.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S17.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S18.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S18.txt index 27a756f..2df2a0c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S18.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S18.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + + + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + + x2 + x3 + + + + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S19.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S19.txt index 81fc173..a38fe49 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S19.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S19.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + + x2 + + + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 - + + + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 + + + + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S2.txt index 3214ba0..71a7029 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S3.txt index 794897d..0fc49a1 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S4.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S4.txt index 9b0f975..01f66cf 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S4.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S4.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S5.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S5.txt index 5fcdb39..977a87e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S5.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S5.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S6.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S6.txt index ec91806..6f17af5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S6.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S6.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + y1 + y2 + = + x0 + + + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + + + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + x2 + + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 5, related_n = 3 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S7.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S7.txt index ea9a13e..a0ecc55 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S7.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S7.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + + x0x2 + + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 + + y2 + y3 = + + + x2 + + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S8.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S8.txt index 2424c65..3bec54d 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S8.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S8.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y2 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 5, related_n = 3 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + y1 + y2 + y3 = + + + + + x0x1 + + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + + + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + + + x3 + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + + y3 = 1 + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + + + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + x1 + + + x0x1 + + + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S9.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S9.txt index 9eedb59..d614226 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S9.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Serpent_type_S9.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + + + = + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + + + + + + ; deg = 2, term_n = 4, related_n = 4 y0 + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + + + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + + + + x3 + x0x1 + + + x0x3 + + + + + + ; deg = 2, term_n = 3, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 9, related_n = 4 -y1 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 8, related_n = 4 +y1 = + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 9, related_n = 4 - + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + x2 + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 4, related_n = 3 +y0 + y1 + + y3 = + x0 + + + + + + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 + + y2 + y3 = + + x1 + + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_TWINE.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_TWINE.txt index d2077e1..4a87988 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_TWINE.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_TWINE.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y3 = + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + + + x3 + + + x1x2 + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T0.txt index a80fa70..df02a71 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + x1 + x2 + + + + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 -y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + x2 + + + + + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 +y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + + + + + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = + + x1 + x2 + + + + + + + + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 y0 + + y2 + = + x0 + + x2 + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + + + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y2 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + x0 + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = + x0 + + + + + + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + + + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + + + ; deg = 2, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T1.txt index 4815799..bade7cb 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y1 = + x0 + + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y2 = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + x0 + + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + + = + x0 + + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + x1 + x2 + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + + + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + + + x2 + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = + x0 + + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -208,26 +208,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y2 = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + + + + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + x2 + + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T2.txt index e6df3b5..a7af575 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = + + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + + + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + + + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + + + + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + + + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -213,26 +213,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 -y2 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 11, related_n = 4 y0 + y1 + + = + + + x2 + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + x1 + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + x0x1 + + x1x2 + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T3.txt index d277e8d..473c19c 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q0_T3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + x1 + + + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y3 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + x1 + + + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y2 = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + x1 + + + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + + + + + x0x1 + x0x2 + x1x2 + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + x1 + + + + + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + + + x1x2 + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + x0 + + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + + x0x2 + + x0x3 + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 -y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y2 = + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 +y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 ANF of components: -y0 + + + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 5, related_n = 3 + + + y2 + = + x0 + x1 + + x3 + + + + + x1x3 + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + + x2 + x3 + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + + + x0x2 + + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T0.txt index 9a21475..76940af 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 = + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y1 = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = + + x1 + x2 + x3 + + + + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y1 + + = 1 + x0 + + + + + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = 1 + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + + + x2 + + x0x1 + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + + x1 + + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = + x0 + + + x3 + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + + + + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + + x2 + x3 + + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 3 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = 1 + + + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = + + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = + + + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y2 = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = 1 + + + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + + x2 + + + + + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + y1 + + = + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + x0 + x1 + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + x0 + x1 + + x3 + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + + + x0x2 + x1x2 + + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + + y2 + y3 = + x0 + + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + + + + + + x0x3 + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T1.txt index 51b66c2..36f3d46 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y2 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y2 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + + x1 + + + x0x1 + + x1x2 + x0x3 + + x2x3 + + + + ; deg = 2, term_n = 6, related_n = 4 + y1 + y2 + = + + x1 + x2 + + + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + x0 + + + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = 1 + + x1 + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + y2 + y3 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y2 = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 -y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + + = + + + + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + + x2 + + x0x1 + + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + + y2 + = 1 + x0 + x1 + + + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 - + + + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 11, related_n = 4 + y1 + + y3 = + + x1 + + + + + + x0x3 + x1x3 + + + + + ; deg = 2, term_n = 3, related_n = 3 -y0 + y1 + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + + x1 + + x3 + + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + + y2 + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + x0 + + + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 +y0 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + + + + + + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T2.txt index d488907..5ecb61f 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y2 = 1 + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = + + x1 + x2 + + + x0x2 + x1x2 + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + x1 + + + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + + + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = 1 + + x1 + x2 + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + + + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = + x0 + x1 + + + + + + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; @@ -214,26 +214,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y3 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y1 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + + + + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + x1 + + + x0x1 + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + x0x1 + + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + x0 + x1 + + x3 + + + + + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + x1 + + + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + + + y3 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + + + + ; deg = 2, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:1, 3:14, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T3.txt index c17b2e5..46b02b5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Twofish_Q1_T3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 +y2 = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + + x2 + x3 + + x0x2 + x1x2 + + x1x3 + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 9, related_n = 4 y0 + y1 + + = + x0 + x1 + + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + y2 + = + + x1 + x2 + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = 1 + + x1 + + + x0x1 + + + + + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = 1 + x0 + + + x3 + + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y0 + y1 + y2 + = 1 + x0 + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + + y3 = + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = 1 + + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + x2 + + + + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + + x0x1 + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = 1 + + + x2 + + x0x1 + + + + + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = + x0 + x1 + + + + + x1x2 + + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -209,26 +209,26 @@ LUT = { }; ANF of coordinates: -y0 = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y2 = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + + + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 +y3 = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 ANF of components: -y0 + + + = + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = 1 + + + x2 + x3 + + x0x2 + + + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + + y3 = + x0 + + + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + x1 + x2 + + x0x1 + + + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + + + + y3 = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + + + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + y1 + + y3 = 1 + + + + x3 + x0x1 + + + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + + x2 + + x0x1 + x0x2 + + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + + x1 + x2 + x3 + + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + + + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_UDCIKMP11.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_UDCIKMP11.txt index 5acadde..bba93fb 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_UDCIKMP11.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_UDCIKMP11.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + + + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 -y1 = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y2 = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 -y3 = 1 + x0 + + + + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 = + + + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 2, related_n = 3 +y1 = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y2 = + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 +y3 = + x0 + + + + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 ANF of components: -y0 + + + = 1 + + + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 - + y1 + + = 1 + + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 +y0 + + + = + + + x2 + + x0x1 + + + + + + + + + ; deg = 2, term_n = 2, related_n = 3 + + y1 + + = + + x1 + + + x0x1 + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + + = + + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 - + + y2 + = 1 + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 5, related_n = 3 + + + y2 + = + + x1 + x2 + x3 + + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 3 y0 + + y2 + = + + x1 + + x3 + x0x1 + + x1x2 + + + + + + + ; deg = 2, term_n = 4, related_n = 4 + y1 + y2 + = + + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + y2 + = 1 + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + + + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 +y0 + y1 + y2 + = + + + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 + + + + y3 = + x0 + + + + + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 3, related_n = 4 y0 + + + y3 = + x0 + + x2 + + x0x1 + + + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + + + x0x1 + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 11, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 + + y1 + y2 + y3 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; @@ -223,26 +223,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 -y1 = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 -y2 = 1 + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 = + x0 + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 +y1 = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 +y2 = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 4, related_n = 3 - + y1 + + = 1 + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 3, related_n = 3 +y0 + + + = + x0 + + + x3 + + x0x2 + + + + + + + + ; deg = 2, term_n = 3, related_n = 3 + + y1 + + = + + x1 + + + + + + + + x2x3 + + + + ; deg = 2, term_n = 2, related_n = 3 y0 + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + + x2x3 + + + + ; deg = 2, term_n = 5, related_n = 4 - + + y2 + = 1 + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = + x0 + + + + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 y0 + + y2 + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + x1 + + + x0x1 + + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + x0x1 + x0x2 + + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + + y3 = + x0 + + x2 + + x0x1 + + + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + + y3 = 1 + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + x0 + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + + + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 Max degree: 3, Min degree: 2, Spectrum of degree: { 2:3, 3:12, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_E.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_E.txt index e7fde79..8942bc2 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_E.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_E.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y1 = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 13, related_n = 4 +y0 = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y1 = + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 ANF of components: -y0 + + + = + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = 1 + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + + + + x3 + x0x1 + x0x2 + + + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = + x0 + + + x3 + x0x1 + + x1x2 + + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + + = 1 + x0 + + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + + + x2 + + + x0x2 + + x0x3 + x1x3 + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 + y1 + y2 + = + x0 + + x2 + + + + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 13, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + + + y3 = + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 y0 + + + y3 = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 12, related_n = 4 + y1 + + y3 = + + x1 + x2 + + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + + y3 = + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + + y2 + y3 = + x0 + x1 + + + + + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 - + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 12, related_n = 4 + + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + + + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 -y1 = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y2 = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 = 1 + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y1 = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 +y2 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 +y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + + = + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y0 + + + = 1 + x0 + + + + x0x1 + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 y0 + y1 + + = + + x1 + + x3 + x0x1 + x0x2 + + + + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + + y2 + = + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 11, related_n = 4 y0 + + y2 + = + + + x2 + x3 + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + x2 + + x0x1 + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + + y3 = + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + + + y3 = 1 + x0 + + + + + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + + + + + x0x1 + x0x2 + x1x2 + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + y1 + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + x0x1 + + x1x2 + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + y1 + y2 + y3 = + + x1 + x2 + + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_R.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_R.txt index 38a7753..7e6541e 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_R.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_Whirlpool_R.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y1 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y2 = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 -y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y1 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 - + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + + x2 + x3 + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + y1 + + = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + x2 + x3 + x0x1 + x0x2 + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + + y2 + = 1 + + x1 + + + x0x1 + + + x0x3 + + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 + y1 + y2 + = + x0 + x1 + + + x0x1 + + x1x2 + + x1x3 + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 7, related_n = 4 - + + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + + + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 y0 + + + y3 = 1 + + x1 + + x3 + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + y1 + + y3 = 1 + + x1 + x2 + + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + x1 + + x3 + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + + + + x1x2 + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = 1 + + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + x0x1 + x0x2 + + + + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + y2 + y3 = + + + x2 + + + + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + + x3 + x0x1 + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 10, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y2 = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 -y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y2 = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y3 = 1 + + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + x0x2 + + x0x3 + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + + + x1x2 + + x1x3 + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = + x0 + + x2 + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + x2x3 + + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + y2 + = + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 + + + y2 + = 1 + + + + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + + y2 + = + x0 + x1 + + + x0x1 + x0x2 + x1x2 + + + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 8, related_n = 4 + y1 + y2 + = + + x1 + x2 + x3 + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + + + y3 = + + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + + x0x1 + x0x2 + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 + + + + y3 = 1 + + + x2 + + + x0x2 + x1x2 + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = + x0 + x1 + x2 + x3 + + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + + y3 = + + x1 + + + + x0x2 + + x0x3 + x1x3 + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 -y0 + y1 + + y3 = + x0 + + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + + + x3 + + + + + x1x3 + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + + x2 + x3 + x0x1 + x0x2 + + + + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + y1 + y2 + y3 = + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 + + y1 + y2 + y3 = 1 + + x1 + + x3 + x0x1 + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + y2 + y3 = + x0 + + + + x0x1 + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S0.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S0.txt index 0b29d1d..0d20faa 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S0.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S0.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S1.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S1.txt index db7195a..62cba99 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S1.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S1.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S2.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S2.txt index ed9f7d9..b90bca5 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S2.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S2.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y1 = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y2 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 -y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 +y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + y1 + + = + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 - + + y2 + = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + + y2 + = 1 + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 10, related_n = 4 y0 + + y2 + = + x0 + x1 + + x3 + + + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + x1x3 + x2x3 + + + + x1x2x3; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 +y0 + y1 + y2 + = 1 + x0 + + x2 + x3 + x0x1 + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 y0 + + + y3 = 1 + + + x2 + + x0x1 + + + x0x3 + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = 1 + x0 + + x2 + + x0x1 + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y0 + y1 + + y3 = 1 + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 +y0 + y1 + + y3 = + + x1 + + + + + x1x2 + x0x3 + + x2x3 + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 10, related_n = 4 -y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + x0 + + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + y1 + y2 + y3 = 1 + + x1 + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 -y1 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 +y1 = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y2 = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = 1 + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 10, related_n = 4 - + y1 + + = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = + x0 + x1 + x2 + x3 + + + + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 + + y1 + + = + x0 + x1 + + x3 + + + x1x2 + + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + y1 + + = + + + x2 + + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + y2 + = + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = 1 + + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 y0 + + y2 + = 1 + x0 + + x2 + + + x0x2 + x1x2 + + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + x0x2 + + x0x3 + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 6, related_n = 4 -y0 + y1 + y2 + = + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 - + + + y3 = 1 + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + x1 + x2 + x3 + + x0x2 + + + + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 7, related_n = 4 + + + + y3 = + x0 + + x2 + x3 + + x0x2 + + + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = + + x1 + + + + x0x2 + + x0x3 + + + + x0x1x3 + + ; deg = 3, term_n = 4, related_n = 4 + y1 + + y3 = + + x1 + x2 + + + x0x2 + x1x2 + + + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = 1 + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + y1 + + y3 = + x0 + + + x3 + + x0x2 + x1x2 + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 + + y2 + y3 = 1 + x0 + x1 + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 3, related_n = 4 - + y1 + y2 + y3 = + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 +y0 + + y2 + y3 = 1 + + + + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 4, related_n = 4 + + y1 + y2 + y3 = 1 + + + x2 + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + + + + + + x1x3 + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S3.txt b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S3.txt index 5f8595d..e060315 100644 --- a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S3.txt +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_mCrypton_S3.txt @@ -4,26 +4,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 -y2 = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 -y3 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 +y2 = + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 +y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 ANF of components: -y0 + + + = + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y0 + + + = 1 + x0 + x1 + + x3 + + + + x0x3 + + x2x3 + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = 1 + x0 + + x2 + x3 + x0x1 + + + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 y0 + y1 + + = + + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 - + + y2 + = 1 + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 + + + y2 + = + + + x2 + x3 + x0x1 + + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 y0 + + y2 + = 1 + x0 + x1 + x2 + + x0x1 + + + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 12, related_n = 4 + y1 + y2 + = 1 + x0 + + + + + + + + + x2x3 + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + y2 + = 1 + + x1 + + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 5, related_n = 4 - + + + y3 = + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = + + x1 + + x3 + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + + y3 = 1 + x0 + + + + + + x1x2 + x0x3 + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 9, related_n = 4 y0 + + + y3 = + + x1 + + x3 + + + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y0 + y1 + + y3 = + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + + y3 = 1 + x0 + x1 + x2 + + x0x1 + + x1x2 + + + x2x3 + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 + + y2 + y3 = 1 + x0 + + x2 + x3 + x0x1 + + x1x2 + x0x3 + + x2x3 + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 -y0 + + y2 + y3 = 1 + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 6, related_n = 4 - + y1 + y2 + y3 = 1 + + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = + + x1 + x2 + + x0x1 + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + + y1 + y2 + y3 = + + + + + + + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + x1 + + x3 + + + x1x2 + + x1x3 + x2x3 + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 9, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; @@ -207,26 +207,26 @@ LUT = { }; ANF of coordinates: -y0 = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 -y1 = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 -y2 = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 -y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y1 = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 +y2 = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 +y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 ANF of components: -y0 + + + = + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 7, related_n = 4 - + y1 + + = 1 + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 8, related_n = 4 +y0 + + + = 1 + x0 + + x2 + + + + x1x2 + x0x3 + x1x3 + + x0x1x2 + + + x1x2x3; deg = 3, term_n = 8, related_n = 4 + + y1 + + = + + x1 + x2 + x3 + + x0x2 + + + x1x3 + + + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 y0 + y1 + + = 1 + x0 + x1 + + x3 + + x0x2 + x1x2 + x0x3 + + + x0x1x2 + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 11, related_n = 4 - + + y2 + = 1 + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 10, related_n = 4 + + + y2 + = + x0 + x1 + x2 + x3 + + x0x2 + x1x2 + + + + x0x1x2 + x0x1x3 + x0x2x3 + ; deg = 3, term_n = 9, related_n = 4 y0 + + y2 + = 1 + + x1 + + x3 + + x0x2 + + x0x3 + x1x3 + + + x0x1x3 + x0x2x3 + x1x2x3; deg = 3, term_n = 9, related_n = 4 + y1 + y2 + = + x0 + + + + + + x1x2 + + x1x3 + + x0x1x2 + + + ; deg = 3, term_n = 4, related_n = 4 -y0 + y1 + y2 + = + + + x2 + + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 3, related_n = 4 - + + + y3 = 1 + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 8, related_n = 4 +y0 + y1 + y2 + = 1 + + + x2 + + + + + x0x3 + + + + + + x1x2x3; deg = 3, term_n = 4, related_n = 4 + + + + y3 = + x0 + + + x3 + + + + x0x3 + x1x3 + + x0x1x2 + + x0x2x3 + x1x2x3; deg = 3, term_n = 7, related_n = 4 y0 + + + y3 = 1 + + + x2 + x3 + + + x1x2 + + + + + + x0x2x3 + ; deg = 3, term_n = 5, related_n = 4 + y1 + + y3 = + x0 + x1 + x2 + + + x0x2 + + x0x3 + + + x0x1x2 + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + y1 + + y3 = + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 +y0 + y1 + + y3 = 1 + + x1 + + + + x0x2 + x1x2 + + x1x3 + + + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y2 + y3 = + + x1 + x2 + + + x0x2 + x1x2 + x0x3 + x1x3 + + + x0x1x3 + + x1x2x3; deg = 3, term_n = 8, related_n = 4 -y0 + + y2 + y3 = + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 5, related_n = 4 - + y1 + y2 + y3 = 1 + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 6, related_n = 4 +y0 + + y2 + y3 = 1 + x0 + x1 + + + + x0x2 + + + + + x0x1x2 + x0x1x3 + + ; deg = 3, term_n = 6, related_n = 4 + + y1 + y2 + y3 = + + + + x3 + + + x1x2 + x0x3 + + + + + x0x2x3 + x1x2x3; deg = 3, term_n = 5, related_n = 4 y0 + y1 + y2 + y3 = 1 + x0 + + x2 + x3 + + + + + x1x3 + + x0x1x2 + + x0x2x3 + ; deg = 3, term_n = 7, related_n = 4 Max degree: 3, Min degree: 3, Spectrum of degree: { 3:15, }; diff --git a/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_sboxes4_Part0.csv b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_sboxes4_Part0.csv new file mode 100644 index 0000000..c89d6e8 --- /dev/null +++ b/EvaluationResults/Sect5.1_CryptographicProperties/Sboxes4/properties_sboxes4_Part0.csv @@ -0,0 +1,208 @@ +Cipher,LUT,bit_slice,Permutation,Involution,Diff,DiffFreq,Diff1,CardD1,Lin,LinFreq,Lin1,CardL1,max_degree,min_degree,MaxDegreeFreq,MinDegreeFreq,Max_ProductDegrees,LS_number,"max_v (v, w)-linear","max_w (v, w)-linear",Optimal_Class,Cost (GE) TSMC65nm,Cost is Best ,inv_LUT,inv_bit_slice,inv_max_degree,inv_min_degree,inv_MaxDegreeFreq,inv_MinDegreeFreq,inv_Max_ProductDegrees,inv_LS_number,"inv_max_v (v, w)-linear","inv_max_w (v, w)-linear",inv_Optimal_Class +KNOT,04000a070b0e010d090f060805020c03,4bb4_56a9_a63c_93d8,True,False,4,24,2,2,8,36,4,2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,01060d0f000c0a030b0802040e070509,936c_782e_35ca_e18d,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Piccolo,0e040b0203080009010a070f060c050d,aaa5_fc03_1e1d_cd94,True,False,4,24,4,4,8,36,8,7,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G8,0,-,06080304010e0c0a050709020d0f000b,b4e2_3369_aaa5_b714,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G8 +Pride,0004080f01050e0902070a0c0b0d0603,3ccc_6a6a_d748_b2b8,True,True,4,24,4,5,8,36,8,8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G8,0,-,0004080f01050e0902070a0c0b0d0603,3ccc_6a6a_d748_b2b8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G8 +Prost,0004080f01050e0902070a0c0b0d0603,3ccc_6a6a_d748_b2b8,True,True,4,24,4,5,8,36,8,8,3,2,12,3,[3|3|3|4],9,"(3, 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3)",-,0,-,04070d0e0809010006030f0a020c0b05,6c3c_a50f_5f0a_c666,3,2,8,7,[3|3|3|4],29,"(3, 2)","(2, 3)",- +Optimal_S11,0001020d04070f06080e0b0a05090c03,6f48_52f8_8ee4_b46a,True,False,4,15,4,7,8,30,8,9,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G11,0,-,0001020f040c0705080d0b0a0e030906,5f28_92f8_bc4c_66ca,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G11 +Optimal_S7,0001020d04070f06080c0e0b0a090305,3f48_86f8_5ce4_e86a,True,False,4,15,2,7,8,30,8,12,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G7,0,-,0001020e040f0705080d0c0b09030a06,5f28_86f8_e86c_3ae2,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G7 +Optimal_S12,0001020d04070f06080e0b0a09030c05,5f48_c2f8_2ee4_b46a,True,False,4,15,4,8,8,30,8,12,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G12,0,-,0001020d040f0705080c0b0a0e030906,5f28_92f8_bc64_64ea,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G12 +Optimal_S6,0001020d04070f06080c0b090a0e0503,3f48_62f8_b4e4_cc6a,True,False,4,15,4,9,8,30,8,9,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G6,0,-,0001020f040e0705080b0c0a09030d06,5f28_c4f8_aa6c_72ca,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G6 +Optimal_S3,0001020d04070f06080c05030a0e0b09,f348_26f8_78e4_cc6a,True,False,4,15,4,9,8,30,8,9,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3,0,-,0001020b040a0705080f0c0e09030d06,5f28_ced0_aa6c_72ca,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3 +Optimal_S13,0001020d04070f06080e0c09050b0a03,6f48_16f8_e2e4_b86a,True,False,4,15,2,9,8,30,8,10,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G13,0,-,0001020f040c0705080b0e0d0a030906,5f28_8cf8_b64c_6aca,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G13 +Optimal_S4,0001020d04070f06080c090b0a0e0503,3f48_62f8_b8e4_cc6a,True,False,4,15,4,9,8,30,8,10,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G4,0,-,0001020f040e0705080a0c0b09030d06,5f28_c4f8_aa6c_78ca,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G4 +Optimal_S5,0001020d04070f06080c0b090a0e0305,3f48_a2f8_74e4_cc6a,True,False,4,15,4,10,8,30,8,10,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G5,0,-,0001020e040f0705080b0c0a09030d06,5f28_c4f8_aa6c_72e2,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G5 +Serpent_type_S16,00030508090c0e070a0d0f04060b0102,2778_1ee4_b5c2_6696,True,False,4,24,0,0,8,36,4,4,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,000e0f010b020c070304080d0509060a,ac56_5ac6_c1b6_399c,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Serpent_type_S7,00030508060c0b070d0a0e04010f0209,a768_2db4_66d2_b1c6,True,False,4,24,0,0,8,36,4,4,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,000c0e010b020407030f090605080a0d,e616_9ac6_4bb4_9798,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Serpent_type_S11,00030508060d0f0207040e0b0a01090c,dc68_8774_1dd2_6966,True,False,4,24,0,0,8,36,8,5,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,000d070109020408030e0c0b0f050a06,5e92_b646_db24_391e,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Serpent_type_S12,00030508060d0f020c090a040b0e0107,3768_a974_b4d2_d266,True,False,4,24,0,0,8,36,8,5,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,000e07010b02040f03090a0c08050d06,5e92_e8c6_85b6_639c,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Serpent_type_S15,0003050807090b0e0a0d0f040c020601,17e8_5e94_65d2_8676,True,False,4,18,0,0,8,32,4,6,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G14,0,-,000f0d010b020e04030508060c09070a,b456_5ac6_c972_631e,3,2,14,1,[3|3|3|4],3,"(3, 1)","(2, 3)",G15 +Serpent_type_S17,000305080a0d09040f0602010c0b070e,b178_d3a4_e712_6966,True,False,4,24,0,0,8,36,8,6,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,000b0a010702090e0306040d0c050f08,d8c6_7e90_43b6_695a,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Serpent_type_S1,0003050806090a070b0c0e02010f0d04,6768_e694_2dd2_71a6,True,False,4,24,0,0,8,36,4,6,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,000c0b010f02040703050608090e0a0d,f816_a6d2_65b4_939c,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Serpent_type_S2,0003050806090b020d040e010a0f070c,b568_e714_74d2_6966,True,False,4,24,0,0,8,36,8,6,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,000b07010902040e03050c060f080a0d,f492_9ec4_59a6_931e,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Serpent_type_S6,00030508060c0b070a0d090e0f010204,1f68_9ab4_59d2_36c6,True,False,4,24,0,0,8,36,4,6,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,000d0e010f020407030a080605090b0c,e616_98d6_4bb4_719a,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Serpent_type_S8,00030508060c0f010a04090e0d0b0207,3d68_9a74_e952_b4c6,True,False,4,18,0,0,8,32,4,6,3,2,14,1,[3|3|3|4],3,"(3, 1)","(2, 3)",G15,0,-,00070e010902040f030a080d050c0b06,6e94_b8c6_c3a6_599a,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G14 +Serpent_type_S10,00030508060d0f01090c020b0a07040e,9b68_e274_bc52_29e6,True,False,4,24,0,0,8,36,8,7,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,00070a010e02040d03080c0b09050f06,5e94_e4d2_c936_798a,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Serpent_type_S9,00030508060c0f020e090b070d0a0401,3768_5974_2dd2_9e46,True,False,4,24,0,0,8,36,8,7,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,000f07010e02040b03090d0a050c0806,6e92_b456_89b6_178e,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Serpent_type_S19,0003050a070c0b060d0402090e01080f,d968_93b4_94da_a956,True,False,4,24,0,0,8,36,4,8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,000d0a01090207040e0b030605080c0f,e316_d9c2_8f64_965a,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Serpent_type_S18,000305080b0c060f0e090207040a0d01,63b8_59e4_2dd2_ca96,True,False,4,24,0,0,8,36,4,8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,000f0a010c02060b03090d04050e0807,6696_bc52_a1e6_978a,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Serpent_type_S14,000305080704090e0f06020b0a0d0c01,79c8_63b4_1f92_a956,True,False,4,24,0,0,8,36,4,8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,000f0a010502090403060c0b0e0d0708,bc46_7692_5b26_695a,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Serpent_type_S13,00030508060f0a0107090e040b0c0d02,7668_6d34_9572_53a6,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9,0,-,00070f010b0204080309060c0d0e0a05,7a94_bc46_6536_931e,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9 +Serpent_type_S0,00030506070a0b0c0d040e090801020f,9de0_879c_c47a_a956,True,False,4,24,0,0,8,36,4,8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,000d0e01090203040c0b050607080a0f,e316_9d86_da64_965a,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Serpent_type_S3,00030508060a0f040e0d090201070c0b,c768_63d4_a972_b646,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10,0,-,000c0b010702040d030a050f0e090806,7a86_9cd2_9b34_2d9c,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10 +Serpent_type_S5,00030508060c0b070a04090e0f01020d,9d68_9ab4_59d2_b4c6,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10,0,-,000d0e0109020407030a0806050f0b0c,e616_b8c6_6ba4_719a,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10 +Serpent_type_S4,00030508060c0b07090e0a0d0f020104,1f68_9ab4_36d2_59c6,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9,0,-,000e0d010f02040703080a06050b090c,e616_98d6_2db2_719c,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9 +Golden_S2,00030508060a0f040e0d090201070c0b,c768_63d4_a972_b646,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10,0,-,000c0b010702040d030a050f0e090806,7a86_9cd2_9b34_2d9c,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10 +Golden_S3,00030508060c0b070a04090e0f01020d,9d68_9ab4_59d2_b4c6,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10,0,-,000d0e0109020407030a0806050f0b0c,e616_b8c6_6ba4_719a,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10 +Golden_S0,0003050806090c070d0a0e04010f0b02,6768_2dd4_e692_71a6,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9,0,-,000c0f010b0204070305090e06080a0d,ec16_9ac6_59b4_879c,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9 +Golden_S1,00030508060c0b07090e0a0d0f020104,1f68_9ab4_36d2_59c6,True,False,4,18,0,0,8,32,4,8,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9,0,-,000e0d010f02040703080a06050b090c,e616_98d6_2db2_719c,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9 +Optimal_S8,0001020d04070f06080e09050a0b030c,b748_8af8_72e4_6c6a,True,False,4,24,4,6,8,36,8,8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G8,0,-,0001020e040b0705080a0c0d0f030906,5f28_9cd8_b26c_78e2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G8 +Optimal_S2,0001020d04070f06080b0e030a0c0509,b748_64f8_1ee4_ca6a,True,False,4,24,2,7,8,36,8,7,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,0001020b040e0705080f0c090d030a06,5f28_96f0_e26c_3aca,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Optimal_S0,0001020d04070f06080b0c09030e0a05,6f48_a4f8_72e4_9a6a,True,False,4,24,4,7,8,36,8,9,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,0001020c040f0705080b0e090a030d06,5f28_c4f8_b664_6ae2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Optimal_S10,0001020d04070f06080e0b050a09030c,b748_8af8_56e4_6c6a,True,False,4,18,4,7,8,32,8,10,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10,0,-,0001020e040b0705080d0c0a0f030906,5f28_96d8_b86c_72e2,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G10 +Optimal_S14,0001020d04070f06080e0c0b0309050a,af48_46f8_9ae4_786a,True,False,4,18,2,7,8,32,8,12,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G14,0,-,0001020c040e0705080d0f0b0a030906,5f28_86f8_bc64_6ec2,3,2,14,1,[3|3|3|4],3,"(3, 1)","(2, 3)",G15 +Optimal_S9,0001020d04070f06080e0b0305090a0c,e748_92f8_4ee4_3c6a,True,False,4,18,2,8,8,32,8,7,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9,0,-,0001020b040c0705080d0e0a0f030906,5f28_96f0_bc4c_72ca,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G9 +Optimal_S1,0001020d04070f06080b0e0305090a0c,e748_94f8_4ee4_3a6a,True,False,4,24,4,8,8,36,8,8,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,0001020b040c0705080d0e090f030a06,5f28_96f0_f44c_3aca,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Optimal_S15,0001020d04070f06080e0c0b09030a05,5f48_86f8_6ae4_b86a,True,False,4,18,2,8,8,32,8,13,3,2,14,1,[3|3|3|4],3,"(3, 1)","(2, 3)",G15,0,-,0001020d040f0705080c0e0b0a030906,5f28_86f8_bc64_68ea,3,2,14,1,[3|3|3|4],3,"(3, 1)","(1, 3)",G14 +Num1_DL_22_3,000e09050f080a07030b060c04010d02,4a76_5c9a_87d2_639c,True,False,4,24,2,2,8,36,4,2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,000d0f080c030a07050206090b0e0104,385e_a596_36e4_59a6,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Num1_DL_13_1,000c09070f020601030b040e0a050d08,da16_6c5a_1b78_639c,True,False,4,24,2,1,8,36,4,3,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,000705080a0d06030f020c09010e0b04,6d38_a566_63d2_59a6,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Num1_DL_22_2,000b06090c05030e0d070804020a0f01,659a_4bb4_72c6_c36a,True,False,4,24,2,2,8,36,4,2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,000f0c060b0502090a030d010408070e,a596_d42e_c35a_4eb2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Num1_DL_13_0,000c090706010f02030b040e0d080a05,7a46_9c5a_4bd8_936c,True,False,4,24,2,1,8,36,4,3,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,000507080a0f04030d020e09010c0b06,6d38_a566_c6b4_59a6,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Num1_DL_22_1,000b0e010a070d04060c090f05080302,2e56_1be4_c936_5c6a,True,False,4,24,2,2,8,36,4,2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1,0,-,00030f0e070c08050d0a04010906020b,936c_25bc_e21e_9996,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G1 +Num1_DL_13_3,000d040b070e0902060a030508010f0c,d26a_c936_47b8_6c5a,True,False,4,24,2,1,8,36,4,3,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,000d070a020b08040c0609030f01050e,956a_d386_9a3c_7c26,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Num1_DL_04_0,000b0c050601090a030e0f080d040207,1ec6_b61c_c792_956a,True,False,4,24,0,0,8,36,4,4,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0,0,-,00050e080d03040f0b060701020c090a,e19c_26d6_97a4_4db2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2 +Num1_DL_22_0,000d08020e0b07050f06030c0401090a,c936_1bd2_8778_65e2,True,False,4,24,2,2,8,36,4,2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,000d030a0c070906020e0f050b010408,965a_4eb2_17ac_3c66,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Num1_DL_04_1,000c0d0a050b0e070f06020103080904,616e_83d6_17e8_59b4,True,False,4,24,0,0,8,36,4,4,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,000b0a0c0f0409070d0e030501020608,835e_4bb8_6696_1dd2,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +Num1_DL_13_2,000b08050f0c03060e04070902010d0a,c936_47b8_95d2_6c5a,True,False,4,24,2,1,8,36,4,3,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G2,0,-,000d0c060903070a020b0f01050e0804,6696_b44e_27e8_1e72,3,2,12,3,[3|3|3|4],9,"(3, 2)","(2, 3)",G0 +mCrypton_S0,040f03080d0a0c000b05070e02060109,897a_2e53_3d26_c716,True,False,4,15,2,5,8,30,4,10,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3,0,-,070e0c0200090d0a030f050806040b01,4ae6_3647_538b_c761,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3 +mCrypton_S1,010c070a060d05030f0b02000804090e,d32a_a176_879c_43e5,True,False,4,15,2,5,8,30,4,10,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3,0,-,0b000a070d0604020c0e030901050f08,cb15_6378_46ad_7c19,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3 +mCrypton_S2,070e0c0200090d0a030f050806040b01,4ae6_3647_538b_c761,True,False,4,15,2,5,8,30,4,10,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3,0,-,040f03080d0a0c000b05070e02060109,897a_2e53_3d26_c716,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3 +mCrypton_S3,0b000a070d0604020c0e030901050f08,cb15_6378_46ad_7c19,True,False,4,15,2,5,8,30,4,10,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3,0,-,010c070a060d05030f0b02000804090e,d32a_a176_879c_43e5,3,3,15,15,[3|3|3|4],0,"(2, 2)","(1, 3)",G3